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The anisotropic potential energy surface of the (H$_2$)$_2$ dimer represents a challenging problem for many-body methods. Here, we determine the potential energy curves of five different dimer configurations (T, Z, X, H, L) using the lattice regularized diffusion Monte Carlo (LRDMC) method and a number of approximate functionals within density functional theory (DFT), including advanced orbital-dependent functionals based on the random phase approximation (RPA). We assess their performance in describing the potential wells, bond distances and relative energies. The repulsive potential wall is studied by looking at the relative stability of the different dimer configurations as a function of an applied force acting along the intermolecular axis. It is shown that most functionals within DFT break down at finite compression, even those that give an accurate description around the potential well minima. Only by including exchange within RPA a qualitatively correct description along the entire potential energy curve is obtained. Finally, we discuss these results in the context of solid molecular hydrogen at finite pressures., Comment: 23 pages, 15 figures

We investigate the structural and thermodynamic properties of high-pressure ice by incorporating quantum anharmonicity at a non-perturbative level. Quantum fluctuations reduce the critical pressure of the phase transition between phase VIII (with asymmetric H-bonds) and phase X (with symmetric H-bonds) by 65 GPa from its classical value of 116 GPa at 0K. Moreover, quantum effects make it temperature-independent over a wide temperature range (0K-300K), in agreement with experimental estimates obtained through vibrational spectroscopy and in striking contrast to the strong temperature dependence found in the classical approximation. The equation of state shows fingerprints of the transition in accordance with experimental evidence. Additionally, we demonstrate that, within our approach, proton disorder in phase VII has a negligible impact on the occurrence of phase X. Finally, we reproduce with high accuracy the 10 GPa isotope shift due to the hydrogen-to-deuterium substitution.

Ab initio quantum Monte Carlo (QMC) is a state-of-the-art numerical approach for evaluating accurate expectation values of many-body wavefunctions. However, one of the major drawbacks that still hinders widespread QMC applications is the lack of an affordable scheme to compute unbiased atomic forces. In this study, we propose a very efficient method to obtain unbiased atomic forces and pressures in the Variational Monte Carlo (VMC) framework with the Jastrow-correlated Slater determinant ansatz, exploiting the gauge-invariant and locality properties of its geminal representation. We demonstrate the effectiveness of our method for H$_2$ and Cl$_2$ molecules and for the cubic boron nitride crystal. Our framework has a better algorithmic scaling with the system size than the traditional finite-difference method, and, in practical applications, is as efficient as single-point VMC calculations. Thus, it paves the way to study dynamical properties of materials, such as phonons, and is beneficial for pursuing more reliable machine-learning interatomic potentials based on unbiased VMC forces., Comment: 7 pages, 5 figures

In the quest of new exotic phases of matter due to the interplay of various interactions, iridates hosting a spin-orbit entangled $j_{\mathrm{eff}}=1/2$ ground state have been in the spotlight in recent years. Also in view of parallels with the low-energy physics of high-temperature superconducting cuprates, the validity of a single- or few-band picture in terms of the $j_{\mathrm{eff}}$ states is key. However, in particular for its structurally simple member Ba$_2$IrO$_4$, such a systematic construction and subsequent analysis of minimal low-energy models are still missing. Here we show by means of a combination of different ab initio techniques with dynamical mean-field theory that a three-band model in terms of Ir-$j_{\mathrm{eff}}$ states fully retains the low-energy physics of the system as compared to a full Ir-$5d$ model. Providing a detailed study of the three-band model in terms of spin-orbit coupling, Hund's coupling and Coulomb interactions, we map out a rich phase diagram and identify a region of effective one-band metal-insulator transition relevant to Ba$_2$IrO$_4$. Compared to available angle-resolved photoemission spectra, we find good agreement of salient aspects of the calculated spectral function and identify features which require the inclusion of non-local fluctuations. In a broader context, we envisage the three- and five-band models developed in this study to be relevant for the study of doped Ba$_2$IrO$_4$ and to clarify further the similarities and differences with cuprates., Comment: 14+1 pages, 13+2 figures, 3+1 tables; comments are welcome

TurboGenius is an open-source Python package designed to fully control ab initio quantum Monte Carlo (QMC) jobs using a Python script, which allows one to perform high-throughput calculations combined with TurboRVB [K. Nakano et al. J. Phys. Chem. 152, 204121 (2020)]. This paper provides an overview of the TurboGenius package and showcases several results obtained in a high-throughput mode. For the purpose of performing high-throughput calculations with TurboGenius, we implemented another open-source Python package, TurboWorkflows, that enables one to construct simple workflows using TurboGenius. We demonstrate its effectiveness by performing (1) validations of density functional theory (DFT) and QMC drivers as implemented in the TurboRVB package and (2) benchmarks of Diffusion Monte Carlo (DMC) calculations for several data sets. For (1), we checked inter-package consistencies between TurboRVB and other established quantum chemistry packages. By doing so, we confirmed that DFT energies obtained by PySCF are consistent with those obtained by TurboRVB within the local density approximation (LDA), and that Hartree-Fock (HF) energies obtained by PySCF and Quantum Package are consistent with variational Monte Carlo energies obtained by TurboRVB with the HF wavefunctions. These validation tests constitute a further reliability check of the TurboRVB package. For (2), we benchmarked atomization energies of the Gaussian-2 set, binding energies of the S22, A24, and SCAI sets, and equilibrium lattice parameters of 12 cubic crystals using DMC calculations. We found that, for all compounds analyzed here, the DMC calculations with the LDA nodal surface give satisfactory results, i.e., consistent either with high-level computational or with experimental reference values., Comment: 44 pages

We study the structural phase transition, originally associated with the highest superconducting critical temperature $T_c$ measured in high-pressure sulfur hydride. A quantitative description of its pressure dependence has been elusive for any \emph{ab initio} theory attempted so far, raising questions on the actual mechanism leading to the maximum of $T_c$. Here, we estimate the critical pressure of the hydrogen bond symmetrization in the Im$\bar{3}$m structure, by combining density functional theory and quantum Monte Carlo simulations for electrons with path integral molecular dynamics for quantum nuclei. We find that the $T_c$ maximum corresponds to pressures where local dipole moments dynamically form on the hydrogen sites, as precursors of the ferroelectric Im$\bar{3}$m-R3m transition, happening at lower pressures. For comparison, we also apply the self-consistent harmonic approximation, whose ferroelectric critical pressure lies in between the ferroelectric transition estimated by path integral molecular dynamics and the local dipole formation. Nuclear quantum effects play a major role in a significant reduction ($\approx$ 50 GPa) of the classical ferroelectric transition pressure at 200K and in a large isotope shift ($\approx$ 25 GPa) upon hydrogen-to-deuterium substitution of the local dipole formation pressure, in agreement with the corresponding change in the $T_c$ maximum location.

We present a robust reciprocal-space implementation of the temperature-dependent effective potential method. Our implementation can scale easily to large cell and long sampling time. It is interoperable with standard ab-initio molecular dynamics and with Langevin dynamics. We prove that both sampling methods can be efficient and accurate if a thermostat is used to control temperature and dynamics parameters are used to optimize the sampling efficiency. By way of example, we apply it to study anharmonic phonon renormalization in weakly and strongly anharmonic materials, reproducing the temperature effect on phonon frequencies, crossing of phase transition, and stabilization of high-temperature phases.

The interplay of quantum and classical fluctuations in the vicinity of a quantum critical point (QCP) gives rise to various regimes or phases with distinct quantum character. In this work, we show that the R\'enyi entropy is a precious tool to characterize the phase diagram of critical systems not only around the QCP but also away from it, thanks to its capability to detect the emergence of local order at finite temperature. For an efficient evaluation of the R\'enyi entropy, we introduce a new algorithm based on a path integral Langevin dynamics combined with a previously proposed thermodynamic integration method built on regularized paths. We apply this framework to study the critical behavior of a linear chain of anharmonic oscillators, a particular realization of the $\phi^4$ model. We fully resolved its phase diagram, as a function of both temperature and interaction strength. At finite temperature, we find a sequence of three regimes - para, disordered and quasi long-range ordered -, met as the interaction is increased. The R\'enyi entropy divergence coincides with the crossover between the para and disordered regime, which shows no temperature dependence. The occurrence of quasi long-range order, on the other hand, is temperature dependent. The two crossover lines merge in proximity of the QCP, at zero temperature, where the R\'enyi entropy is sharply peaked. Via its subsystem-size scaling, we confirm that the transition belongs to the two-dimensional Ising universality class. This phenomenology is expected to happen in all $\phi^4$-like systems, as well as in the elusive water ice transition across phases VII, VIII and X., Comment: 11 + 4 pages, 12 figures

By means of a combined x-ray diffraction, magnetic susceptibility and specific heat study, we investigate the interplay between orthorhombic distortion and stripe-like antiferromagnetic (AFM) order in the Mott insulator BaCoS$_{2}$ at $T_N=290$ K. The data give evidence of a purely electronic AFM transition with no participation of the lattice. The observation of large thermal fluctuations in the vicinity of $T_N$ and a Schottky anomaly unveils competing ground states within a minute $\sim$1 meV energy range that differ in the orbital and spin configurations of the Co ions. This interpretation suggests that the stripe-like order results from a spontaneous symmetry breaking of the geometrically frustrated pristine tetragonal phase, which offers an ideal playground to study the driving force of multi-orbital Mott transitions without the participation of the lattice., Comment: 5 pages, 4 figures, Supplemental Information

At $T_N\simeq 305~\text{K}$ the layered insulator BaCoS$_2$ transitions to a columnar antiferromagnet that signals non-negligible magnetic frustration despite the relatively high $T_N$, all the more surprising given its quasi two-dimensional structure. Here, we show by combining ab initio and model calculations that the magnetic transition is an order-from-disorder phenomenon, which not only drives the columnar $C_4\to C_2$ symmetry breaking, but also, and more importantly, the inter-layer coherence responsible for the finite N\'eel transition temperature. This uncommon ordering mechanism, actively contributed by orbital degrees of freedom, hints at an abundance of low energy excitations below and, especially, above $T_N$, not in disagreement with experimental evidences, and might as well emerge in other layered correlated compounds showing frustrated magnetism at low temperature., Comment: 12 pages, 6 figures

We present a study of the principal deuterium Hugoniot for pressures up to $150$ GPa, using Machine Learning potentials (MLPs) trained with Quantum Monte Carlo (QMC) energies, forces and pressures. In particular, we adopted a recently proposed workflow based on the combination of Gaussian kernel regression and $\Delta$-learning. By fully taking advantage of this method, we explicitly considered finite-temperature electrons in the dynamics, whose effects are highly relevant for temperatures above $10$ kK. The Hugoniot curve obtained by our MLPs shows a good agreement with the most recent experiments, particularly in the region below 60 GPa. At larger pressures, our Hugoniot curve is slightly more compressible than the one yielded by experiments, whose uncertainties generally increase, however, with pressure. Our work demonstrates that QMC can be successfully combined with $\Delta$-learning to deploy reliable MLPs for complex extended systems across different thermodynamic conditions, by keeping the QMC precision at the computational cost of a mean-field calculation., Comment: 7 + 10 pages; new version with improved QMC dataset. Hugoniot curve and discussion updated accordingly, main physical outcomes unchanged

Water is a key ingredient for life and plays a central role as solvent in many biochemical reactions. However, the intrinsically quantum nature of the hydrogen nucleus, revealing itself in a large variety of physical manifestations, including proton transfer, gives rise to unexpected phenomena whose description is still elusive. Here we study, by an unprecedented combination of state-of-the-art quantum Monte Carlo methods and path-integral molecular dynamics, the structure and hydrogen-bond dynamics of the protonated water hexamer, the fundamental unit for the hydrated proton. We report a remarkably low thermal expansion of the hydrogen bond from zero temperature up to 300 K, owing to the presence of short-Zundel configurations, characterised by proton delocalisation and favoured by the synergy of nuclear quantum effects and thermal activation. The hydrogen bond strength progressively weakens above 300 K, when localised Eigen-like configurations become relevant. Our analysis, supported by the instanton statistics of shuttling protons, reveals that the near-room-temperature range from 250 K to 300 K is a ``sweet spot'' for proton transfer, and thus for many phenomena depending on it, including life., Comment: 25 pages, 5 figures, 23 pages of supplementary information, 14 additional figures in the supplementary information

The high-pressure II-III phase transition in solid hydrogen is investigated using the random phase approximation and diffusion Monte Carlo. Good agreement between the methods is found confirming that an accurate treatment of exchange and correlation increases the transition pressure by more than 100 GPa with respect to semilocal density functional approximations. Using an optimized hybrid functional, we then reveal a low-symmetry structure for phase II generated by an out-of-plane librational instability of the C2/c phase III structure. This instability weakens the in-plane polarization of C2/c leading to the well-known experimental signatures of the II-III phase transition such as a sharp shift in vibron frequency, infrared activity and $c/a$ lattice parameter ratio. Finally, we discuss the zero-point vibrational energy that plays an important role in stabilizing phase III at lower pressures., Comment: 7 pages, 4 figures + Supplemental Materials (10 pages), to appear in Physical Review Research

We devise a framework to compute accurate phonons in molecular crystals even in case of strong quantum anharmonicity. Our approach is based on the calculation of the static limit of the phononic Matsubara Green's function from path integral molecular dynamics simulations. Our method enjoys a remarkably low variance, which allows one to compute accurate phonon frequencies after a few picoseconds of nuclear dynamics, and it is further stabilized by the use of appropriate constrained displacement operators. We applied it to solid hydrogen at high pressure. For phase III, our predicted infrared (IR) and Raman active vibrons agree very well with experiments. We then characterize the crystalline symmetry of phase IV by direct comparison with vibrational data and we determine the character of its Raman and IR vibron peaks.

The interplay between electron correlation and nuclear quantum effects makes our understanding of elemental hydrogen a formidable challenge. Here, we present the phase diagram of hydrogen and deuterium at low temperatures and high-pressure ($P > 300$ GPa by accounting for highly accurate electronic and nuclear enthalpies. We evaluated internal electronic energies by diffusion quantum Monte Carlo, while nuclear quantum motion and anharmonicity have been included by the stochastic self-consistent harmonic approximation. Our results show that the long-sought atomic metallic hydrogen, predicted to host room-temperature superconductivity, forms at $577\pm 10$ GPa ($640\pm 14$ GPa in deuterium). Indeed, anharmonicity pushes the stability of this phase towards pressures much larger than previous theoretical estimates or attained experimental values. Before atomization, molecular hydrogen transforms from a conductive phase III to another metallic structure that is still molecular (phase VI) at $422\pm 40$ GPa ($442\pm30$ GPa in deuterium). We predict clear-cut signatures in optical spectroscopy and DC conductivity that can be used experimentally to distinguish between the two structural transitions. According to our findings, the experimental evidence of metallic hydrogen has so far been limited to molecular phases.

Despite being a well-established operational approach to quantify entanglement, R\'enyi entropy calculations have been plagued by their computational complexity. We introduce here a theoretical framework based on an optimal thermodynamic integration scheme, where the R\'enyi entropy can be efficiently evaluated using regularizing paths. This approach avoids slowly convergent fluctuating contributions and leads to low-variance estimates. In this way, large system sizes and high levels of entanglement in model or first-principles Hamiltonians are within our reach. We demonstrate it in the one-dimensional quantum Ising model and perform the evaluation of entanglement entropy in the formic acid dimer, by discovering that its two shared protons are entangled even above room temperature., Comment: 7 + 4 pages, 9 figures

By means of quantum Monte Carlo (QMC) calculations from first principles, we study the ground-state properties of the narrowest zigzag graphene nanoribbon, with an infinite linear acene structure. We show that this quasi-one-dimensional system is correlated and its ground state is made of localized $\pi$ electrons whose spins are antiferromagnetically (AFM) ordered. The AFM stablization energy (36(3) meV per carbon atom) and the absolute magnetization (1.13(1) $\mu_\textrm{B}$ per unit cell) predicted by QMC are sizable, and they suggest the survival of antiferromagnetic correlations above room temperature. These values can be reproduced to some extent by density functional theory (DFT) only by assuming strong interactions, either within the DFT+U framework or using hybrid functionals. Based on our QMC results, we then provide the strength of Hubbard repulsion in DFT+U suitable for this class of systems., Comment: 12 pages, 7 figures

Using a real-time implementation of the self-consistent $GW$ method, we theoretically investigate the photo-induced changes in the electronic structure of the quasi two-dimensional semi-metal BaNiS$_2$. This material features four Dirac cones in the unit cell and our simulation of the time- and momentum-resolved nonequilibrium spectral function reveals a flattening of the Dirac bands after a photo-doping pulse with a 1.5 eV laser. The simulation results are consistent with the recently reported experimental data on photo-doped BaNiS$_2$ and ZrSiSe, another Dirac semi-metal. A detailed analysis of the numerical data allows us to attribute the nonequilibrium modifications of the Dirac bands to (i) an increased effective temperature after the photo-excitation, which affects the screening properties of the system, and (ii) to nontrivial band shifts in the photo-doped state, which are mainly induced by the Fock term.

We devise an efficient scheme to determine vibrational properties from Path Integral Molecular Dynamics (PIMD) simulations. The method is based on zero-time Kubo-transformed correlation functions and captures the anharmonicity of the potential due to both temperature and quantum effects. Using analytical derivations and numerical calculations on toy-model potentials, we show that two different estimators built upon PIMD correlation functions fully characterize the phonon spectra and the anharmonicity strength. The first estimator is associated with force-force quantum correlators and gives access to the fundamental frequencies and thermodynamic properties of the quantum system. The second one is instead connected to displacement-displacement correlators and probes the lowest-energy phonon excitations with high accuracy. We also prove that the use of generalized eigenvalue equations, in place of the standard normal mode equations, leads to a significant speed-up in the PIMD phonon calculations, both in terms of faster convergence rate and smaller time-step bias. Within this framework, using ab initio PIMD simulations, we compute phonon dispersions of diamond and of the high-pressure I41/amd phase of atomic hydrogen. We find that, in the latter case, the anharmonicity is stronger than previously estimated and yields a sizeable red-shift in the vibrational spectrum of atomic hydrogen.

We reproduce the electronic properties of FeSe in the high-temperature phase within an ab initio framework that includes screened Fock exchange and local dynamical correlations. We robustly capture the experimental band structure, as long as the system is in the Hund's metal phase. In particular, we account for the shrinking of the Fermi pockets and the sinking below the Fermi level of the hole pocket with $xy$ orbital character. This entails the elusive correct estimate of the Sommerfeld coefficient, and supports the interpretation of non-compensated Fermi pockets seen in ARPES in terms of surface electron doping. More stringently, our modeling matches well the experimental interband optical spectrum, and captures qualitatively the temperature dependence of the thermoelectric power, extremely sensitive to the details of the bands around the Fermi level., Comment: 7 pages, 2 figures, Supplementary Material

We report the first successful application of the {\it ab initio} quantum Monte Carlo (QMC) framework to a phonon dispersion calculation. A full phonon dispersion of diamond is successfully calculated at the variational Monte Carlo (VMC) level, based on the frozen-phonon technique. The VMC-phonon dispersion is in good agreement with the experimental results, giving renormalized harmonic optical frequencies very close to the experimental values, by significantly improving upon density functional theory (DFT) in the generalized gradient approximation. Key to success for the QMC approach is the statistical error reduction in atomic force evaluation. We show that this can be achieved by using well conditioned atomic basis sets, by explicitly removing the basis-set redundancy, which reduces the statistical error of forces by up to two orders of magnitude. This leads to affordable and accurate QMC-phonons calculations, up to $10^{4}$ times more efficient than previous attempts, and paves the way to new applications, particularly in correlated materials, where phonons have been poorly reproduced so far., Comment: 10 pages

TurboRVB is a computational package for {\it ab initio} Quantum Monte Carlo (QMC) simulations of both molecular and bulk electronic systems. The code implements two types of well established QMC algorithms: Variational Monte Carlo (VMC), and Diffusion Monte Carlo in its robust and efficient lattice regularized variant. A key feature of the code is the possibility of using strongly correlated many-body wave functions. The electronic wave function (WF) is obtained by applying a Jastrow factor, which takes into account dynamical correlations, to the most general mean-field ground state, written either as an antisymmetrized geminal product with spin-singlet pairing, or as a Pfaffian, including both singlet and triplet correlations. This wave function can be viewed as an efficient implementation of the so-called resonating valence bond (RVB) ansatz, first proposed by L. Pauling and P. W. Anderson in quantum chemistry and condensed matter physics, respectively. The RVB ansatz implemented in TurboRVB has a large variational freedom, including the Jastrow correlated Slater determinant as its simplest, but nontrivial case. Moreover, it has the remarkable advantage of remaining with an affordable computational cost, proportional to the one spent for the evaluation of a single Slater determinant. The code implements the adjoint algorithmic differentiation that enables a very efficient evaluation of energy derivatives, comprising the ionic forces. Thus, one can perform structural optimizations and molecular dynamics in the canonical NVT ensemble at the VMC level. For the electronic part, a full WF optimization is made possible thanks to state-of-the-art stochastic algorithms for energy minimization. The code has been efficiently parallelized by using a hybrid MPI-OpenMP protocol, that is also an ideal environment for exploiting the computational power of modern GPU accelerators., Comment: 41 pages, 21 figures, 3 tables

By means of pump-probe time- and angle-resolved photoelectron spectroscopy, we provide evidence of a sizeable reduction of the Fermi velocity of out-of-equilibrium Dirac bands in the quasi-two-dimensional semimetal BaNiS$_2$. First-principle calculations indicate that this band renormalization is ascribed to a change in non-local electron correlations driven by a photo-induced enhancement of screening properties. This effect is accompanied by a slowing down of the Dirac fermions and by a non-rigid shift of the bands at the center of the Brillouin zone. This result suggests that other similar electronic structure renormalizations may be photoinduced in other materials in presence of strong non-local correlations.

The cohesive energies and structural properties of recently predicted, and never synthesized, B$_2$O$_3$ polymorphs are investigated from first principles using density functional theory and high-accuracy many-body methods, namely, the random phase approximation and quantum Monte Carlo. We demonstrate that the van der Waals forces play a key role in making the experimentally known polymorph (B$_2$O$_3$-I) the lowest in energy, with many competing metastable structures lying only a few kcal/mol above. Remarkably, all metastable crystals are comparable in energy and density to the glass, while having anisotropic and mechanically soft structures. Furthermore, the best metastable polymorph according to our stability criteria has a structural motif found in both the glass and a recently synthesized borosulfate compound. Our findings provide new perspectives for understanding the B$_2$O$_3$ anomalous behavior, namely, its propensity to vitrify in a glassy structure drastically different from the known crystal.

Using x-ray emission spectroscopy, we find appreciable local magnetic moments until 30-40 GPa in the high-pressure phase of iron, however no magnetic order is detected with neutron powder diffraction down to 1.8 K contrary to previous predictions. Our first-principles calculations reveal a "spin-smectic" state lower in energy than previous results. This state forms antiferromagnetic bilayers separated by null spin bilayers, which allows a complete relaxation of the inherent frustration of antiferromagnetism on a hexagonal close-packed lattice. The magnetic bilayers are likely orientationally disordered, owing to the soft interlayer excitations and the near-degeneracy with other smectic phases. This possible lack of long-range correlation agrees with the null results from neutron powder diffraction. An orientationally-disordered, spin-smectic state resolves previously perceived contradictions in high pressure iron and could be integral to explaining its puzzling superconductivity.

By means of the Jastrow correlated antisymmetrized geminal power (JAGP) wave function and quantum Monte Carlo (QMC) methods, we study the ground state properties of the oligoacene series, up to the nonacene. The JAGP is the accurate variational realization of the resonating-valence-bond (RVB) ansatz proposed by Pauling and Wheland to describe aromatic compounds. We show that the long-ranged RVB correlations built in the acenes' ground state are detrimental for the occurrence of open-shell diradical or polyradical instabilities, previously found by lower-level theories. We substantiate our outcome by a direct comparison with another wave function, tailored to be an open-shell singlet (OSS) for long-enough acenes. By comparing on the same footing the RVB and OSS wave functions, both optimized at a variational QMC level, and further projected by the lattice regularized diffusion Monte Carlo (LRDMC) method, we prove that the RVB wave function has always a lower variational energy and better nodes than the OSS, for all molecular species considered in this work. The entangled multi-reference RVB state acts against the electron edge localization implied by the OSS wave function, and weakens the diradical tendency for higher oligoacenes. These properties are reflected by several descriptors, including wave function parameters, bond length alternation, aromatic indices, and spin-spin correlation functions. In this context, we propose a new aromatic index estimator suitable for geminal wave functions. For the largest acenes taken into account, the long-range decay of the charge-charge correlation functions is compatible with a quasi-metallic behavior., Comment: 16 pages, 11 figures

A widely used approximation to the exchange-correlation functional in density functional theory is the local density approximation (LDA), typically derived from the properties of the homogeneous electron gas (HEG). We previously introduced a set of alternative LDAs constructed from one-dimensional systems of one, two, and three electrons that resemble the HEG within a finite region. We now construct a HEG-based LDA appropriate for spinless electrons in one dimension and find that it is remarkably similar to the finite LDAs. As expected, all LDAs are inadequate in low-density systems where correlation is strong. However, exploring the small but significant differences between the functionals, we find that the finite LDAs give better densities and energies in high-density exchange-dominated systems, arising partly from a better description of the self-interaction correction., Comment: Manuscript: 9 pages, 10 figures; Supplemental material: 2 pages

By means of Shubnikov-de-Haas and de-Haas-van-Alphen oscillations, and ab initio calculations, we have studied the Fermi surface of high-quality BaNiS$_2$ single crystals, with mean free path $l \sim 400 ~\text{\AA}$. The angle and temperature dependence of quantum oscillations indicates a quasi-two-dimensional Fermi surface, made of an electron-like tube centred at $\Gamma$, and of 4 hole-like cones, generated by Dirac bands, weakly dispersive in the out-of-plane direction. Ab initio electronic structure calculations, in the density functional theory framework, show that the inclusion of screened exchange is necessary to account for the experimental Fermi pockets. Therefore, the choice of the functional becomes crucial. A modified HSE hybrid functional with 7% of exact exchange outperforms both GGA and GGA+U density functionals, signalling the importance of non-local screened-exchange interactions in BaNiS$_2$, and, more generally, in $3d$ compensated semimetals., Comment: 8 figures

QMCPACK is an open source quantum Monte Carlo package for ab-initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow type trial wave functions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performance computing architectures, including multicore central processing unit (CPU) and graphical processing unit (GPU) systems. We detail the program's capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://www.qmcpack.org .

We introduce a novel approach for a fully quantum description of coupled electron-ion systems from first principles. It combines the variational quantum Monte Carlo (QMC) solution of the electronic part with the path integral (PI) formalism for the quantum nuclear dynamics. On the one hand, the PI molecular dynamics includes nuclear quantum effects by adding a set of fictitious classical particles (beads) aimed at reproducing nuclear quantum fluctuations via a harmonic kinetic term. On the other hand, variational QMC can provide Born-Oppenheimer (BO) potential energy surfaces with a precision comparable to the most advanced post Hartree-Fock approaches, and with a favorable scaling with the system size. To deal with the intrinsic QMC noise, we generalize the PI molecular dynamics using a Langevin thermostat correlated according to the covariance matrix of QMC nuclear forces. The variational parameters of the QMC wave function are evolved during the nuclear dynamics, such that the BO potential energy surface is unbiased. Statistical errors on the wave function parameters are reduced by resorting to bead grouping average, which we show to be accurate and well controlled. Our general algorithm relies on a Trotter breakup between the dynamics driven by ionic forces and the one set by the harmonic interbead couplings. The latter is exactly integrated even in presence of the Langevin thermostat, thanks to the mapping onto an Ornstein-Uhlenbeck process. This framework turns out to be very efficient also in the case of deterministic ionic forces. The new implementation is validated on the Zundel ion by direct comparison with standard PI Langevin dynamics calculations made with a coupled cluster potential energy surface. Nuclear quantum effects are confirmed to be dominant over thermal effects well beyond room temperature giving the excess proton an increased mobility by quantum tunneling., Comment: 21 pages, 7 figures

Resolving the interplay between magnetic interactions and structural properties in strongly correlated materials through a quantitatively accurate approach has been a major challenge in condensed matter physics. Here we apply highly accurate first principles quantum Monte Carlo (QMC) techniques to obtain structural and magnetic properties of the iron selenide (FeSe) superconductor under pressure. Where comparable, the computed properties are very close to the experimental values. Of potential ordered magnetic configurations, collinear spin configurations are the most energetically favorable over the explored pressure range. They become nearly degenerate in energy with bicollinear spin orderings at around 7 GPa, when the experimental critical temperature $T_c$ is the highest. On the other hand, ferromagnetic, checkerboard, and staggered dimer configurations become relatively higher in energy as the pressure increases. The behavior under pressure is explained by an accurate analysis of the charge compressibility and the orbital occupation as described by the QMC many-body wave function, which reveals how spin, charge and orbital degrees of freedom are strongly coupled in this compound. This remarkable pressure evolution suggests that stripe-like magnetic fluctuations may be responsible for the enhanced $T_c$ in FeSe and that higher T$_c$ is associated with nearness to a crossover between collinear and bicollinear ordering.

Recent progress in treating the dynamically screened nature of the Coulomb interaction in strongly correlated lattice models and materials is reviewed with a focus on computational schemes based on the dynamical mean field approximation. We discuss approximate and exact methods for the solution of impurity models with retarded interactions, and explain how these models appear as auxiliary problems in various extensions of the dynamical mean field formalism. The current state of the field is illustrated with results from recent applications of these schemes to U-V Hubbard models and correlated materials., Comment: invited review article, comments are welcome

We introduce an efficient method to construct optimal and system adaptive basis sets for use in electronic structure and quantum Monte Carlo calculations. The method is based on an embedding scheme in which a reference atom is singled out from its environment, while the entire system (atom and environment) is described by a Slater determinant or its antisymmetrized geminal power (AGP) extension. The embedding procedure described here allows for the systematic and consistent contraction of the primitive basis set into geminal embedded orbitals (GEOs), with a dramatic reduction of the number of variational parameters necessary to represent the many-body wave function, for a chosen target accuracy. Within the variational Monte Carlo method, the Slater or AGP part is determined by a variational minimization of the energy of the whole system in presence of a flexible and accurate Jastrow factor, representing most of the dynamical electronic correlation. The resulting GEO basis set opens the way for a fully controlled optimization of many-body wave functions in electronic structure calculation of bulk materials, namely, containing a large number of electrons and atoms. We present applications on the water molecule, the volume collapse transition in cerium, and the high-pressure liquid hydrogen., Comment: 15 pages, 7 figures

We report on a systematic study of the thermodynamic, electronic and charge transport properties of high-quality single crystals of BaNiS$_2$, the metallic end-member of the quasi-twodimensional BaCo$_{1-x}$Ni$_x$S$_2$ system characterized by a metal-insulator transition at $x_{cr}=0.22$. Our analysis of magnetoresistivity and specific heat data consistently suggests a picture of compensated semimetal with two hole- and one electron-bands, where electron-phonon scattering dominates charge transport and the minority holes exhibit, below $\sim$100 K, a very large mobility, $\mu_h\sim$ 15000 cm$^2$V$^{-1}$s$^{-1}$, which is explained by a Dirac-like band. Evidence of unconventional metallic properties is given by an intriguing crossover of the resistivity from a Bloch-Gr\"uneisen regime to a linear$-T$ regime occurring at 2 K and by a strong linear term in the paramagnetic susceptibility above 100 K. We discuss the possibility that these anomalies reflect a departure from conventional Fermi-liquid properties in presence of short-range AF fluctuations and of a large Hund coupling., Comment: 21 pages 9 figures (colors)

Understanding the Fermi surface and low-energy excitations of iron or cobalt pnictides is crucial for assessing electronic instabilities such as magnetic or superconducting states. Here, we propose and implement a new approach to compute the low-energy properties of correlated electron materials, taking into account both screened exchange beyond the local density approximation and local dynamical correlations. The scheme allows us to resolve the puzzle of BaCo2As2, for which standard electronic structure techniques predict a ferromagnetic instability not observed in nature., Comment: 6 pages, 4 figures + Supplementary material

We propose an electron-phonon parameterization which reliably reproduces the geometry and harmonic frequencies of a real system. With respect to standard electron-phonon models, it adds a "double-counting" correction, which takes into account the lattice deformation as the system is dressed by low-energy electron-phonon processes. We show the importance of this correction by studying potassium-doped picene (K$_3$Picene), recently claimed to be a superconductor with a $T_c$ of up to 18 K. The Hamiltonian parameters are derived from ab-initio density functional theory, and the lattice model is solved by dynamical mean-field theory. Our calculations include the effects of electron-electron interactions and local electron-phonon couplings. Even with the inclusion of a strongly coupled molecular phonon, the Hubbard repulsion prevails and the system is an insulator with a small Mott gap of $\approx$ 0.2 eV.

The very first dynamical implementation of the combined GW and dynamical mean field scheme "GW+DMFT" for a real material was achieved recently [J.M. Tomczak et al., Europhys. Lett. 100 67001 (2012)], and applied to the ternary transition metal oxide SrVO3. Here, we review and extend that work, giving not only a detailed account of full GW+DMFT calculations, but also discussing and testing simplified approximate schemes. We give insights into the nature of exchange and correlation effects: Dynamical renormalizations in the Fermi liquid regime of SrVO3 are essentially local, and nonlocal correlations mainly act to screen the Fock exchange term. The latter substantially widens the quasi-particle band structure, while the band narrowing induced by the former is accompanied by a spectral weight transfer to higher energies. Most interestingly, the exchange broadening is much more pronounced in the unoccupied part of spectrum. As a result, the GW+DMFT electronic structure of SrVO3 resembles the conventional density functional based dynamical mean field (DFT+DMFT) description for occupied states, but is profoundly modified in the empty part. Our work leads to a reinterpretation of inverse photoemission spectroscopy (IPES) data. Indeed, we assign a prominent peak at about 2.7 eV dominantly to eg states, rather than to an upper Hubbard band of t2g character. Similar surprises can be expected for other transition metal oxides, calling for more detailed investigations of the conduction band states., Comment: 24 pages

We report an extensive theoretical study of the protonated water dimer (Zundel ion) by means of the highly correlated variational Monte Carlo and lattice regularized Monte Carlo approaches. This system represents the simplest model for proton transfer (PT) and a correct description of its properties is essential in order to understand the PT mechanism in more complex acqueous systems. Our Jastrow correlated AGP wave function ensures an accurate treatment of electron correlations. Exploiting the advantages of contracting the primitive basis set over atomic hybrid orbitals, we are able to limit dramatically the number of variational parameters with a systematic control on the numerical precision, crucial in order to simulate larger systems. We investigate energetics and geometrical properties of the Zundel ion as a function of the oxygen-oxygen distance, taken as reaction coordinate. In both cases, our QMC results are found in excellent agreement with coupled cluster CCSD(T) technique, the quantum chemistry "gold standard". Calculations on proton transfer static barriers and dissociation energies display the same agreement. A comparison with density functional theory (DFT) results in the PBE approximation points out the crucial role of electron correlations for a correct description of the PT in the dimer. Our method is able to resolve the tiny energy differences (~ 0.1 Kcal/mol) and the corresponding structural variations at which the proton transfer takes place; it combines these features with a N^3-N^4 scaling with number of particles (favorable with respect to other post-DFT methods), as proven by a benchmark calculation on a larger protonated water cluster. The QMC approach used here represents a promising candidate to provide the first high-level ab initio description of PT in water., Comment: 16 pages, 6 figures

By means of space-group symmetry arguments, we argue that the electronic pairing in iron-based high temperature superconductors shows a structure which is a linear combination of planar s-wave and d-wave symmetry channels, both preserving the 3-dimensional A_1g irreducible representation of the corresponding crystal point-group. We demonstrate that the s- and d-wave channels are determined by the parity under reflection of the electronic orbitals through the iron planes, and by improper rotations around the iron sites. We provide evidence of these general properties by performing accurate quantum Monte Carlo ab-initio calculations of the pairing function, for a FeSe lattice with tetragonal experimental geometry at ambient pressure. We find that this picture survives even in the FeSe under pressure and at low temperatures, when the tetragonal point-group symmetry is slightly broken. In order to achieve a higher resolution in momentum space we introduce a BCS model that faithfully describes our QMC variational pairing function on the simulated 4x4 FeSe unit cell. This allows us to provide a k-resolved image of the pairing function, and show that non-isotropic contributions in the BCS gap function are related to the improper s-wave symmetry. Our theory can rationalize and explain a series of contradictory experimental findings, such as the observation of twofold symmetry in the FeSe superconducting phase, the anomalous drop of T_c with Co-impurity in LaFeAsO_(1-x)F_x, the s-to-d-wave gap transition in BaFe_2As_2 under K doping, and the nodes appearing in the LiFeAs superconducting gap upon P isovalent substitution., Comment: 13 pages, 9 figures, extended version (published on October 21) of a previously submitted manuscript

We present the first dynamical implementation of the combined GW and dynamical mean field scheme ("GW+DMFT") for first principles calculations of the electronic properties of correlated materials. The application to the ternary transition metal oxide SrVO3 demonstrates that this schemes inherits the virtues of its two parent theories: a good description of the local low energy correlation physics encoded in a renormalized quasi-particle band structure, spectral weight transfer to Hubbard bands, and the physics of screening driven by long-range Coulomb interactions. Our data is in good agreement with available photoemission and inverse photoemission spectra; our analysis leads to a reinterpretation of the commonly accepted "three-peak structure" as originating from orbital effects rather than from the electron addition peak within the t2g manifold., Comment: replaced with published version (6 pages, 3 figures); first version was submitted to PRL on June 19, 2012

We analyze the properties of electron-phonon couplings in K3Picene by exploiting a molecular orbital representation derived in the maximally localized Wannier function formalism. This allows us to go beyond the analysis done in Phys. Rev. Lett. 107, 137006 (2011), and separate not only the intra- and intermolecular phonon contributions but also the local and non-local electronic states in the electron-phonon matrix elements. Despite the molecular nature of the crystal, we find that the purely molecular contributions (Holstein-like couplings where the local deformation potential is coupled to intramolecular phonons) account for only 20% of the total electron-phonon interaction lambda. In particular, the Holstein-like contributions to lambda in K3Picene are four times smaller than those computed for an isolated neutral molecule, as they are strongly screened by the metallic bands of the doped crystal. Our findings invalidate the use of molecular electron-phonon calculations to estimate the total electron-phonon coupling in metallic picene, and possibly in other doped metallic molecular crystals. The major contribution (80%) to lambda in K3Picene comes from non-local couplings due to phonon modulated hoppings. We show that the crystal geometry together with the molecular picene structure leads to a strong 1D spatial anisotropy of the non-local couplings. Finally, based on the parameters derived from our density functional theory calculations, we propose a lattice modelization of the electron-phonon couplings in K3Picene which gives 90% of ab-initio lambda., Comment: 13 pages, 8 figures, 3 tables

Over the last years, superconductivity has been discovered in several families of iron-based compounds. Despite intense research, even basic electronic properties of these materials, such as Fermi surfaces, effective electron masses, or orbital characters are still subject to debate. Here, we address an issue that has not been considered before, namely the consequences of dynamical screening of the Coulomb interactions among Fe-d electrons. We demonstrate its importance not only for correlation satellites seen in photoemission spectroscopy, but also for the low-energy electronic structure. From our analysis of the normal phase of BaFe2As2 emerges the picture of a strongly correlated compound with strongly doping- and temperature-dependent properties. In the hole overdoped regime, an incoherent metal is found, while Fermi-liquid behavior is recovered in the undoped compound. At optimal doping, the self-energy exhibits an unusual square-root energy dependence which leads to strong band renormalizations near the Fermi level.