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We demonstrate that the isotope shift in isotopomers of diatomic molecules, where the nucleus of one of its constituent atoms is replaced by another isotope, can be expressed as the sum of a field shift and a mass shift, similar to the atomic case. We show that a linear relation holds between atomic and molecular isotopes shifts, thus extending the King-plot analysis to molecular isotope shifts. Optical isotope shifts in YbF and ZrO and infrared isotope shifts in SnH are analyzed with a molecular King-plot approach, utilizing Yb$^{+}$ and Zr$^{+}$ ionic isotope shifts and charge radii of Sn obtained with non-optical methods. The changes in the mean-squared nuclear charge radii $\delta \langle r^2 \rangle$ of $^{170-174,176}$Yb and $^{90-92,94,96}$Zr extracted from the molecular transitions are found to be in excellent agreement with the values from the spectroscopy of Yb$^{+}$ and Zr$^{+}$, respectively. On the contrary, in the case of the vibrational-rotational transition in SnH, no sensitivity to the nuclear volume could be deduced within the experimental resolution, which makes it unsuitable for the extraction of nuclear charge radii but provides insights into the molecular electronic wave function not accessible via other methods. The new opportunities offered by the molecular King-plot analysis for research in nuclear structure and molecular physics are discussed., Comment: Accepted at Physical Review X. Link to abstract: https://journals.aps.org/prx/accepted/be075Kf7E0c16505459d9fa833408356a593fd904

We present a comprehensive study shedding light on how thermal fluctuations affect correlations in a Bose gas with contact repulsive interactions in one spatial dimension. The pair correlation function, the static structure factor, and the one-body density matrix are calculated as a function of the interaction strength and temperature with the exact ab-initio Path Integral Monte Carlo method. We explore all possible gas regimes from weak to strong interactions and from low to high temperatures. We provide a detailed comparison with a number of theories, such as perturbative (Bogoliubov and decoherent classical), effective (Luttinger liquid) and exact (ground-state and thermal Bethe Ansatz) ones. Our Monte Carlo results exhibit an excellent agreement with the tractable limits and provide a fundamental benchmark for future observations which can be achieved in atomic gases, cavity quantum-electrodynamic and superconducting-circuit platforms., Main Text: 13 pages, 9 figures. Appendix: 1 page

The energy of ultra-dilute quantum many-body systems is known to exhibit a universal dependence on the gas parameter x=n a_0^dx=na0d, with nn the density, dd the dimensionality of the space (d=1,2,3d=1,2,3) and a_0a0 the ss-wave scattering length. The universal regime typically extends up to x\approx 0.001x≈0.001, while at larger values specific details of the interaction start to be relevant and different model potentials lead to different results. Dipolar systems are peculiar in this regard since the anisotropy of the interaction makes a_0a0 depend on the polarization angle \alphaα, so different combinations of n and \alphaα can lead to the same value of the gas parameter x. In this work we analyze the scaling properties of dipolar bosons in two dimensions as a function of the density and polarization dependent scattering length up to very large gas parameter values. Using Quantum Monte Carlo (QMC) methods we study the energy and the main structural and coherence properties of the ground state of a gas of dipolar bosons by varying the density and scattering length for a fixed gas parameter. We find that the dipolar interaction shows relevant scaling laws up to unusually large values of xx that hold almost to the boundaries in the phase diagram where a transition to a stripe phase takes place.

BaCuSi$_2$O$_6$ is a quasi-two-dimensional (2D) quantum antiferromagnet containing three different types of stacked, square-lattice bilayer hosting spin-1/2 dimers. Although this compound has been studied extensively over the last two decades, the critical applied magnetic field required to close the dimer spin gap and induce magnetic order, which exceeds 23 T, has to date precluded any kind of neutron scattering investigation. However, the HFM/EXED instrument at the Helmholtz-Zentrum Berlin made this possible at magnetic fields up to 25.9 T. Thus we have used HFM/EXED to investigate the field-induced ordered phase, in particular to look for quasi-2D physics arising from the layered structure and from the different bilayer types. From neutron diffraction data, we determined the global dependence of the magnetic order parameter on both magnetic field and temperature, finding a form consistent with 3D quantum critical scaling; from this we deduce that the quasi-2D interactions and nonuniform layering of BaCuSi$_2$O$_6$ are not anisotropic enough to induce hallmarks of 2D physics. From neutron spectroscopy data, we measured the dispersion of the strongly Zeeman-split magnetic excitations, finding good agreement with the zero-field interaction parameters of BaCuSi$_2$O$_6$. We conclude that HFM/EXED allowed a significant extension in the application of neutron scattering techniques to the field range above 20 T and in particular opened new horizons in the study of field-induced magnetic quantum phase transitions., 19 pages, 8 figures

At the familiar liquid-gas phase transition in water, the density jumps discontinuously at atmospheric pressure, but the line of these first-order transitions defined by increasing pressures terminates at the critical point, a concept ubiquitous in statistical thermodynamics. In correlated quantum materials, a critical point was predicted and measured terminating the line of Mott metal-insulator transitions, which are also first-order with a discontinuous charge density. In quantum spin systems, continuous quantum phase transitions (QPTs) have been investigated extensively, but discontinuous QPTs have received less attention. The frustrated quantum antiferromagnet SrCu$_2$(BO$_3$)$_2$ constitutes a near-exact realization of the paradigmatic Shastry-Sutherland model and displays exotic phenomena including magnetization plateaux, anomalous thermodynamics and discontinuous QPTs. We demonstrate by high-precision specific-heat measurements under pressure and applied magnetic field that, like water, the pressure-temperature phase diagram of SrCu$_2$(BO$_3$)$_2$ has an Ising critical point terminating a first-order transition line, which separates phases with different densities of magnetic particles (triplets). We achieve a quantitative explanation of our data by detailed numerical calculations using newly-developed finite-temperature tensor-network methods. These results open a new dimension in understanding the thermodynamics of quantum magnetic materials, where the anisotropic spin interactions producing topological properties for spintronic applications drive an increasing focus on first-order QPTs., 8+4 pages, 4+3 figures

We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of spatial periodicity. Our variational state is parameterized in terms of a permutationally-invariant part described by the Deep Sets neural-network architecture. The input coordinates to the Deep Sets are periodically transformed such that they are suitable to directly describe periodic bosonic systems. We show example applications to both one and two-dimensional interacting quantum gases with Gaussian interactions, as well as to $^4$He confined in a one-dimensional geometry. For the one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods., 8 pages, 6 figures

The phase diagrams of highly frustrated quantum spin systems can exhibit first-order quantum phase transitions and thermal critical points even in the absence of any long-ranged magnetic order. However, all unbiased numerical techniques for investigating frustrated quantum magnets face significant challenges, and for generic quantum Monte Carlo methods the challenge is the sign problem. Here we report on a general quantum Monte Carlo approach with a loop-update scheme that operates in any basis, and we show that, with an appropriate choice of basis, it allows us to study a frustrated model of coupled spin-1/2 trimers: simulations of the trilayer Heisenberg antiferromagnet in the spin-trimer basis are sign-problem-free when the intertrimer couplings are fully frustrated. This model features a first-order quantum phase transition, from which a line of first-order transitions emerges at finite temperatures and terminates in a thermal critical point. The trimer unit cell hosts an internal degree of freedom that can be controlled to induce an extensive entropy jump at the quantum transition, which alters the shape of the first-order line. We explore the consequences for the thermal properties in the vicinity of the critical point, which include profound changes in the lines of maxima defined by the specific heat. Our findings reveal trimer quantum magnets as fundamental systems capturing in full the complex thermal physics of the strongly frustrated regime., 27 pages, 10 figures, Resubmission to SciPost

Using density matrix renormalization group simulations on open chains, we map out the wave vector in the incommensurate disordered phase of a realistic model of Rydberg chains with 1/r6 interactions, and we locate and characterize the points along the commensurate lines where the transition out of the period 3 and 4 phases is conformal. We confirm that it is three-state Potts for the period-3 phase, and we show that it is Ashkin-Teller with v similar or equal to 0.80 for the period-4 phase. We further show that close to these points, the transition is still continuous, but with a completely different scaling of the wave vector, in agreement with a chiral transition. Finally, we propose to use the conformal points as benchmarks for Kibble-Zurek experiments, defining a roadmap towards a conclusive identification of the chiral universality class.

Classical and quantum phase transitions (QPTs), with their accompanying concepts of criticality and universality, are a cornerstone of statistical thermodynamics. An exemplary controlled QPT is the field-induced magnetic ordering of a gapped quantum magnet. Although numerous "quasi-one-dimensional" coupled spin-chain and -ladder materials are known whose ordering transition is three-dimensional (3D), quasi-2D systems are special for several physical reasons. Motivated by the ancient pigment Han Purple (BaCuSi$_{2}$O$_{6}$), a quasi-2D material displaying anomalous critical properties, we present a complete analysis of Ba$_{0.9}$Sr$_{0.1}$CuSi$_{2}$O$_{6}$. We measure the zero-field magnetic excitations by neutron spectroscopy and deduce the magnetic Hamiltonian. We probe the field-induced transition by combining magnetization, specific-heat, torque and magnetocalorimetric measurements with low-temperature nuclear magnetic resonance studies near the QPT. By a Bayesian statistical analysis and large-scale Quantum Monte Carlo simulations, we demonstrate unambiguously that observable 3D quantum critical scaling is restored by the structural simplification arising from light Sr-substitution in Han Purple., 19 pages, 5 figures

Ideal magnetic frustration forms the basis for the emergence of exotic quantum spin states that are entirely nonmagnetic. Such singlet spin states are the defining feature of the Shastry-Sutherland model, and of its faithful materials realization in the quantum antiferromagnet SrCu$_2$(BO$_3$)$_2$. To address these states on ultrafast timescales, despite their lack of any microscopic order parameter, we introduce a nonlinear magnetophononic mechanism to alter the quantum spin dynamics by driving multiple optical phonon modes coherently and simultaneously. We apply intense terahertz pulses to create a nonequilibrium modulation of the magnetic interactions that breaks the ideal frustration of SrCu$_2$(BO$_3$)$_2$, such that previously forbidden physics can be driven in a coherent manner. Specifically, this driving populates a purely magnetic excitation, the singlet branch of the two-triplon bound state, by resonance with the difference frequency of two pumped phonons. Our results demonstrate how light-driven phonons can be used for the ultrafast and selective manipulation of interactions in condensed matter, even at frequencies far from those of the pump spectrum, offering valuable additional capabilities for the dynamical control of quantum many-body phenomena., 21 pages, 13 figures

Complex organic molecules with three carbon atoms are found in the earliest stages of star formation. In particular, propenal (C$_2$H$_3$CHO) is a species of interest due to its implication in the formation of more complex species and even biotic molecules. This study aims to search for the presence of C$_2$H$_3$CHO and other three-carbon species such as propylene (C$_3$H$_6$) in the hot corino region of the low-mass protostellar binary IRAS 16293--2422 to understand their formation pathways. We use ALMA observations in Band 6 and 7 from various surveys to search for the presence of C$_3$H$_6$ and C$_2$H$_3$CHO towards the protostar IRAS 16293--2422 B (IRAS 16293B). We report the detection of both C$_3$H$_6$ and C$_2$H$_3$CHO towards IRAS 16293B, however, no unblended lines were found towards the other component of the binary system, IRAS 16293A. We derive column density upper limits for C$_3$H$_8$, HCCCHO, n-C$_3$H$_7$OH, i-C$_3$H$_7$OH, C$_3$O, and cis-HC(O)CHO towards IRAS 16293B. We then use a three-phase chemical model to simulate the formation of these species in a typical prestellar environment followed by its hydrodynamical collapse until the birth of the central protostar. Different formation paths, such as successive hydrogenation and radical-radical additions on grain surfaces, are tested and compared to the observational results. The simulations reproduce the abundances within one order of magnitude from those observed towards IRAS 16293B, with the best agreement found for a rate of $10^{-12}$ cm$^3$ s$^{-1}$ for the gas-phase reaction C$_3$ + O $\rightarrow$ C$_2$ + CO. Successive hydrogenations of C$_3$, HC(O)CHO, and CH$_3$OCHO on grain surfaces are a major and crucial formation route of complex organics molecules, whereas both successive hydrogenation pathways and radical-radical addition reactions contribute to the formation of C$_2$H$_5$CHO., Comment: Accepted for publication in A&A. 24 pages, 17 figures

According to Landau's Fermi liquid theory, the main properties of the quasiparticle excitations of an electron gas are embodied in the effective mass $m^*$, which determines the energy of a single quasiparticle, and the Landau interaction function, which indicates how the energy of a quasiparticle is modified by the presence of other quasiparticles. This simple paradigm underlies most of our current understanding of the physical and chemical behavior of metallic systems. The quasiparticle effective mass of the three-dimensional homogeneous electron gas has been the subject of theoretical controversy and there is a lack of experimental data. In this work, we deploy diffusion Monte Carlo (DMC) methods to calculate $m^*$ as a function of density for paramagnetic and ferromagnetic three-dimensional homogeneous electron gases. The DMC results indicate that $m^*$ decreases when the density is reduced, especially in the ferromagnetic case. The DMC quasiparticle energy bands exclude the possibility of a reduction in the occupied bandwidth relative to that of the free-electron model at density parameter $r_s=4$, which corresponds to Na metal., Comment: Accepted for the publication

We describe the new version (v3.06h) of the code HFODD that solves the universal nonrelativistic nuclear DFT Hartree-Fock or Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we implemented the following new features: (i) zero-range three- and four-body central terms, (ii) zero-range three-body gradient terms, (iii) zero-range tensor terms, (iv) zero-range isospin-breaking terms, (v) finite-range higher-order regularized terms, (vi) finite-range separable terms, (vii) zero-range two-body pairing terms, (viii) multi-quasiparticle blocking, (ix) Pfaffian overlaps, (x) particle-number and parity symmetry restoration, (xi) axialization, (xii) Wigner functions, (xiii) choice of the harmonic-oscillator basis, (xiv) fixed Omega partitions, (xv) consistency formula between energy and fields, and we corrected several errors of the previous versions., Comment: 52 LaTeX pages, revised version

Temperature fluctuations of a finite system follows the Landau bound $\delta T^2 = T^2/C(T)$ where $C(T)$ is the heat capacity of the system. In turn, the same bound sets a limit to the precision of temperature estimation when the system itself is used as a thermometer. In this paper, we employ graph theory and the concept of Fisher information to assess the role of topology on the thermometric performance of a given system. We find that low connectivity is a resource to build precise thermometers working at low temperatures, whereas highly connected systems are suitable for higher temperatures. Upon modelling the thermometer as a set of vertices for the quantum walk of an excitation, we compare the precision achievable by position measurement to the optimal one, which itself corresponds to energy measurement., Comment: 16 pages, 8 figures, accepted version

Filopodia are actin-rich structures, present on the surface of practically every known eukaryotic cell. These structures play a pivotal role in specific cell-cell and cell-matrix interactions by allowing cells to explore their environment, generate mechanical forces, perform chemical signaling, or convey signals via intercellular tunneling nano-bridges. The dynamics of filopodia appear quite complex as they exhibit a rich behavior of buckling, pulling, length and shape changes. Here, we find that filopodia additionally explore their 3D extracellular space by combining growth and shrinking with axial twisting and buckling of their actin rich core. Importantly, we show the rotational dynamics of the filamentous actin inside filopodia for a range of highly distinct and cognate cell types spanning from earliest development to highly differentiated tissue cells. Non-equilibrium physical modeling of actin and myosin confirm that twist, and hence rotation, is an emergent phenomenon of active filaments confined in a narrow channel which points to a generic mechanism present in all cells. Our measurements confirm that filopodia exert traction forces and form helical buckles in a range of different cell types that can be ascribed to accumulation of sufficient twist. These results lead us to conclude that activity induced twisting of the actin shaft is a general mechanism underlying fundamental functions of filopodia.

Ab initio methods using weakly interacting nucleons give a good description of condensed nuclear matter up to densities comparable to the nuclear saturation density. At higher densities palpable strong interactions between overlapping nucleons become important; we propose that the interactions will continuously switch over to follow a holographic model in this region. In order to implement this, we construct hybrid equations of state (EoSs) where various models are used for low density nuclear matter, and the holographic V-QCD model is used for non-perturbative high density nuclear matter as well as for quark matter. We carefully examine all existing constraints from astrophysics of compact stars and discuss their implications for the hybrid EoSs. Thanks to the stiffness of the V-QCD EoS for nuclear matter, we obtain a large family of viable hybrid EoSs passing the constraints. We find that quark matter cores in neutron stars are unstable due to the strongly first order deconfinement transition, and predict bounds on the tidal deformability as well as on the radius of neutron stars. By relying on universal relations, we also constrain characteristic peak frequencies of gravitational waves produced in neutron star mergers., 40 pages, 19 figures; v2: analysis of I-Love-Q relations added

We present fully numerical electronic structure calculations on diatomic molecules exposed to an external magnetic field at the unrestricted Hartree-Fock limit, using a modified version of a recently developed finite element program, HelFEM. We have performed benchmark calculations on a few low-lying states of H2, HeH+, LiH, BeH+, BH, and CH+ as a function of the strength of an external magnetic field parallel to the molecular axis. The employed magnetic fields are in the range of $B=[0,10]~B_0$ atomic units, where $B_0 \approx 2.35 \times 10^5$ T. We have compared the results of the fully numerical calculations to ones obtained with the LONDON code using a large uncontracted gauge-including Cartesian Gaussian (GICG) basis set with exponents adopted from the Dunning aug-cc-pVTZ basis set. By comparison to the fully numerical results, we find that the basis set truncation error in the gauge-including Gaussian basis set is of the order of 1 kcal/mol at zero field, that the truncation error grows rapidly when the strength of the magnetic field increases, and that the largest basis set truncation error at $B=10~B_0$ exceeds 1000 kcal/mol. Studies in larger Gaussian basis sets suggest that reliable results can be obtained in GICG basis sets at fields stronger than $B=B_0$, provided that a sufficient coverage of higher-angular-momentum functions is included in the basis set., Comment: 21 pages and 2 figures, and a further 18 pages and 16 figures of supporting information

Many recent studies show that superconductivity not only exists in atomically thin monolayers but can exhibit enhanced properties such as a higher transition temperature and a stronger critical field. Nevertheless, besides being unstable in air, the weak tunability in these intrinsically metallic monolayers has limited the exploration of monolayer superconductivity, hindering their potential in electronic applications (e.g., superconductor-semiconductor hybrid devices). Here we show that using field effect gating, we can induce superconductivity in monolayer WS2 grown by chemical vapor deposition, a typical ambient-stable semiconducting transition metal dichalcogenide (TMD), and we are able to access a complete set of competing electronic phases over an unprecedented doping range from band insulator, superconductor, to a reentrant insulator at high doping. Throughout the superconducting dome, the Cooper pair spin is pinned by a strong internal spin-orbit interaction, making this material arguably the most resilient superconductor in the external magnetic field. The reentrant insulating state at positive high gating voltages is attributed to localization induced by the characteristically weak screening of the monolayer, providing insight into many dome-like superconducting phases observed in field-induced quasi-2D superconductors.

The thermodynamic properties of the Shastry-Sutherland model have posed one of the longest-lasting conundrums in frustrated quantum magnetism. Over a wide range on both sides of the quantum phase transition (QPT) from the dimer-product to the plaquette-based ground state, neither analytical nor any available numerical methods have come close to reproducing the physics of the excited states and thermal response. We solve this problem in the dimer-product phase by introducing two qualitative advances in computational physics. One is the use of thermal pure quantum (TPQ) states to augment dramatically the size of clusters amenable to exact diagonalization. The second is the use of tensor-network methods, in the form of infinite projected entangled pair states (iPEPS), for the calculation of finite-temperature quantities. We demonstrate convergence as a function of system size in TPQ calculations and of bond dimension in our iPEPS results, with complete mutual agreement even extremely close to the QPT. Our methods reveal a remarkably sharp and low-lying feature in the magnetic specific heat around the QPT, whose origin appears to lie in a proliferation of excitations composed of two-triplon bound states. The surprisingly low energy scale and apparently extended spatial nature of these states explain the failure of less refined numerical approaches to capture their physics. Both of our methods will have broad and immediate application in addressing the thermodynamic response of a wide range of highly frustrated magnetic models and materials., 21 pages, 19 figures

We provide a systematic study of the isospin composition and neutron-to-proton $\left( \frac{N}{Z} \right)$ ratio dependence of nuclear short-range correlations (SRC) across the nuclear mass table. We use the low-order correlation operator approximation (LCA) to compute the SRC contribution to the single-nucleon momentum distributions for 14 different nuclei from $A=4$ to $A=208$. Ten asymmetric nuclei are included for which the neutrons outnumber the protons by a factor of up to 1.54. The computed momentum distributions are used to extract the pair composition of the SRC. We find that there is a comprehensive picture for the isospin composition of SRC and their evolution with nucleon momentum. We also compute the non-relativistic kinetic energy of neutrons and protons and its evolution with nuclear mass $A$ and $\frac{N}{Z}$. Confirming the conclusions from alternate studies it is shown that the minority species (protons) become increasingly more short-range correlated as the neutron-to-proton ratio increases. We forge connections between measured nucleon-knockout quantities sensitive to SRC and single-nucleon momentum distributions. It is shown that the LCA can account for the observed trends in the data, like the fact that in neutron-rich nuclei the protons are responsible for an unexpectedly large fraction of the high-momentum components., 8 pages, 7 figures

The variations of short-range correlations (SRC) across nuclei can be quantified in an approximately model-independent fashion in terms of the so-called SRC scaling factors. We provide predictions for the SRC scaling factors for both bound protons and bound neutrons across the nuclear periodic table and determine the contribution of the different nucleon pair combinations to this quantity. Thereby we employ the low-order correlation operator approximation (LCA) to compute the SRC contribution to the single-nucleon momentum distribution. We do this for a sample of fifteen nuclei from He to Pb thereby gaining access to the evolution of the SRC scaling factor with the nuclear mass and the neutron-to-proton ratio. For the studied sample of fifteen nuclei, the total SRC scaling factor is in the range 4.05-5.14. The computed SRC scaling factors in the LCA are in line with those of ab-initio calculations and with measured quantities from SRC-sensitive inclusive electron-scattering data. In asymmetric nuclei there are sizeable differences between the SRC scaling factors for protons and neutrons. It is suggested that this phenomenon may impact the variations of the magnitude of the European muon collaboration (EMC) effect across nuclei. Our results corroborate the finding that SRC physics can be qualitatively understood by universal principles that build on local modifications of mean-field wave functions of nucleon pairs., Comment: 14 pages, 9 figures ; Updated to the published version with added comments and corrections

We study the triangular-lattice Ising model with dipolar interactions, inspired by its realisation in artificial arrays of nanomagnets. We show that a classical spin-liquid forms at intermediate temperatures, and that its behaviour can be tuned by temperature and/or a small lattice distortion between a string Luttinger liquid and a domain-wall-network state. At low temperature there is a transition into a magnetically ordered phase, which can be first-order or continous with a crossover in the critical behaviour between Pokrovsky-Talapov and 2D-Ising universality. When the Pokrovsky-Talapov criticality dominates, the transition is essentially of the Kasteleyn type.

In a recent Letter [T.~Dornheim \textit{et al.}, Phys. Rev. Lett. \textbf{117}, 156403 (2016)], we presented the first \textit{ab initio} quantum Monte-Carlo (QMC) results of the warm dense electron gas in the thermodynamic limit. However, a complete parametrization of the exchange-correlation free energy with respect to density, temperature, and spin polarization remained out of reach due to the absence of (i) accurate QMC results below $\theta=k_\text{B}T/E_\text{F}=0.5$ and (ii) of QMC results for spin polarizations different from the paramagnetic case. Here we overcome both remaining limitations. By closing the gap to the ground state and by performing extensive QMC simulations for different spin polarizations, we are able to obtain the first complete \textit{ab initio} exchange-correlation free energy functional; the accuracy achieved is an unprecedented $\sim 0.3\%$. This also allows us to quantify the accuracy and systematic errors of various previous approximate functionals.

We provide a unified method for obtaining upper bounds for certain functional integrals appearing in quantum mechanics and non-relativistic quantum field theory, functionals of the form $${E[\rm {exp}(\mathcal{A}_T)]}$$ , the (effective) action $${\mathcal{A}_T}$$ being a function of particle trajectories up to time T. The estimates in turn yield rigorous lower bounds for ground state energies, via the Feynman–Kac formula. The upper bounds are obtained by writing the action for these functional integrals in terms of stochastic integrals. The method is illustrated in familiar quantum mechanical settings: for the hydrogen atom, for a Schrodinger operator with $${1/|x|^2}$$ potential with small coupling, and, with a modest adaptation of the method, for the harmonic oscillator. We then present our principal applications of the method, in the settings of non-relativistic quantum field theories for particles moving in a quantized Bose field, including the optical polaron and Nelson models.

Short-range correlations (SRC) in asymmetric nuclei with an unusual neutron-to-proton ratio can be studied with quasi-free two-nucleon knockout processes following the collision between accelerated ions and a proton target. We derive an approximate factorized cross section for those SRC-driven $p(A,p^{\prime} N_1 N_2)$ reactions. Our reaction model hinges on the factorization properties of SRC-driven $A(e, e^\prime N_1 N_2)$ reactions for which strong indications are found in theory-experiment comparisons. In order to put our model to the test we compare its predictions with results of $^{12}\text{C}(p,p^{\prime} pn)$ measurements conducted at Brookhaven National Laboratory (BNL) and find a fair agreement. The model can also reproduce characteristic features of SRC-driven two-nucleon knockout reactions, like back-to-back emission of the correlated nucleons. We study the asymmetry dependence of nuclear SRC by providing predictions for the ratio of proton-proton to proton-neutron knockout cross sections for the carbon isotopes $^{9-15}$C thereby covering neutron excess values $(N-Z)/Z$ between -0.5 and +0.5., Comment: 20 pages, 5 figures. Final version published in Physics Letters B, minor changes in the text

Density matrix embedding theory (DMET) is a relatively new technique for the calculation of strongly correlated systems. Recently, block product DMET (BPDMET) was introduced for the study of spin systems such as the antiferromagnetic $J_1 - J_2$ model on the square lattice. In this paper, we extend the variational Ansatz of BPDMET using spin-state optimization, yielding improved results. We apply the same techniques to the Kitaev-Heisenberg model on the honeycomb lattice, comparing the results when using several types of clusters. Energy profiles and correlation functions are investigated. A diagonalization in the tangent space of the variational approach yields information on the excited states and the corresponding spectral functions., 12 pages, 12 figures

Rotation of molecules embedded in He nanodroplets is explored by a combination of fs laser-induced alignment experiments and angulon quasiparticle theory. We demonstrate that at low fluence of the fs alignment pulse, the molecule and its solvation shell can be set into coherent collective rotation lasting long enough to form revivals. With increasing fluence, however, the revivals disappear -- instead, rotational dynamics as rapid as for an isolated molecule is observed during the first few picoseconds. Classical calculations trace this phenomenon to transient decoupling of the molecule from its He shell. Our results open novel opportunities for studying non-equilibrium solute-solvent dynamics and quantum thermalization., Comment: 6+7 pages; 4+1 figures; 1 table

Using variational wave functions and Monte Carlo techniques, we study the antiferromagnetic Heisenberg model with first-neighbor $J_1$ and second-neighbor $J_2$ antiferromagnetic couplings on the honeycomb lattice. We perform a systematic comparison of magnetically ordered and nonmagnetic states (spin liquids and valence-bond solids) to obtain the ground-state phase diagram. N\'eel order is stabilized for small values of the frustrating second-neighbor coupling. Increasing the ratio $J_2/J_1$, we find strong evidence for a continuous transition to a nonmagnetic phase at $J_2/J_1 \approx 0.23$. Close to the transition point, the Gutzwiller-projected uniform resonating valence bond state gives an excellent approximation to the exact ground-state energy. For $0.23 \lesssim J_2/J_1 \lesssim 0.4$, a gapless $Z_2$ spin liquid with Dirac nodes competes with a plaquette valence-bond solid. In contrast, the gapped spin liquid considered in previous works has significantly higher variational energy. Although the plaquette valence-bond order is expected to be present as soon as the N\'eel order melts, this ordered state becomes clearly favored only for $J_2/J_1 \gtrsim 0.3$. Finally, for $0.36 \lesssim J_2/J_1 \le 0.5$, a valence-bond solid with columnar order takes over as the ground state, being also lower in energy than the magnetic state with collinear order. We perform a detailed finite-size scaling and standard data collapse analysis, and we discuss the possibility of a deconfined quantum critical point separating the N\'eel antiferromagnet from the plaquette valence-bond solid., Comment: 10 pages, 12 figures

We investigate the properties of the Heisenberg S=1 chain with bilinear and biquadratic interactions in a magnetic field using the Density Matrix Renormalization Group, Bethe ansatz and field theoretical considerations. In a large region of the parameter space, we identify a magnetized ferroquadrupolar Luttinger liquid consisting of a quasi-condensate of bound magnon pairs. This liquid undergoes a continuous pair unbinding transition to a more conventional Luttinger liquid region obtained by polarizing the system above the Haldane gap region. This pair unbinding transition is shown to be in the Ising universality class on top of a Luttinger liquid, leading to an effective central charge 3/2. We also revisit the nature of the partially polarized Luttinger liquid around and above the Uimin-Lai-Sutherland point. Our results confirm that this is a two-component liquid and rule out the formation of a single-component vector chiral phase., Comment: revised version, as published in PRB

We perform ab initio quantum Monte Carlo (QMC) simulations of the warm dense uniform electron gas in the thermodynamic limit. By combining QMC data with the linear response theory, we are able to remove finite-size errors from the potential energy over the substantial parts of the warm dense regime, overcoming the deficiencies of the existing finite-size corrections by Brown et al. [Phys. Rev. Lett. 110, 146405 (2013)]. Extensive new QMC results for up to $N=1000$ electrons enable us to compute the potential energy $V$ and the exchange-correlation free energy ${F}_{\mathrm{xc}}$ of the macroscopic electron gas with an unprecedented accuracy of $|\mathrm{\ensuremath{\Delta}}V|/|V|,|\mathrm{\ensuremath{\Delta}}{F}_{\mathrm{xc}}|/|F{|}_{\mathrm{xc}}\ensuremath{\sim}{10}^{\ensuremath{-}3}$. A comparison of our new data to the recent parametrization of ${F}_{\mathrm{xc}}$ by Karasiev et al. [Phys. Rev. Lett. 112, 076403 (2014)] reveals significant deviations to the latter.

We present a conjugate-gradient method for the ground-state optimization of projected entangled-pair states (PEPS) in the thermodynamic limit, as a direct implementation of the variational principle within the PEPS manifold. Our optimization is based on an efficient and accurate evaluation of the gradient of the global energy functional by using effective corner environments, and is robust with respect to the initial starting points. It has the additional advantage that physical and virtual symmetries can be straightforwardly implemented. We provide the tools to compute static structure factors directly in momentum space, as well as the variance of the Hamiltonian. We benchmark our method on Ising and Heisenberg models, and show a significant improvement on the energies and order parameters as compared to algorithms based on imaginary-time evolution.

The neutron-rich nucleus $^{144}$Ba ($t_{1/2}$=11.5 s) is expected to exhibit some of the strongest octupole correlations among nuclei with mass numbers $A$ less than 200. Until now, indirect evidence for such strong correlations has been inferred from observations such as enhanced $E1$ transitions and interleaving positive- and negative-parity levels in the ground-state band. In this experiment, the octupole strength was measured directly by sub-barrier, multi-step Coulomb excitation of a post-accelerated 650-MeV $^{144}$Ba beam on a 1.0-mg/cm$^2$ $^{208}$Pb target. The measured value of the matrix element, $\langle 3_1^- \| \mathcal{M}(E3) \| 0_1^+ \rangle=0.65(^{+17}_{-23})$ $e$b$^{3/2}$, corresponds to a reduced $B(E3)$ transition probability of 48($^{+25}_{-34}$) W.u. This result represents an unambiguous determination of the octupole collectivity, is larger than any available theoretical prediction, and is consistent with octupole deformation., Comment: 5 pages, 2 figures, 1 table, Physical Review Letters 2016

We consider the one-band Hubbard model on the square lattice by using variational and Green's function Monte Carlo methods, where the variational states contain Jastrow and backflow correlations on top of an uncorrelated wave function that includes BCS pairing and magnetic order. At half filling, where the ground state is antiferromagnetically ordered for any value of the on-site interaction $U$, we can identify a hidden critical point $U_{\rm Mott}$, above which a finite BCS pairing is stabilized in the wave function. The existence of this point is reminiscent of the Mott transition in the paramagnetic sector and determines a separation between a Slater insulator (at small values of $U$), where magnetism induces a potential energy gain, and a Mott insulator (at large values of $U$), where magnetic correlations drive a kinetic energy gain. Most importantly, the existence of $U_{\rm Mott}$ has crucial consequences when doping the system: We observe a tendency to phase separation into a hole-rich and a hole-poor region only when doping the Slater insulator, while the system is uniform by doping the Mott insulator. Superconducting correlations are clearly observed above $U_{\rm Mott}$, leading to the characteristic dome structure in doping. Furthermore, we show that the energy gain due to the presence of a finite BCS pairing above $U_{\rm Mott}$ shifts from the potential to the kinetic sector by increasing the value of the Coulomb repulsion., Comment: 10 pages, 7 figures

Radiation pressure has recently been used to effectively couple the quantum motion of mechanical elements to the fields of optical or microwave light. Integration of all three degrees of freedom—mechanical, optical and microwave—would enable a quantum interconnect between microwave and optical quantum systems. We present a platform based on silicon nitride nanomembranes for integrating superconducting microwave circuits with planar acoustic and optical devices such as phononic and photonic crystals. Using planar capacitors with vacuum gaps of 60 nm and spiral inductor coils of micron pitch we realize microwave resonant circuits with large electromechanical coupling to planar acoustic structures of nanoscale dimensions and femtoFarad motional capacitance. Using this enhanced coupling, we demonstrate microwave backaction cooling of the 4.48 MHz mechanical resonance of a nanobeam to an occupancy as low as 0.32. These results indicate the viability of silicon nitride nanomembranes as an all-in-one substrate for quantum electro-opto-mechanical experiments., Preparation and detection of mechanical objects at the quantum zero-point level has been achieved in both the optical and microwave regimes. Here, the authors develop silicon nitride nanomembranes that are suitable for integrating nanophotonic, nanomechanical and superconducting microwave circuits together.

The topological Kondo (TK) model has been proposed in solid-state quantum devices as a way to realize non-Fermi liquid behaviors in a controllable setting. Another motivation behind the TK model proposal is the demand to demonstrate the quantum dynamical properties of Majorana fermions, which are at the heart of their potential use in topological quantum computation. Here we consider a junction of crossed Tonks-Girardeau gases arranged in a star-geometry (forming a Y -junction), and we perform a theoretical analysis of this system showing that it provides a physical realization of the topological Kondo model in the realm of cold atom systems. Using computer-generated holography, we experimentally implement a Y-junction suitable for atom trapping, with controllable and independent parameters. The junction and the transverse size of the atom waveguides are of the order of 5 micrometers, leading to favorable estimates for the Kondo temperature and for the coupling across the junction. Since our results show that all the required theoretical and experimental ingredients are available, this provides the demonstration of an ultracold atom device that may in principle exhibit the topological Kondo effect., Comment: 20 pages, 3 figures. v2: main text expanded, references added

We present a systematic investigation of the special twist method introduced by Rajagopal $\textit{et al.}$ [ Phys. Rev. B 51, 10591 (1995) ] for reducing finite-size effects in correlated calculations of periodic extended systems with Coulomb interactions and Fermi statistics. We propose a procedure for finding special twist values which, at variance with previous applications of this method, reproduce the energy of the mean-field infinite-size limit solution within an adjustable (arbitrarily small) numerical error. This choice of the special twist is shown to be the most accurate single-twist solution for curing one-body finite-size effects in correlated calculations. For these reasons we dubbed our procedure "exact special twist" (EST). EST only needs a fully converged independent-particles or mean-field calculation within the primitive cell and a simple fit to find the special twist along a specific direction in the Brillouin zone. We first assess the performances of EST in a simple correlated model such as the 3D electron gas. Afterwards, we test its efficiency within $\textit{ab initio}$ quantum Monte Carlo simulations of metallic elements of increasing complexity. We show that EST displays an overall good performance in reducing finite-size errors comparable to the widely used twist average technique but at a much lower computational cost, since it involves the evaluation of just one wavefunction. We also demonstrate that the EST method shows similar performances in the calculation of correlation functions, such as the ionic forces for structural relaxation and the pair radial distribution function in liquid hydrogen. Our conclusions point to the usefulness of EST for correlated supercell calculations, our method will be particularly relevant when the physical problem under consideration requires large periodic cells., 15 pages, 8 figures

Over the years many He-He interaction potentials have been developed, some very sophisticated, including various corrections beyond Born-Oppenheimer approximation. Most of them were used to predict properties of helium dimers and trimers, examples of exotic quantum states, whose experimental study proved to be very challenging. Recently, detailed structural properties of helium trimers were measured for the first time, allowing a comparison with theoretical predictions and possibly enabling the evaluation of different interaction potentials. The comparisons already made included adjusting the maxima of both theoretical and experimental correlation functions to one, so the overall agreement between theory and experiment appeared satisfactory. However, no attempt was made to evaluate the quality of the interaction potentials used in the calculations. In this work, we calculate the experimentally measured correlation functions using both new and old potentials, compare them with experimental data and rank the potentials. We use diffusion Monte Carlo simulations at $T=0\ \mathrm{K}$, which give within statistical noise exact results of the ground state properties. All models predict both trimers $^4\mathrm{He}_{3}$ and $^4\mathrm{He}_2{}^3\mathrm{He}$ to be in a quantum halo state., Comment: 21 pages, 7 figures, 4 tables

Quantum control of engineered mechanical oscillators can be achieved by coupling the oscillator to an auxiliary degree of freedom, provided that the coherent rate of energy exchange exceeds the decoherence rate of each of the two sub-systems. We achieve such quantum-coherent coupling between the mechanical and optical modes of a micro-optomechanical system. Simultaneously, the mechanical oscillator is cooled to an average occupancy of n = 1.7 \pm 0.1 motional quanta. Pulsed optical excitation reveals the exchange of energy between the optical light field and the micromechanical oscillator in the time domain at the level of less than one quantum on average. These results provide a route towards the realization of efficient quantum interfaces between mechanical oscillators and optical fields., Comment: 23 pages, 11 figures

Several quantum gravity scenarios lead to physics below the Planck scale characterised by nonlocal, Lorentz invariant equations of motion. We show that such non-local effective field theories lead to a modified Schr\"odinger evolution in the nonrelativistic limit. In particular, the nonlocal evolution of opto-mechanical quantum oscillators is characterised by a spontaneous periodic squeezing that cannot be generated by environmental effects. We discuss constraints on the nonlocality obtained by past experiments, and show how future experiments (already under construction) will either see such effects or otherwise cast severe bounds on the non-locality scale (well beyond the current limits set by the Large Hadron Collider). This paves the way for table top, high precision experiments on massive quantum objects as a promising new avenue for testing some quantum gravity phenomenology., Comment: 5 pages, 1 figure. Final version matching the published one in PRL

International audience; Numerical results for ground state and excited state properties (energies, double occupancies, and Matsubara-axis self energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed node approximation, unrestricted coupled cluster theory, and multi-reference projected Hartree-Fock. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.

Do the laws of quantum physics still hold for macroscopic objects - this is at the heart of Schr\"odinger's cat paradox - or do gravitation or yet unknown effects set a limit for massive particles? What is the fundamental relation between quantum physics and gravity? Ground-based experiments addressing these questions may soon face limitations due to limited free-fall times and the quality of vacuum and microgravity. The proposed mission MAQRO may overcome these limitations and allow addressing those fundamental questions. MAQRO harnesses recent developments in quantum optomechanics, high-mass matter-wave interferometry as well as state-of-the-art space technology to push macroscopic quantum experiments towards their ultimate performance limits and to open new horizons for applying quantum technology in space. The main scientific goal of MAQRO is to probe the vastly unexplored "quantum-classical" transition for increasingly massive objects, testing the predictions of quantum theory for truly macroscopic objects in a size and mass regime unachievable in ground-based experiments. The hardware for the mission will largely be based on available space technology. Here, we present the MAQRO proposal submitted in response to the (M4) Cosmic Vision call of the European Space Agency for a medium-size mission opportunity with a possible launch in 2025., Comment: 38 pages, 10 tables, 23 figures

We present a self-consistent analytic theory of the intra-layer and inter-layer pair correlation functions in electron-electron and electron-hole fluid bilayer systems. Our approach involves the solution of a zero-energy scattering Schroedinger equation with an effective potential which includes a Bose-like term from Jastrow-Feenberg correlations and a Fermi term from kinetic energy and exchange, tailored to yield the Hartree-Fock limit at high carrier density. The theory is also shown to satisfy the plasmon sum rule and the charge neutrality condition. We obtain good agreement with the available Quantum Diffusion Monte Carlo (DMC) data in symmetric bilayers over a wide range of carrier density and layer spacing, and stress the role of three-body correlation terms in yielding fully quantitative agreement at strong coupling. Signals of impending transitions to density-modulated states at strong coupling and low layer spacing appear in the calculated pair correlations through inter-layer in-phase oscillations for electron-hole bilayers and out-of-phase oscillations for electron-electron bilayers, in agreement with the DMC findings., 8 pages, 3 figures, submitted

By using variational wave functions and quantum Monte Carlo techniques, we investigate the complete phase diagram of the Heisenberg model on the anisotropic triangular lattice, where two out of three bonds have super-exchange couplings $J$ and the third one has instead $J^\prime$. This model interpolates between the square lattice and the isotropic triangular one, for $J^\prime/J \le 1$, and between the isotropic triangular lattice and a set of decoupled chains, for $J/J^\prime \le 1$. We consider all the fully-symmetric spin liquids that can be constructed with the fermionic projective-symmetry group classification [Y. Zhou and X.-G. Wen, arXiv:cond-mat/0210662] and we compare them with the spiral magnetic orders that can be accommodated on finite clusters. Our results show that, for $J^\prime/J \le 1$, the phase diagram is dominated by magnetic orderings, even though a spin-liquid state may be possible in a small parameter window, i.e., $0.7 \lesssim J^\prime/J \lesssim 0.8$. In contrast, for $J/J^\prime \le 1$, a large spin-liquid region appears close to the limit of decoupled chains, i.e., for $J/J^\prime \lesssim 0.6$, while magnetically ordered phases with spiral order are stabilized close to the isotropic point., Comment: 11 pages, 11 figures

We solve the Dyson equation for atoms and diatomic molecules within the GW approximation, in order to elucidate the effects of self-consistency on the total energies and ionization potentials. We find GW to produce accurate energy differences although the self-consistent total energies differ significantly from the exact values. Total energies obtained from the Luttinger-Ward functional E_LW[G] with simple, approximate Green functions as input, are shown to be in excellent agreement with the self-consistent results. This demonstrates that the Luttinger-Ward functional is a reliable method for testing the merits of different self-energy approximations without the need to solve the Dyson equation self-consistently. Self-consistent GW ionization potentials are calculated from the Extended Koopmans Theorem, and shown to be in good agreement with the experimental results. We also find the self-consistent ionization potentials to be often better than the non-self-consistent G0W0 values. We conclude that GW calculations should be done self-consistently in order to obtain physically meaningful and unambiguous energy differences., Comment: 7 pages, 2 figures

The ground-state properties of one-dimensional 3He are studied using quantum Monte Carlo methods. The equation of state is calculated in a wide range of physically relevant densities and is well reproduced by a power-series fit. The Luttinger liquid theory is found to describe the long-range properties of the correlation function. The density dependence of the Luttinger parameter is explicitly found and interestingly it shows a non-monotonic behavior. Depending on the density, the static structure factor can be a smooth function of the momentum or might contain a peak of a finite or infinite height. Although no phase transitions are present in the system, we identify a number of physically different regimes, including an ideal Fermi gas, a "Bose-gas", a "super-Tonks-Girardeau" regime, and a "quasi-crystal"., 4 figures, published version

The results of extensive microscopic Relativistic Mean Field (RMF) calculations for the nuclei appearing in the alpha - decay chains of recently discovered superheavy elements with Z = 109 to 118 are presented and discussed. The calculated ground state properties like total binding energies, Q values, deformations, radii and densities closely agree with the corresponding experimental data, where available. The double folding (t-rho-rho) approximation is used to calculate the interaction potential between the daughter and the alpha, using RMF densities along with the density dependent nucleon - nucleon interaction (M3Y). This in turn, is employed within the WKB approximation to estimate the half lives without any additional parameter for alpha - decay. The half lives are highly sensitive to the Q values used and qualitatively agree with the corresponding experimental values. The use of experimental Q values in the WKB approximation improves the agreement with the experiment, indicating that the resulting interaction potential is reliable and can be used with confidence as the real part of the optical potential in other scattering and reaction processes., Accepted for publication in Annals of Physics (NY)

We study the zero-temperature quantum phase transition between liquid and hcp solid $^{4}\mathrm{He}$. We use the variational method with a simple yet exchange-symmetric and fully explicit wave function. It is found that the optimized wave function undergoes spontaneous symmetry breaking and describes the quantum solidification of helium at 22 atm. The explicit form of the wave function allows us to consider various contributions to the phase transition. We find that the employed wave function is an excellent candidate for describing both a first-order quantum phase transition and the ground state of a Bose solid.

Ground state of weakly bound dimers and trimers with a radius extending well into the classically forbidden region is explored, with the goal to test the predicted universality of quantum halo states. The focus of the study are molecules consisting of T$\downarrow$, D$\downarrow$, $^3$He, $^4$He and alkali atoms, where interaction between particles is much better known than in the case of nuclei, which are traditional examples of quantum halos. The study of realistic systems is supplemented by model calculations in order to analyze how low-energy properties depend on the interaction potential. The use of variational and diffusion Monte Carlo methods enabled very precise calculation of both size and binding energy of the trimers. In the quantum halo regime, and for large values of scaled binding energies, all clusters follow almost the same universal line. As the scaled binding energy decreases, Borromean states separate from tango trimers., Comment: 5 pages, 3 figures, accepted for publication in Phys. Rev. Lett

We investigate the factorization properties of the exclusive electroinduced two-nucleon knockout reaction $A(e,e'pN)$. A factorized expression for the cross section is derived and the conditions for factorization are studied. The $A(e,e'pN)$ cross section is shown to be proportional to the conditional center-of-mass (c.m.) momentum distribution for close-proximity pairs in a state with zero relative orbital momentum and zero radial quantum number. The width of this conditional c.m. momentum distribution is larger than the one corresponding with the full c.m. momentum distribution. It is shown that the final-state interactions (FSIs) only moderately affect the shape of the factorization function for the $A(e,e'pN)$ cross sections. Another prediction of the proposed factorization is that the mass dependence of the $A(e,e'pp)$ $[A(e,e'pn)]$ cross sections is much softer than $\frac{Z(Z-1)}{2}$ $[NZ]$., Comment: 12 pages, 11 figures, 2 tables. Accepted for publication in PRC. Small differences in discussion throughout article ("scaling" replaced by "factorization")

We investigate the Hubbard model on the anisotropic triangular lattice with two hopping parameters $t$ and $t^\prime$ in different spatial directions, interpolating between decoupled chains ($t=0$) and the isotropic triangular lattice ($t=t^\prime$). Variational wave functions that include both Jastrow and backflow terms are used to compare spin-liquid and magnetic phases with different pitch vectors describing both collinear and coplanar (spiral) order. For relatively large values of the on-site interaction $U/t^\prime \gtrsim 10$ and substantial frustration, i.e., $0.3\lesssim t/t^\prime \lesssim 0.8$, the spin-liquid state is clearly favored over magnetic states. Spiral magnetic order is only stable in the vicinity of the isotropic point, while collinear order is obtained in a wide range of inter-chain hoppings from small to intermediate frustration., 10 pages, 8 figures