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We propose introducing an extended Hubbard Hamiltonian derived via the ab initio downfolding method, which was originally formulated for periodic materials, toward efficient quantum computing of molecular electronic structure calculations. By utilizing this method, the first-principles Hamiltonian of chemical systems can be coarse-grained by eliminating the electronic degrees of freedom in higher energy space and reducing the number of terms of electron repulsion integral from O ( N 4 ) to O ( N 2 ). Our approach is validated numerically on the vertical excitation energies and excitation characters of ethylene, butadiene, and hexatriene. The dynamical electron correlation is incorporated within the framework of the constrained random phase approximation in advance of quantum computations, and the constructed models capture the trend of experimental and high-level quantum chemical calculation results. As expected, the L1-norm of the fermion-to-qubit mapped model Hamiltonians is significantly lower than that of conventional ab initio Hamiltonians, suggesting improved scalability of quantum computing. Those numerical outcomes and the results of the simulation of excited-state sampling demonstrate that the ab initio extended Hubbard Hamiltonian may hold significant potential for quantum chemical calculations using quantum computers. [ABSTRACT FROM AUTHOR]

The one-particle reduced density-matrix (1-RDM) functional theory is a promising alternative to density-functional theory (DFT) that uses the 1-RDM rather than the electronic density as a basic variable. However, long-standing challenges such as the lack of the Kohn–Sham scheme and the complexity of the pure N-representability conditions are still impeding its wild utilization. Fortunately, ensemble N-representability conditions derived in the natural orbital basis are known and trivial such that almost every functional of the 1-RDM is actually natural orbital functional, which does not perform well for all the correlation regimes. In this work, we propose a variational minimization scheme in the ensemble N-representable domain that is not restricted to the natural orbital representation of the 1-RDM. We show that splitting the minimization into the diagonal and off-diagonal parts of the 1-RDM can open the way toward the development of functionals of the orbital occupations, which remains a challenge for the generalization of site-occupation functional theory in chemistry. Our approach is tested on the uniform Hubbard model using the Müller and the Töws–Pastor functionals, as well as on the dihydrogen molecule using the Müller functional. [ABSTRACT FROM AUTHOR]

The interaction between the magnetic moment of an electron and the magnetic field generated by a moving charge is one component of the spin–orbit interaction. The nuclei in a molecule or solid are charged, are generally in vibrational motion, and so contribute to this interaction, but the direct coupling between nuclear momentum and electron spin is normally ignored in discussions of spin-forbidden phenomena such as transitions between states of different spin, even when the nuclei are recognized as playing a fundamental role (spin–vibronic coupling). Here, we investigate the spin–orbit interaction in a Heisenberg model interacting with vibrating point charges representing nearby bridging ligands. To reach the model, we apply second order perturbation theory to the Hubbard model with the spin–orbit interaction. In contrast to the other components of the spin–orbit interaction, the part that directly couples the momentum of the charge and electron spin appears at first order as an effective magnetic field at each site. We find that the inclusion of this nuclear-motion induced spin–orbit coupling can increase the rate of otherwise spin-forbidden transitions between different spin states of the Heisenberg model by many orders of magnitude. This overlooked interaction may, therefore, play a significant role in spin-forbidden phenomena such as spin relaxation in coupled spin-qubits. [ABSTRACT FROM AUTHOR]

We have studied the electron–electron interactions in the system composed of two metallic one-dimensional point contact and zero-sized wires, in the applied electric field and exposed to the influence of the external Zeeman magnetic field. The interactions between the electrons within wires have been taken into account within the usual Hubbard model. We have considered different limits of particle-filling on the atomic lattice site positions. We show the existence of the excitonic pairing in this one-dimensional system in different limits of the electron–electron interactions, magnetic field, and temperature. We demonstrate that the usual Hubbard- U interaction leads to strong electron localization, which enhances the local antiferromagnetic order in the system. [ABSTRACT FROM AUTHOR]

Quantum-chemical calculations aimed at deriving magnetic coupling constants in exchange-coupled spin clusters commonly utilize a broken-symmetry (BS) approach. This involves calculating several distinct collinear spin configurations, predominantly by density-functional theory. The energies of these configurations are interpreted in terms of the Heisenberg model, H ̃ = ∑ i < j J i j s ̃ i ⋅ s ̃ j , to determine coupling constants Jij for spin pairs. However, this energy-based procedure has inherent limitations, primarily in its inability to provide information on isotropic spin interactions beyond those included in the Heisenberg model. Biquadratic exchange or multi-center terms, for example, are usually inaccessible and hence assumed to be negligible. The present work introduces a novel approach employing BS mean-field solutions, specifically Hartree–Fock wave functions, for the construction of effective spin Hamiltonians. This expanded method facilitates the extraction of a broader range of coupling parameters by considering not only the energies, but also Hamiltonian and overlap elements between different BS states. We demonstrate how comprehensive s = 1 2 Hamiltonians, including multi-center terms, can be straightforwardly constructed from a complete set of BS solutions. The approach is exemplified for small clusters within the context of the half-filled single-band Hubbard model. This allows to contrast the current strategy against exact results, thereby offering an enriched understanding of the spin-Hamiltonian construction from BS solutions. [ABSTRACT FROM AUTHOR]

Studying noncommuting conserved quantities, or 'charges,' has revealed a conceptual puzzle: noncommuting charges hinder thermalization in some ways yet promote it in others. While many quantum systems thermalize according to the Eigenstate Thermalization Hypothesis (ETH), systems with 'dynamical symmetries' violate the ETH and exhibit non-stationary dynamics, preventing them from equilibrating, much less thermalizing. We demonstrate that each pair of dynamical symmetries corresponds to a specific charge. We find that introducing new charges that do not commute with existing ones disrupts these symmetries, thereby eliminating non-stationary dynamics and facilitating thermalization. We illustrate this behavior across various models, including the Hubbard model and Heisenberg spin chains. Our findings demonstrate that noncommuting charges can enhance thermalization by reducing the number of local observables that thermalize according to the ETH. Noncommuting charges pose a puzzle: they hinder thermalization in some ways yet promote it in others. Here, the authors demonstrate how noncommuting charges enhance thermalization by reducing the number of local observables that thermalize. [ABSTRACT FROM AUTHOR]

The conductivity for half-filled disordered Hubbard model in different interaction regimes is studied using a typical medium dynamical mean-field theory. The Kubo formula with the geometrically averaged Green function is used to calculate the optical and dc conductivity of the system. The dependence of the conductivities in the model on the random potential and temperature in the weak and intermediate interaction regimes is investigated numerically. It is shown that in the weak interaction regime at a fixed temperature the optical conductivity at low frequencies as well as the dc conductivity get decreased as disorder strength increases. Whereas in the intermediate interaction regime, the results show a reentrant effect of the insulating phases. Our dc conductivity of a non-interacting disordered system is consistent with those known in the literature and our other results are in agreement with the phase diagram obtained by using typical medium theory with different impurity solvers. [ABSTRACT FROM AUTHOR]

Feynman's diagrammatic series is a common language for a formally exact theoretical description of systems of infinitely-many interacting quantum particles, as well as a foundation for precision computational techniques. Here we introduce a universal framework for efficient summation of connected or skeleton Feynman diagrams for generic quantum many-body systems. It is based on an explicit combinatorial construction of the sum of the integrands by dynamic programming, at a computational cost that can be made only exponential in the diagram order on a classical computer and potentially polynomial on a quantum computer. We illustrate the technique by an unbiased diagrammatic Monte Carlo calculation of the equation of state of the 2D SU(N) Hubbard model in an experimentally relevant regime, which has remained challenging for state-of-the-art numerical methods. Feynman's diagrammatic technique is widely used in the description of quantum many-body systems. This work demonstrates an efficient method for summing Feynman diagrams with exponential computational cost in the diagram order, translating into polynomial scaling of the calculation time with the required accuracy. [ABSTRACT FROM AUTHOR]

Using the strong coupling diagram technique, we find three phases of the half-filled isotropic Hubbard model on a triangular lattice at finite temperatures. The weak-interaction ( U ≲ 5 t ) and strong-interaction ( U ≳ 9 t ) phases are similar to those obtained by zero-temperature methods—the former is a metal without perceptible spin excitations; the latter is a Mott insulator with the 120 ∘ short-range spin ordering. Zero-temperature approaches predict a nonmagnetic insulating spin-liquid phase sandwiched between these two regions. In our finite-temperature calculations, the Mott gap in the intermediate phase is filled by the Fermi-level peak, which is a manifestation of the bound states of electrons with pronounced spin excitations. We relate the appearance of these excitations at finite temperatures to the Pomeranchuk effect. [ABSTRACT FROM AUTHOR]

Using the unrestricted Hartree-Fock variational method, we study the extended Hubbard model in the triangular lattice at 3/4 filling. Due to the nesting instability of the Fermi surface, various density wave states compatible with the 2 × 2 supercell are found as the ground state by tuning the onsite and nearest neighbor repulsions U and V. Surprisingly, the flux phases with complex bond order parameters are realized in a wide range of the U-V phase diagram. They also acquire nontrivial topological properties due to the spontaneous breaking of the time-reversal symmetry. Our study suggests that the flux phases can be stabilized by the interplay between short-range repulsive interactions in correlated electron systems. [ABSTRACT FROM AUTHOR]

A recent work (arXiv:2401.04685) has merged N‐centered ensembles of neutral and charged electronic ground states with ensembles of neutral ground and excited states, thus providing a general and in‐principle exact (so‐called extended N‐centered) ensemble density functional theory of neutral and charged electronic excitations. This formalism made it possible to revisit the concept of density‐functional derivative discontinuity, in the particular case of single excitations from the highest occupied Kohn–Sham (KS) molecular orbital, without invoking the usual "asymptotic behavior of the density" argument. In this work, we address a broader class of excitations, with a particular focus on double excitations. An exact implementation of the theory is presented for the two‐electron Hubbard dimer model. A thorough comparison of the true physical ground‐ and excited‐state electronic structures with that of the fictitious ensemble density‐functional KS system is also presented. Depending on the choice of the density‐functional ensemble as well as the asymmetry of the dimer and the correlation strength, an inversion of states can be observed. In some other cases, the strong mixture of KS states within the true physical system makes the assignment "single excitation" or "double excitation" irrelevant. [ABSTRACT FROM AUTHOR]

The ionic Hubbard model in a two-dimensional square lattice is revisited using determinant quantum Monte Carlo (DQMC) and numerical analytic continuation. From the dc conductivity extracted by stochastic maximum entropy of the DQMC data, we find that the band insulator induced by a staggered potential Δ goes through a metallic phase before entering a Mott insulator as the on-site Hubbard interaction U is increased. Moreover, we map out the phase diagram in the (Δ , U) plane, and reveal a smaller metallic region than that found in the previous studies. Our results provide a more exact location of the phase boundaries, and are an important complement to those obtained by an approximate approach. [ABSTRACT FROM AUTHOR]

Context: In the realm of quantum chemistry, the accurate prediction of electronic structure and properties of nanostructures remains a formidable challenge. Density functional theory (DFT) and density matrix renormalization group (DMRG) have emerged as two powerful computational methods for addressing electronic correlation effects in diverse molecular systems. We compare ground-state energies ( e 0 ), density profiles ( n ), and average entanglement entropies ( S ¯ ) in metals, insulators and at the transition from metal to insulator, in homogeneous, superlattices, and harmonically confined chains described by the fermionic one-dimensional Hubbard model. While for the homogeneous systems, there is a clear hierarchy between the deviations, D % (S ¯) < D % (e 0) < D ¯ % (n) , and all the deviations decrease with the chain size; for superlattices and harmonic confinement, the relation among the deviations is less trivial and strongly dependent on the superlattice structure and the confinement strength considered. For the superlattices, in general, increasing the number of impurities in the unit cell represents lower precision in the DFT calculations. For the confined chains, DFT performs better for metallic phases, while the highest deviations appear for the Mott and band-insulator phases. This work provides a comprehensive comparative analysis of these methodologies, shedding light on their respective strengths, limitations, and applications. Methods: The DFT calculations were performed using the standard Kohn-Sham scheme within the BALDA approach. It integrated the numerical Bethe-Ansatz (BA) solution of the Hubbard model as the homogeneous density functional within a local-density approximation (LDA) for the exchange-correlation energy. The DMRG algorithms were implemented using the ITensor library, which is based on the matrix product states (MPS) ansatz. The calculations were performed until the energy reaches convergence of at least 10 - 8 . [ABSTRACT FROM AUTHOR]

Spin- and charge- stripe order has been extensively studied in the superconducting cuprates, among which underdoped La2−xSrxCuO4 (LSCO) is an archetype with static spin stripes at low temperatures. An intriguing, but not completely understood, phenomenon in LSCO is that the stripes are tilted away from the high-symmetry Cu-Cu directions. Using high-resolution neutron scattering on LSCO with x = 0.12, we find two coexisting phases at low temperatures, one with static spin stripes and the other with fluctuating ones, both sharing the same tilt angle. Our numerical calculations using the doped Hubbard model elucidate the tilting's origin, attributing it to anisotropic next-nearest neighbor hopping t ′ , consistent with the material's slight orthorhombicity. Our results underscore the model's success in describing specific details of the ground state of this real material and highlight the role of t ′ in the Hamiltonian, revealing the delicate interplay between stripes and superconductivity across theoretical and experimental contexts. Cuprate superconductors have interesting charge and spin ordering patterns in the form of stripes. By combining experimental and numerical tools, the authors reveal that the stripes are always tilted from the underlying lattice directions, with the origin well explained by the anisotropy of the next-nearest neighbor electron hopping. [ABSTRACT FROM AUTHOR]

A model of tunneling (jumping) migration of charge carriers near their mobility edge in the upper band of neutral states of majority hydrogen‐like impurities is proposed to calculate the energy of thermal activation of electrical ε 2 $\left(\epsilon\right)_{2}$ ‐conductivity of weakly compensated semiconductors. The difference from the known Hubbard model consists in the scheme of interimpurity transitions of charge carriers and in the method of calculating the position of their tunnel mobility edge. The drift mobility edge of free charge carriers corresponds to the thermal ionization energy of majority impurities ε 1 > ε 2 $\left(\epsilon\right)_{1}&amp;amp;amp;amp;amp;amp;amp;amp;amp;gt; \left(\epsilon\right)_{2}$ , which is located near the c‐band bottom or the v‐band top in n‐ and p‐type semiconductors, respectively, and is due to the overlap of excited states of electrically neutral majority impurities. The position of the tunnel mobility edge for ε 2 $\left(\epsilon\right)_{2}$ ‐conductivity is determined by taking into account the Coulomb interaction of the majority impurities in the charge states ( − 1 ) $\left(\right. - 1 \left.\right)$ and ( + 1 ) $\left(\right. &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;plus; 1 \left.\right)$ . It is assumed that doping and compensating impurities form a single simple nonstoichiometric cubic lattice in a crystal matrix. The calculations of the activation energy ε 2 $\left(\epsilon\right)_{2}$ on the insulator side of the insulator–metal concentration phase transition for weakly compensated p‐Si:B, n‐Si:P, and n‐Ge:Sb crystals quantitatively agree with known experimental data. [ABSTRACT FROM AUTHOR]

We analyze the coexisting ordered phases that arise in the half-filled ε -t-U-V extended Hubbard Model on the square lattice when tackled within the Kotliar and Ruckenstein slave boson representation in the thermodynamical limit. Particular emphasis is put on the dependence of the quasi-particle dispersions, the gaps, the spin-resolved renormalization factors, and the distribution of double occupancy on the microscopical parameters of the model. Our calculations are performed in a parameter range that is most suitable for resistive switching. In particular, the main contributions to the gaps are shown to either arise from ε in the weak coupling regime, or from U and V when they are the largest scales. The gaps are thus from joint spin and charge origin, and so are the order parameters. [ABSTRACT FROM AUTHOR]

We employ constrained path Auxiliary Field Quantum Monte Carlo (AFQMC) in the pursuit of studying physical nuclear systems using a lattice formalism. Since AFQMC has been widely used in the study of condensed-matter systems such as the Hubbard model, we benchmark our method against published results for both one- and two-dimensional Hubbard model calculations. We then turn our attention to cold atomic and nuclear systems. We use an onsite contact interaction that can be tuned in order to reproduce the known scattering length and effective range of a given interaction. Developing this machinery allows us to extend our calculations to study nuclear systems within a lattice formalism. We perform initial calculations for a range of nuclear systems from two- to few-body neutron systems. This article is part of the theme issue 'The liminal position of Nuclear Physics: from hadrons to neutron stars'. [ABSTRACT FROM AUTHOR]

The functional integral formulation of the Hubbard model when treated in its Kotliar‐Ruckenstein representation in the radial gauge involves fermionic, as well as complex and radial slave boson fields. In order to improve on the understanding of the interplay of the three types of fields, and on the nature of the latter, a comprehensive investigation of an exactly solvable two‐site cluster is performed, as it entails all pitfalls embodied in this approach. It is first shown that the exact partition function is recovered, even when incorporating in the calculation the square root factors that are at the heart of the representation, when suitably regularized. It is shown that using radial slave boson fields allows to overcome all hurdles following from the normal ordering procedure. It is then demonstrated that this applies to the Green's function as well, and to the correlation functions of physical interest, thereby answering the criticisms raised by Schönhammer [K. Schönhammer, Phys. Rev. B 199042, 2591]. In addition, the investigation generalizes the calculations to the Hubbard model extended by a non‐local Coulomb interaction. [ABSTRACT FROM AUTHOR]

For the first time, in this computational aspect, we have reported the various intrinsic physical properties of newly inorganic halide double perovskite semiconductors Rb2GeMnX6 (X = Cl, Br) upon the basis of full potential linearized augmented plane wave (FP-LAPW) integrated in Wien2k package. Primarily, the attempt was made to define the structural stability of both these perovskite structures by evaluating their total ground state energies, via from the Brich Murnaghan equation of state, which addresses the possible ground state energy in ferromagnetic (FM) rather than competing anti-ferromagnetic (AFM) phases. Meanwhile, the retrieved optimized lattice constants are in rational accord with benchmark studies reported by others. Later on, the electronic structures of these alloys has been executed by the calibration of certain functional schemes viz; Perdew-Burke Ernzerhof-Generalized Gradient Approximation (PBE-GGA) in conjunction with the Hubbard model (GGA + U) and along with the Tran-Blaha modified Becke-Johnson (TB-mBJ), which portrays the existence of semiconducting nature via seen from their corresponding band structures as well as density of states. More likely, the spin-splitting from their two-dimensional band structures discloses a net magnetism of 5µB within each alloy, specifies their facial route for spintronic applications. Subsequently, the mechanical stability by enumerating the three distinct elastic constants due to their cubic symmetry has been computed via Cubic Elastic Package. With the help of density functional perturbation theory (DFPT), the context of phonon stability has been studied. In addition, semi-classical Boltzmann theory integrated within the sophisticated BoltzTraP package has been properly applied to forecast various transport results. Being displaying the necessary stability conditions and also the various promising features lends their way towards the cutting-edge applications in spintronics and sustainable green energy harvesting technologies. [ABSTRACT FROM AUTHOR]

Abstract Spin transport theory of non-Hermitian quantum systems, where the non-Hermiticity led to a series of exotic phenomena when the system experiences dissipation to an environment is proposed. The goal is a better understanding of the spin diffusion in the one-dimensional non-Hermitian XXZ model which allows the transport coefficients be computed analytically. Moreover, we analyzed the electric transport in the one-dimensional non-Hermitian Hubbard model which is a very important model of electrons strongly correlated, where we have investigated the effect of non-Hermitian parameters like the imaginary hopping on AC and DC conductivities of the system. We analyzed the large U limit of this model, where such non-Hermiticity contributes with a minus sign in the virtual exchange of quasiparticles and the behavior of the ground state energy and low-lying excitations is reversed.

Recently, a bulk nickelate superconductor La3Ni2O7 is discovered at pressures with a remarkable high transition temperature Tc ∼ 80 K. Here, we study a Hubbard model with tight-binding parameters derived from ab initio calculations of La3Ni2O7, by employing large scale determinant quantum Monte Carlo and cellular dynamical mean-field theory. Our result suggests that the superexchange couplings in this system are comparable to that of cuprates. The system is a charge transfer insulator as the hole concentration becomes four per site at large Hubbard U. Upon hole doping, two low-energy spin-singlet bands emerge in the system exhibiting distinct correlation properties: while the one composed of the out-of-plane Ni- d 3 z 2 − r 2 and O-pz orbitals demonstrates strong antiferromagnetic correlations and narrow effective bandwidth, the in-plane singlet band consisting of the Ni- d x 2 − y 2 and O-px/py orbitals is in general more itinerant. Over a broad range of hole doping, the doped holes occupy primarily the d x 2 − y 2 and px/py orbitals, whereas the d 3 z 2 − r 2 and pz orbitals retain underdoped. We propose an effective t-J model to capture the relevant physics and discuss the implications of our result for comprehending the La3Ni2O7 superconductivity. [ABSTRACT FROM AUTHOR]

Ultracold-atom simulations of the Hubbard model provide insights into the character of charge and spin correlations in and out of equilibrium. The corresponding numerical simulations, on the other hand, remain a significant challenge. We build on recent progress in the quantum Monte Carlo (QMC) simulation of electrons in continuous space and apply similar ideas to the square-lattice Hubbard model. We devise and benchmark two discrete-time QMC methods, namely the fermionic-propagator QMC (FPQMC) and the alternating-basis QMC (ABQMC). In FPQMC, the time evolution is represented by snapshots in real space, whereas the snapshots in ABQMC alternate between real and reciprocal space. The methods may be applied to study equilibrium properties within the grand-canonical or canonical ensemble, external field quenches, and even the evolution of pure states. Various real-space/reciprocal-space correlation functions are also within their reach. Both methods deal with matrices of size equal to the number of particles (thus independent of the number of orbitals or time slices), which allows for cheap updates. We benchmark the methods in relevant setups. In equilibrium, the FPQMC method is found to have an excellent average sign and, in some cases, yields correct results even with poor imaginary-time discretization. ABQMC has a significantly worse average sign, but also produces good results. Out of equilibrium, FPQMC suffers from a strong dynamical sign problem. On the contrary, in ABQMC, the sign problem is not time-dependent. Using ABQMC, we compute survival probabilities for several experimentally relevant pure states. [ABSTRACT FROM AUTHOR]

Quantum fluctuations in low-dimensional systems and near quantum phase transitions have significant influences on material properties. Yet, it is difficult to experimentally gauge the strength and importance of quantum fluctuations. Here we provide a resonant inelastic x-ray scattering study of magnon excitations in Mott insulating cuprates. From the thin film of SrCuO2, single- and bi-magnon dispersions are derived. Using an effective Heisenberg Hamiltonian generated from the Hubbard model, we show that the single-magnon dispersion is only described satisfactorily when including significant quantum corrections stemming from magnon-magnon interactions. Comparative results on La2CuO4 indicate that quantum fluctuations are much stronger in SrCuO2 suggesting closer proximity to a magnetic quantum critical point. Monte Carlo calculations reveal that other magnetic orders may compete with the antiferromagnetic Néel order as the ground state. Our results indicate that SrCuO2—due to strong quantum fluctuations—is a unique starting point for the exploration of novel magnetic ground states. Magnetic excitations in infinite-layer cuprates have been intensively studied. Here the authors use resonant inelastic x-ray scattering and theoretical calculations to study magnons in thin films of SrCuO2, finding distinct magnon dispersion attributed to renormalization due to quantum fluctuations. [ABSTRACT FROM AUTHOR]

Flat electronic bands are expected to show proportionally enhanced electron correlations, which may generate a plethora of novel quantum phases and unusual low-energy excitations. They are increasingly being pursued in d-electron-based systems with crystalline lattices that feature destructive electronic interference, where they are often topological. Such flat bands, though, are generically located far away from the Fermi energy, which limits their capacity to partake in the low-energy physics. Here we show that electron correlations produce emergent flat bands that are pinned to the Fermi energy. We demonstrate this effect within a Hubbard model, in the regime described by Wannier orbitals where an effective Kondo description arises through orbital-selective Mott correlations. Moreover, the correlation effect cooperates with symmetry constraints to produce a topological Kondo semimetal. Our results motivate a novel design principle for Weyl Kondo semimetals in a new setting, viz. d-electron-based materials on suitable crystal lattices, and uncover interconnections among seemingly disparate systems that may inspire fresh understandings and realizations of correlated topological effects in quantum materials and beyond. Flat electronic bands can give rise to correlation-driven phases but for this, they need to be tuned to the Fermi level. Here the authors predict flat bands pinned at the Fermi level due to orbital-selective interactions and discuss implications for the design of topological Kondo semimetal in d-electron systems. [ABSTRACT FROM AUTHOR]

Numerically simulating large, spinful, fermionic systems is of great interest in condensed matter physics. However, the exponential growth of the Hilbert space dimension with system size renders exact quantum state parameterizations impractical. Owing to their representative power, neural networks often allow to overcome this exponential scaling. Here, we investigate the ability of neural quantum states (NQS) to represent the bosonic and fermionic t − J model – the high interaction limit of the Hubbard model – on various 1D and 2D lattices. Using autoregressive, tensorized recurrent neural networks (RNNs), we study ground state representations upon hole doping the half-filled system. Additionally, we propose a method to calculate quasiparticle dispersions, applicable to any network architecture or lattice geometry, and allowing to infer the low-energy physics from NQS. By analyzing the strengths and weaknesses of the RNN ansatz we shed light on the challenges and promises of NQS for simulating bosonic and fermionic systems. Neural network quantum states (NQS) are a promising method to simulate large fermionic systems. This work reports on accurate simulations of the t-J model in 1D and 2D lattices by means of NQS based on a recurrent neural network (RNN) architecture focusing on the calculation of dispersion relations, for which a general method is introduced, and on the performance of the RNN ansatz upon doping. [ABSTRACT FROM AUTHOR]

Quantum computers have a potential for solving quantum chemistry problems with higher accuracy than classical computers. Quantum computing quantum Monte Carlo (QC-QMC) is a QMC with a trial state prepared in quantum circuit, which is employed to obtain the ground state with higher accuracy than QMC alone. We propose an algorithm combining QC-QMC with a hybrid tensor network to extend the applicability of QC-QMC beyond a single quantum device size. In a two-layer quantum-quantum tree tensor, our algorithm for the larger trial wave function can be executed than preparable wave function in a device. Our algorithm is evaluated on the Heisenberg chain model, graphite-based Hubbard model, hydrogen plane model, and MonoArylBiImidazole using full configuration interaction QMC. Our algorithm can achieve energy accuracy (specifically, variance) several orders of magnitude higher than QMC, and the hybrid tensor version of QMC gives the same energy accuracy as QC-QMC when the system is appropriately decomposed. Moreover, we develop a pseudo-Hadamard test technique that enables efficient overlap calculations between a trial wave function and an orthonormal basis state. In a real device experiment by using the technique, we obtained almost the same accuracy as the statevector simulator, indicating the noise robustness of our algorithm. These results suggests that the present approach will pave the way to electronic structure calculation for large systems with high accuracy on current quantum devices. [ABSTRACT FROM AUTHOR]

As a typical quantum many body problem, we consider the time evolution of density matrix elements in the Bose-Hubbard model. For an arbitrary initial state, these quantities can be obtained from an SDE or stochastic differential equation system. To this SDE system, a Girsanov transformation can be applied. This has the effect that all the information from the initial state moves into the drift part, into the mean field part, of the transformed system. In the large N limit with g = U N fixed, the diffusive part of the transformed system vanishes and as a result, the exact quantum dynamics is given by an ODE system which turns out to be the time dependent discrete Gross Pitaevskii equation. For the two site Bose-Hubbard model, the GP equation reduces to the mathematical pendulum and the difference of expected number of particles at the two lattice sites is equal to the velocity of that pendulum which is either oscillatory or it can have rollovers which then corresponds to the self trapping or insulating phase. As a by-product, we also find an equivalence of the mathematical pendulum with a quartic double well potential. Collapse and revivals are a more subtle phenomenom, in order to see these the diffusive part of the SDE system or quantum corrections have to be taken into account. This can be done with an approximation and collapse and revivals can be reproduced, numerically and also through an analytic calculation. Since expectation values of Fresnel or Wiener diffusion processes, we write the density matrix elements exactly in this way, can be obtained from parabolic second order PDEs, we also obtain various exact PDE representations. The paper has been written with the goal to come up with an efficient calculation scheme for quantum many body systems and as such the formalism is generic and applies to arbitrary dimension, arbitrary hopping matrices and, with suitable adjustments, to fermionic models. [ABSTRACT FROM AUTHOR]

We rigorously prove that the local conserved quantities in the one-dimensional Hubbard model are uniquely determined for each locality up to the freedom to add lower-order ones. From this, we can conclude that the local conserved quantities are exhausted by those obtained from the expansion of the transfer matrix. [ABSTRACT FROM AUTHOR]

The wide tunability of strongly correlated transition metal (TM) oxides stems from their complex electronic properties and the coupled degrees of freedom. Among the perovskite oxides family, LaMO3 (M = Ti-Ni) allows an M-dependent systematic study of the electronic structure within the same-structure-family motif. While most of the studies have been focusing on the 3d TMs and oxygen sites, the role of the rare-earth site has been far less explored. In this work, we use resonant inelastic X-ray scattering (RIXS) at the lanthanum N4,5 edges and density functional theory (DFT) to investigate the hybridization mechanisms in LaMO3. We link the spatial-overlap-driven hybridization to energetic-overlap-driven hybridization by comparing the RIXS chemical shifts and the DFT band widths. The scope is extended to highly covalent Ruddlesden-Popper perovskite La2CuO4 by intercalating lanthanum atoms to rock-salt layers. Our work evidences an observable contribution of localized lanthanum 5p and 4f orbitals in the band structure. Understanding the hybridization due to orbital overlap in solids allows justification for adjusting electron correlation and hopping integral under the Hubbard model. This work links spatial-overlap-driven to energetic-overlap-driven hybridization from perovskite oxides by resonant inelastic X-ray scattering at La N4,5 edges. [ABSTRACT FROM AUTHOR]

The wide tunability of strongly correlated transition metal (TM) oxides stems from their complex electronic properties and the coupled degrees of freedom. Among the perovskite oxides family, LaMO3 (M = Ti-Ni) allows an M-dependent systematic study of the electronic structure within the same-structure-family motif. While most of the studies have been focusing on the 3d TMs and oxygen sites, the role of the rare-earth site has been far less explored. In this work, we use resonant inelastic X-ray scattering (RIXS) at the lanthanum N4,5 edges and density functional theory (DFT) to investigate the hybridization mechanisms in LaMO3. We link the spatial-overlap-driven hybridization to energetic-overlap-driven hybridization by comparing the RIXS chemical shifts and the DFT band widths. The scope is extended to highly covalent Ruddlesden-Popper perovskite La2CuO4 by intercalating lanthanum atoms to rock-salt layers. Our work evidences an observable contribution of localized lanthanum 5p and 4f orbitals in the band structure. Understanding the hybridization due to orbital overlap in solids allows justification for adjusting electron correlation and hopping integral under the Hubbard model. This work links spatial-overlap-driven to energetic-overlap-driven hybridization from perovskite oxides by resonant inelastic X-ray scattering at La N4,5 edges. [ABSTRACT FROM AUTHOR]

The electronic structure of 7/9-AGNR superlattices with up to eight unit cells has been studied by means of state-of-the-art Density Functional Theory (DFT) and also by two model Hamiltonians, the first one including only local interactions (Hubbard model, Hu) while the second one is extended to allow long-range Coulomb interactions (Pariser, Parr and Pople model, PPP). Both are solved within mean field approximation. At this approximation level, our calculations show that 7/9 interfaces are better described by spin non-polarized solutions than by spin-polarized wavefunctions. Consequently, both Hu and PPP Hamiltonians lead to electronic structures characterized by a gap at the Fermi level that diminishes as the size of the system increases. DFT results show similar trends although a detailed analysis of the density of states around the Fermi level shows quantitative differences with both Hu and PPP models. Before improving model Hamiltonians, we interpret the electronic structure obtained by DFT in terms of bands of topological states: topological states localized at the system edges and extended bulk topological states that interact between them due to the long-range Coulomb terms of Hamiltonian. After careful analysis of the interaction among topological states, we find that the discrepancy between ab initio and model Hamiltonians can be resolved considering a screened long-range interaction that is implemented by adding an exponential cutoff to the interaction term of the PPP model. In this way, an adjusted cutoff distance λ = 2 allows a good recovery of DFT results. In view of this, we conclude that the correct description of the density of states around the Fermi level (Dirac point) needs the inclusion of long-range interactions well beyond the Hubbard model but not completely unscreened as is the case for the PPP model. [ABSTRACT FROM AUTHOR]

This work proposes a protocol for Fermionic Hamiltonian learning. For the Hubbard model defined on a bounded-degree graph, the Heisenberg-limited scaling is achieved while allowing for state preparation and measurement errors. To achieve ϵ -accurate estimation for all parameters, only O ˜ (ϵ − 1) total evolution time is needed, and the constant factor is independent of the system size. Moreover, our method only involves simple one or two-site Fermionic manipulations, which is desirable for experiment implementation. [ABSTRACT FROM AUTHOR]

We investigate the quantum phases and phase transitions for spin–orbit coupled two-species bosons with nearest-neighbor (NN) interaction in a two-dimensional square lattice using inhomogeneous dynamical Guztwiller mean-field method. Under the effect of spin–orbit coupling and NN interaction, we uncover a rich variety of different magnetic supersolid (SS) phases. In the presence of intraspecies NN interaction, the phase diagram exhibits the phase-twisted double-checkerboard SS (PT-DCSS) and phase-striped double-checkerboard SS (PS-DCSS) phases. For both intra- and interspecies NN interactions, apart from the phase-twisted lattice SS (PT-LSS) and phase-striped lattice SS (PS-LSS) phases, some nontrivial SS phases with interesting properties occur. More importantly, we find that the emergences of these nontrivial SS phases are dependent of the interspecies on-site interaction. To further characterize the SS phases, we also discuss the spin-dependent momentum distributions and magnetic textures. The magnetic textures, such as antiferromagnetic, spiral and stripe orders are shown. Finally, we give the fully analytical insights into the numerical results. [ABSTRACT FROM AUTHOR]

We conduct a theoretical examination of the electronic and magnetic characteristics of end-modified 7-atom wide armchair graphene nanoribbons (AGNRs). Our investigation is performed within the framework of a single-band Hubbard model, beyond a mean-field approximation. First, we carry out a comprehensive comparison of various approaches for accommodating di-hydrogenation configurations at the AGNR ends. We demonstrate that the application of an on-site potential to the modified carbon atom, coupled with the addition of an electron, replicates phenomena such as the experimentally observed reduction of the bulk-states (BS) gap. These results for the density of states (DOS) and electronic densities align closely with those obtained through a method explicitly designed to account for the orbital properties of hydrogen atoms. Furthermore, our study enables a clear differentiation between magnetic moments already described in a mean-field (MF) approach, which are spatially confined to the same sites as the topological end-states (ES), and correlation-induced magnetic moments, which exhibit localization along all edges of the AGNRs. Notably, we show the robustness of these correlation-induced magnetic moments relative to end modifications, within the scope of the method we employ.

Experiments on the fermionic Hubbard model can now be made much larger, more uniform, and more quantitative. [ABSTRACT FROM AUTHOR]

We investigate the exact full configuration interaction quantum Monte Carlo algorithm (without the initiator approximation) applied to weak sign-problem fermionic systems, namely, systems in which the energy gap to the corresponding sign-free or "stoquastized" state is small. We show that the minimum number of walkers required to exactly overcome the sign problem can be significantly reduced via an importance-sampling similarity transformation even though the similarity-transformed Hamiltonian has the same stoquastic gap as the untransformed one. Furthermore, we show that in the off-half-filling Hubbard model at U/t = 8, the real-space (site) representation has a much weaker sign problem compared to the momentum space representation. By applying importance sampling using a Gutzwiller-like guiding wavefunction, we are able to substantially reduce the minimum number of walkers in the case of 2 × ℓ Hubbard ladders, enabling us to get exact energies for sizable ladders. With these results, we calculate the fundamental charge gap ΔEfund = E(N + 1) + E(N − 1) − 2E(N) for the ladder systems compared to strictly one-dimensional Hubbard chains and show that the ladder systems have a reduced fundamental gap compared to the 1D chains. [ABSTRACT FROM AUTHOR]

The asymmetric Hubbard dimer is a model that allows for explicit expressions of the Hartree–Fock (HF) and Kohn–Sham (KS) states as analytical functions of the external potential, Δv, and of the interaction strength, U. We use this unique circumstance to establish a rigorous comparison between the individual contributions to the correlation energies stemming from the two theories in the {U, Δv} parameter space. Within this analysis of the Hubbard dimer, we observe a change in the sign of the HF kinetic correlation energy, compare the indirect repulsion energies, and derive an expression for the "traditional" correlation energy, i.e., the one that corrects the HF estimate, in a pure site-occupation function theory spirit [Eq. (45)]. Next, we test the performances of the Liu–Burke and the Seidl–Perdew–Levy functionals, which model the correlation energy based on its weak- and strong-interaction limit expansions and can be used for both the traditional and the KS correlation energies. Our results show that, in the Hubbard dimer setting, they typically work better for the HF reference, despite having been originally devised for KS. These conclusions are somewhat in line with prior assessments of these functionals on various chemical datasets. However, the Hubbard dimer model allows us to show the extent of the error that may occur in using the strong-interaction ingredient for the KS reference in place of the one for the HF reference, as has been carried out in most of the prior assessments. [ABSTRACT FROM AUTHOR]

The bad metallic phase with resistivity above the Mott-Ioffe-Regel (MIR) limit, which appears also in cuprate superconductors, was recently understood by cold atom and computer simulations of the Hubbard model via charge susceptibility and charge diffusion constant. However, since reliable simulations can be typically done only at temperatures above the experimental temperatures, the question for cuprate superconductors is still open. This paper addresses this question by resorting to heat transport, which allows for the estimate of electronic diffusion and it further combines it with the resistivity to estimate the charge susceptibility. The doping and temperature dependencies of diffusion constant and charge susceptibilities are shown and discussed for two samples of YBa2Cu3O6+x. Results indicate strongly incoherent transport, mean free path corresponding to the MIR limit for the underdoped sample at temperatures above ~200 K and significant effect of the charge susceptibility on the resistivity. [ABSTRACT FROM AUTHOR]

The bad metallic phase with resistivity above the Mott-Ioffe-Regel (MIR) limit, which appears also in cuprate superconductors, was recently understood by cold atom and computer simulations of the Hubbard model via charge susceptibility and charge diffusion constant. However, since reliable simulations can be typically done only at temperatures above the experimental temperatures, the question for cuprate superconductors is still open. This paper addresses this question by resorting to heat transport, which allows for the estimate of electronic diffusion and it further combines it with the resistivity to estimate the charge susceptibility. The doping and temperature dependencies of diffusion constant and charge susceptibilities are shown and discussed for two samples of YBa2Cu3O6+x. Results indicate strongly incoherent transport, mean free path corresponding to the MIR limit for the underdoped sample at temperatures above ~200 K and significant effect of the charge susceptibility on the resistivity. [ABSTRACT FROM AUTHOR]

Recent studies have revealed the potential of 2D moiré superlattices as a condensed matter quantum simulator. The realization of different lattice model Hamiltonians in moiré superlattices has become the focus of researches. Here, it shows that, compared to bilayer moiré superlattices where there is only one interface, the interference between moiré patterns at different interfaces in 2D multilayer structures allows the physical realization of more complicated lattice models. The concept is demonstrated by trilayer moiré superlattices (TMSLs) of MoS2, where it finds that isolated flat moiré bands appear near the valence band edge, and they can be described by the honeycomb lattice ionic Hubbard model. More importantly, the hopping strength, the on‐site Coulomb repulsion, and the staggered potential in the TMSLs are highly tunable through the control of the twist angle, the dielectric environment, and the perpendicular electric field. It is possible to achieve various transitions between distinct quantum phases in the TMSLs, spanning from weak to strong correlation regimes. Therefore, the proposed TMSLs can serve as a good platform to study the strong correlation physics in the honeycomb lattice ionic Hubbard model. [ABSTRACT FROM AUTHOR]

The halide perovskite TiF3, renowned for its intricate interplay between structure, electronic correlations, magnetism, and thermal expansion, is investigated. Despite its simple structure, understanding its low‐temperature magnetic behavior has been a challenge. Previous theories propose antiferromagnetic ordering. In contrast, experimental signatures for an ordered magnetic state are absent down to 10 K. The current study has successfully reevaluated the theoretical modeling of TiF3, unveiling the significance of strong electronic correlations as the key driver for its insulating behavior and magnetic frustration. In addition, frequency‐dependent optical reflectivity measurements exhibit clear signs of an insulating state. The analysis of the calculated magnetic data gives an antiferromagnetic exchange coupling with a net Weiss temperature of order 25 K as well as a magnetic response consistent with a S = 1/2 local moment per Ti3+. Yet, the system shows no susceptibility peak at this temperature scale and appears free of long‐range antiferromagnetic order down to 1 K. Extending ab initio modeling of the material to larger unit cells shows a tendency for relaxing into a noncollinear magnetic ordering, with a shallow energy landscape between several magnetic ground states, promoting the status of this simple, nearly cubic perovskite structured material as a candidate spin liquid. [ABSTRACT FROM AUTHOR]

The first-order reversible phase transition in vanadium dioxide (VO2), popularly coined as metal-insulator transition (MIT), is a matter of significant interest since its genesis in the late 1950s. VO2 in its bulk form exhibits MIT at a transition temperature (Tt) of 340 K. Below Tt, VO2 crystallizes in the monoclinic insulting phase while above Tt, the crystal structure transforms into a more symmetrical tetragonal-rutile phase which is conducting. Such a structural phase transformation (SPT) draws attention to several oxides of vanadium. Vanadate has been a subject of specific correlated compounds where numerous attempts have been made to develop a single theory that can fully define the peculiar nature of phase transition. Two major models namely Peierls and Mott have been proposed to understand the phase transitions. The structural modification in VO2 is responsible for several applications such as thermochromism, Mott-based transistors, bimorph actuators, hydrogen storage capability, microbolometers, and so on. Ferromagnetism (FM) in the doped VO2 films would enhance the data storage capacity. This review focuses on the systematic advancement in the thin films and nanostructures of VO2 over the past decades and the comprehensive understanding between MIT and SPT for advanced applications. A brief account is also given on various methods of synthesis of these oxides. [ABSTRACT FROM AUTHOR]

The halide perovskite TiF3, renowned for its intricate interplay between structure, electronic correlations, magnetism, and thermal expansion, is investigated. Despite its simple structure, understanding its low‐temperature magnetic behavior has been a challenge. Previous theories propose antiferromagnetic ordering. In contrast, experimental signatures for an ordered magnetic state are absent down to 10 K. The current study has successfully reevaluated the theoretical modeling of TiF3, unveiling the significance of strong electronic correlations as the key driver for its insulating behavior and magnetic frustration. In addition, frequency‐dependent optical reflectivity measurements exhibit clear signs of an insulating state. The analysis of the calculated magnetic data gives an antiferromagnetic exchange coupling with a net Weiss temperature of order 25 K as well as a magnetic response consistent with a S = 1/2 local moment per Ti3+. Yet, the system shows no susceptibility peak at this temperature scale and appears free of long‐range antiferromagnetic order down to 1 K. Extending ab initio modeling of the material to larger unit cells shows a tendency for relaxing into a noncollinear magnetic ordering, with a shallow energy landscape between several magnetic ground states, promoting the status of this simple, nearly cubic perovskite structured material as a candidate spin liquid. [ABSTRACT FROM AUTHOR]

Entanglement in many‐body systems may display quantum phase transition signatures, and analogous insights are emerging in the study of work fluctuations. Here, the fermionic superfluid‐to‐insulator transition (SIT) is considered and related to its entanglement properties and its work distribution statistics. Using the attractive fermionic Hubbard model with randomly distributed impurities, the work distribution is analyzed under two quench protocols triggering the SIT. In the first, the concentration of impurities is increased; in the second, the impurities' disorder strength is varied. The results indicate that, at criticality, the entanglement is minimized while the average work is maximized. This study demonstrates that, for this state, density fluctuations vanish at all orders, resulting in all central moments of the work probability distribution being precisely zero. For systems undergoing a precursor to the transition (short chains with finite impurity potential) numerical results confirm these predictions, with higher moments further from the ideal results. For both protocols, at criticality, the system absorbs the most energy with almost no penalty in terms of fluctuations: ultimately this feature can be used to implement a quantum critical battery. The impact of temperature on this critical behaviour is also investigated and shown to favor work extraction for high enough temperatures. [ABSTRACT FROM AUTHOR]

The first-order reversible phase transition in vanadium dioxide (VO2), popularly coined as metal-insulator transition (MIT), is a matter of significant interest since its genesis in the late 1950s. VO2 in its bulk form exhibits MIT at a transition temperature (Tt) of 340 K. Below Tt, VO2 crystallizes in the monoclinic insulting phase while above Tt, the crystal structure transforms into a more symmetrical tetragonal-rutile phase which is conducting. Such a structural phase transformation (SPT) draws attention to several oxides of vanadium. Vanadate has been a subject of specific correlated compounds where numerous attempts have been made to develop a single theory that can fully define the peculiar nature of phase transition. Two major models namely Peierls and Mott have been proposed to understand the phase transitions. The structural modification in VO2 is responsible for several applications such as thermochromism, Mott-based transistors, bimorph actuators, hydrogen storage capability, microbolometers, and so on. Ferromagnetism (FM) in the doped VO2 films would enhance the data storage capacity. This review focuses on the systematic advancement in the thin films and nanostructures of VO2 over the past decades and the comprehensive understanding between MIT and SPT for advanced applications. A brief account is also given on various methods of synthesis of these oxides. [ABSTRACT FROM AUTHOR]

Electronic properties of spin polarized antiferromagnetic ACrO3 (A = La, Y) are explored with Hubbard model using density functional theory (DFT). These two isostructural systems are investigated using the different Hubbard energy and analyzed the hybridization of chromium 3d orbitals and oxygen 2p orbitals and the change in energy bandgaps against the Hubbard energy. The bond length and bond angle affect significantly the orbital contributions of Cr-3d and O-2p electrons for both the system. We noticed that the Cr–O hybridization affects the orbital degeneracy and is substantiated with partial density of states. These results emphasize the contribution of Hubbard energy in correlated electron systems. [ABSTRACT FROM AUTHOR]