We present the exact solution of the one-dimensional extended Hubbard model in the atomic limit within the Green's function and equation of motion formalism. We provide a comprehensive and systematic analysis of the model by considering all the relevant response and correlation functions as well as thermodynamic quantities in the whole parameter space. At zero temperature we identify four phases in the plane (U,n) [U is the onsite potential and n is the filling] and relative phase transitions as well as different types of charge ordering. These features are endorsed by investigating at T=0 the chemical potential and pertinent local correlators, the particle and double occupancy correlation functions, the entropy, and by studying the behavior in the limit T going to zero of the charge and spin susceptibilities. A detailed study of the thermodynamic quantities is also presented at finite temperature. This study evidences that a finite-range order persists for a wide range of the temperature, as shown by the behavior of the correlation functions and by the two-peak structure exhibited by the charge susceptibility and by the entropy. Moreover, the equation of motion formalism, together with the use of composite operators, allows us to exactly determine the set of elementary excitations. As a result, the density of states can be determined exactly and a detailed analysis of the specific heat allows for identifying the excitations and for ascribing its two-peak structure to a redistribution of the charge density.
We study the phase diagram at finite temperature of a system of Fermi particles on the sites of the Bethe lattice with coordination number z and interacting through onsite U and nearest-neighbor V interactions. This is a physical realization of the extended Hubbard model in the atomic limit. By using the equations of motion method, we exactly solve the model. For an attractive intersite potential, we find, at half filling, a phase transition towards a broken particle-hole symmetry state. The critical temperature, as a function of the relevant parameters, has a re-entrant behavior as already ob…
Integrable open-boundary condition for the q-deformed Essler-Korepin-Schoutens extended Hubbard model of strongly correlated electrons, are studied in the framework of the boundary quantum inverse scattering method. Diagonal boundary K-matrices are found, and nine classes of integrable boundary terms are determined.
Integrable extended Hubbard models arising from symmetric group solutions are examined in the framework of the graded Quantum Inverse Scattering Method. The Bethe ansatz equations for all these models are derived by using the algebraic Bethe ansatz method.
The phase diagram of the one-dimensional extended Hubbard model at half-filling is investigated by a weak coupling renormalization group method applicable beyond the usual continuum limit for the electron spectrum and coupling constants. We analyze the influence of irrelevant momentum dependent interactions on asymptotic properties of the correlation functions and the nature of dominant phases for the lattice model under study.
Three kinds of integrable Kondo problems in one-dimensional extended Hubbard models are studied by means of the boundary graded quantum inverse scattering method. The boundary K matrices depending on the local moments of the impurities are presented as a nontrivial realization of the graded reflection equation algebras acting in a $(2 s_α+1)$-dimensional impurity Hilbert space. Further, these models are solved using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained.
Using a straightforward extension of the analysis of Lieb and Wu, we derive a simple analytic form for the ground state energy of a one-dimensional Hubbard ring in the atomic limit. This result is valid for an \textit{arbitrary} number of lattice sites $L$ and electrons $N \leq L$. Furthermore, our analysis, including an application of the theory of stochastic matrices, provides insight into the degeneracy and spin properties of the ground states in the atomic limit. We give numerical results which illustrate how the atomic limit is approached.
We review the recent theoretical developments towards understanding the Mott phases and quantum phase transition of extended Bose-Hubbard models on lattices in two spatial dimensions . We focuss on the description of these systems using the dual vortex picture and point out the crucial role played by the geometry of underlying lattices in determining the nature of both the Mott phases and the quantum phase transitions. We also briefly compare the results of dual vortex theory with quantum Monte Carlo results.
We study the one-dimensional quarter-filled extended Hubbard model with an alternating transfer integral. In the strong-dimerization limit the charge part is described by the quantum Ising model which shows the two-dimensional Ising criticality at the self-dual point, and it is naturally connected to the double-frequency sine-Gordon theory in the weak dimerization. Treating low-lying excitations in finite-size systems, we numerically determine a phase boundary between two types of $4k_{\rm F}$ density-wave states and clarify the ground-state phase diagram. Further, we refer to its relevances t…
We consider strongly-correlated systems described by the multi-orbital Hubbard model in the atomic limit and obtain exact expressions for the chemical potential and thermopower. We show that these expressions reduce to the Heikes formula in the appropriate limits ($k_BT \gg U$) and ($k_BT \ll U$) and obtain the full temperature dependence in between these regimes. We also investigate the effect of a magnetic field introduced through a Zeeman term and observe that the thermopower of the multi-orbital Hubbard model displays spikes as a function of magnetic field at certain special values of the …
We study the two-orbital Hubbard model in the limit of vanishing kinetic energy. The phase diagram in the $V-J$ plane, with $V$ and $J$ denoting the interorbital hybridization and exchange coupling respectively, at half filling is obtained. A singlet(dimer)-triplet transition is found for a critical value of the ratio $V/J.$ The entropy of formation, both in the mode and in the particle picture, presents a jump as the same critical line in conformity with the suggested relation between criticality and entanglement.
We study the geometrical frustration of extended Hubbard model on diamond chain, where vertical lines correspond to the hopping and repulsive Coulomb interaction terms between sites, while the rest of them represent only the Coulomb repulsion one. The phase diagrams at zero temperature show quite curious phases: five types of frustrated states and four types of non-frustrated ones, ordered antiferromagnetically. Although decoration transformation was derived to spin coupling systems, this approach can be applied to electron coupling ones. Thus the extended Hubbard model can be mapped onto anot…
Zhang recently conjectured an approximate SO(5) symmetry relating antiferromagnetic and superconducting states in high-T_c cuprates. Here, an exact SO(5) symmetry is implemented in a generalized Hubbard model (with long-range interactions) on a lattice. The possible relation to a more realistic extended Hubbard Hamiltonian is discussed.
We apply the recently proposed susy Hubbard operators to an atomic model. In the limiting case of free spins, we derive exact results for the entropy which are compared with a mean field + gaussian corrections description. We show how these results can be extended to the case of charge fluctuations and calculate exact results for the partition function, free energy and heat capacity of an atomic model for some simple examples. Wavefunctions of possible states are listed. We compare the accuracy of large N expansions of the susy spin operators with those obtained using `Schwinger bosons' and `A…
We transform the quartic Hubbard terms in the extended Hubbard model to a quadratic form by making the Hubbard-Stratonovich transformation for the electron operators. This transformation allows us to derive exact results for mass operator and charge-charge and spin-spin correlation functions for s-wave superconductivity. We discuss the application of the method to the d-wave superconductivity.
We investigated the fidelity susceptibility in the one-dimension (1D) Hubbard model and the extended Hubbard model at half-filling via the density matrix renormalization group. From the numerical results, we argue that in the 1D Hubbard model, the fidelity susceptibility shows a divergence at two points which is infinitesimally close to the critical point while it is always extensive exactly at the critical point. For the extended Hubbard model, we found that for a properly chosen driving parameter, the fidelity susceptibility is able to reveal the quantum phase transitions between the PS (pha…
We refer to our recent calculations (Eur. Phys. J. B, \textbf{86}, 252 (2013)) of metallization pressure of the three-dimensional simple-cubic crystal of atomic hydrogen and study the effect on the crucial results concocting from approximating the $1s$ Slater-type orbital function with a series of $p$ Gaussians. As a result, we find the critical metallization pressure $p_C = 102\ GPa$. The latter part is a discussion of the influence of zero-point motion on the stabilizing pressure. We show that in our model the estimate magnitude of zero-point motion carries a little effect on the critical me…
We demonstrate that supervised machine learning (ML) with entanglement spectrum can give useful information for constructing phase diagram in the half-filled one-dimensional extended Hubbard model. Combining ML with infinite-size density-matrix renormalization group, we confirm that bond-order-wave phase remains stable in the thermodynamic limit.
We consider the one-dimensional extended Hubbard model in the presence of an explicit dimerization $δ$. For a sufficiently strong nearest neighbour repulsion we establish the existence of a quantum phase transition between a mixed bond-order wave and charge-density wave phase from a pure bond-order wave phase. This phase transition is in the universality class of the two-dimensional Ising model.
In PRB 68, 153101 (2003), Guoping Zhang presented density-matrix renormalization group (DMRG) results which contradict my DMRG calculations and Hirsch's quantum Monte Carlo (QMC) simulations for the charge-density-wave (CDW) phase boundary in the one-dimensional extended Hubbard model at half filling. In this Comment I show that Zhang's results are inaccurate and that his criticism of my work is groundless.
We extend previous real-space Hartree-Fock studies of static stripe stability to determine the phase diagram of the Hubbard model with anisotropic nearest-neighbor hopping t, by varying the on-site Coulomb repulsion U and investigating locally stable structures for representative hole doping levels x=1/8 and x=1/6. We also report the changes in stability of these stripes in the extended Hubbard model due to next-neighbor hopping t' and to a nearest-neighbor Coulomb interaction V.
We study the extended Jaynes-Cummings-Hubbard model on triangular cavity lattices and zigzag ladders. By using density-matrix renormalization group methods, we observe various types of solids with different density patterns and find evidence for light supersolids, which exist in extended regions of the phase diagram of the zigzag ladder. Furthermore, we observe strong pair correlations in the supersolid phase due to the interplay between the atoms in the cavities and atom-photon interaction. By means of cluster mean-field simulations and a scaling of the cluster size extending our analysis to …
In contrast to the Hubbard model, the extended Hubbard model, which additionally accounts for non-local interactions, lacks systemic studies of thermodynamic properties especially across the metal-insulator transition. Using a variational principle, we perform such a systematic study and describe how non-local interactions screen local correlations differently in the Fermi-liquid and in the insulator. The thermodynamics reveal that non-local interactions are at least in parts responsible for first-order metal-insulator transitions in real materials.
We consider the most general form of extended Hubbard Hamiltonian conserving the total spin and number of electrons, and find all the 1-dimensional completely integrable models which can be derived from first degree polynomial solution of the Yang-Baxter equation. It is shown that such models are 96. They are identified with the 16-dimensional representation of a new class of solutions of symmetric group relations, acting as generalized permutators. As particular examples, the EKS and some other known models are obtained.
The extended Hubbard model in the atomic limit (AL-EHM) on a square lattice with periodic boundary conditions is studied with use of the Monte Carlo (MC) method. Within the grand canonical ensemble the phase and order-order boundaries for charge orderings are obtained. The phase diagrams include three types of charge ordered phases and the nonordered phase. The system exhibits very rich structure and shows unusual multicritical behavior. In the limiting case of tij = 0, the EHM is equivalent to the pseudospin model with single-ion anisotropy 1/2U, exchange interaction W in an effective magneti…
We study with exact diagonalization the zero temperature properties of the quarter-filled extended Hubbard model on a square lattice. We find that increasing the ratio of the intersite Coulomb repulsion, $V$, to the band width drives the system from a metal to a charge ordered insulator. The evolution of the optical conductivity spectrum with increasing $V$ is compared to the observed optical conductivity of several layered molecular crystals with the theta and beta'' crystal structures.
The theory of correlated electron systems is formulated in a form which allows to use as a reference point an ab initio band structure theory (AIBST). The theory is constructed in two steps. As a first step the total Hamiltonian is transformed into a correlated form. In order to elucidate the microscopical origin of the parameters of the periodical Hubbard-Anderson model (PHAM) the terms of the full Hamiltonian which have the operator structure of PHAM are separated. It is found that the matrix element of mixing interaction includes ion-configuration and number-of-particles dependent contribut…
We show that the charge transfer excitons in a Hubbard model system including nearest neighbor Coulomb interactions effectively attain some charge in doped systems and become visible in photoelectron and inverse photoelectron spectroscopies. This shows that the description of a doped system by an extended Hubbard model differs substantially from that of a simple Hubbard model. Longer range Coulomb interactions cause satellites in the one electron removal and addition spectra and the appearance of spectral weight if the gap of doped systems at energies corresponding to the excitons of the undop…
Without any knowledge of the symmetry existing in the system, we derive the exact forms of the order parameters which show long-range correlation in the ground state of the one-dimensional extended Hubbard model using a quantum information approach. Our work demonstrates that the quantum information approach can help us to find the explicit form of the order parameter, which cannot be derived systematically via traditional methods in the condensed matter theory.
We study the lattice dynamics of antiferromagnetic transition-metal oxides by using self-consistent Hubbard functionals. We calculate the ground states of the oxides with the on-site and intersite Hubbard interactions determined self-consistently within the framework of density functional theory. The on-site and intersite Hubbard terms fix the errors associated with the electron self-interaction in the local and semilocal functionals. Inclusion of the intersite Hubbard terms in addition to the on-site Hubbard terms produces accurate phonon dispersion of the transition-metal oxides. Calculated …
We investigate Knight shift and nuclear spin relaxation rate in a charge ordered state of the one-dimensional extended Hubbard model with a quarter filled band by using RPA around the mean-field solution. It is shown that both quantities show splitting below the critical temperature of the charge order, as is experimentally observed. The relationship between the mount of the splitting in the both quantities and the charge disproportionation rate is discussed.
We propose an effective model called the "charge model", for the half-filled one-dimensional Hubbard and extended Hubbard models. In this model, spin-charge separation, which has been justified from an infinite on-site repulsion ($U$) in the strict sense, is compatible with charge fluctuations. Our analyses based on the many-body Wannier functions succeeded in determining the optical conductivity spectra in large systems. The obtained spectra reproduce the spectra for the original models well even in the intermediate $U$ region of $U=5-10T$, with $T$ being the nearest-neighbor electron hopping…
We show numerically that the nature of the doping induced metal-insulator transition in the two-dimensional Hubbard model is radically altered by the inclusion of a term, $W$, which depends upon a square of a single-particle nearest-neighbor hopping. This result is reached by computing the localization length, $ξ_l$, in the insulating state. At finite values of $W$ we find results consistent with $ξ_l \sim | μ- μ_c|^{- 1/2} $ where $μ_c$ is the critical chemical potential. In contrast, $ξ_l \sim | μ- μ_c|^{-1/4}$ for the Hubbard model. At finite values of $W$, the presented numerical results i…
We numerically and analytically calculate the properties of the bipolaron in an extended Hubbard Holstein model, which has a longer range electron-phonon coupling like the Fr\" ohlich model. In the strong coupling regime, the effective mass of the bipolaron in the extended model is much smaller than the Holstein bipolaron mass. In contrast to the Holstein bipolaron, the bipolaron in the extended model has a lower binding energy and remains bound with substantial binding energy even in the large-U limit. In comparison with the Holstein model where only a singlet bipolaron is bound, in the exten…
We use a density matrix renormalization group method to study quantitatively the phase diagram of a one-dimensional extended Hubbard model at half-filling by investigating the correlation functions and structure factors. We confirm the existence of a novel narrow region with long-rang bond-order-wave order which is highly controversial recently between the charge-density-wave phase and Mott insulator phase. We determined accurately the position of the tricritical point $U_t\simeq 7.2t$, $V_t\simeq 3.746t$ which is quite different from previous studies.
The Hubbard on-site repulsion $U$ between opposite spin electrons on the same atomic orbital is widely regarded to be the most important source of electronic correlation in solids. Here we extend the Hubbard model to account for the fact that the experimentally measured atomic $U$ is different from the one obtained by calculation of the atomic Coulomb integral. The resulting model describes quasiparticles that become increasingly dressed as the number of electrons in the band increases. Superconductivity can result in this model through quasiparticle undressing. Various signatures of this phys…
The aim of this work is to generalize the method of Hubbard fields in fermion Quantum Monte Carlo simulation to the case of link fields. The introduced Hubbard link fields play a role of the interaction fields responsible for the attraction and repulsion of electronic excitations at the nodes. Such improvements leads to a number of advantages concerning thermalization time, autocorrelations, metastable states and probability distributions of the quantities. It is demonstrated that computations using five fields are more stable and reliable in case of energy observables.
Magnetic properties in a charge ordered state are examined for the extended Hubbard model at half-filling. Magnetic excitations, magnetic susceptibilities and a nuclear spin relaxation rate are calculated with taking account of fluctuations around the mean-field solution. The relevance of the present results to the observation in the 1:1 organic conductors, (TTM-TTP)I$_3$, is discussed.
We investigate the dynamical spin and charge structure factors and the one-particle spectral function of the one-dimensional extended Hubbard model at half band-filling using the dynamical density-matrix renormalization group method. The influence of the model parameters on these frequency- and momentum-resolved dynamical correlation functions is discussed in detail for the Mott-insulating regime. We find quantitative agreement between our numerical results and experiments for the optical conductivity, resonant inelastic X-ray scattering, neutron scattering, and angle-resolved photoemission sp…
We present a microscopic theory of fluctuation-mediated pairing mechanism in a two-dimensional extended Hubbard model. In contrast to conventional wisdom, odd-frequency spin-triplet pairing can be stabilized near the spin-density-wave critical point. Favorable conditions for the odd-frequency pairing are the presence of geometrical frustration and off-site Coulomb interaction.
The one-dimensional extended Peierls-Hubbard model is studied at several band fillings using the density matrix renormalization group method. Results show that the ground state evolves from a Mott-Peierls insulator with a correlation gap at half-filling to a soliton lattice with a small band gap away from half-filling. It is also confirmed that the ground state of the Peierls-Hubbard model undergoes a transition to a metallic state at finite doping. These results show that electronic correlations effects should be taken into account in theoretical studies of doped polyacetylene. They also show…
The half-filled extended Hubbard model, in one and two dimensions, is studied by means of the 2-pole approximation within the Composite Operator Method with the aim at improving the possibilities to describe some of the experimental features observed for quasi-1D organic superconductors and Cu-O planes of cuprates. The phase diagrams ($T$-$V$ and $V$-$U$) are analyzed with respect to the paramagnetic metal - paramagnetic insulator - charge ordered phase transitions. The relevant features of the diagrams (rank of the phase transitions, critical points, reentrant behavior) are discussed in detai…
The Hubbard model is used to study an electronic system. In this paper we present the new path integral representation for Hubbard model. We have constructed the new supercoherent state which appears from a set of eigenfunctions of atomic limit of strongly correlated systems. Exact calculation of nonlinear representation of a supergroup has been carried. This group defines the transformation of atomic base. The general formalism we elaborate for Hubbard model is the one widely used in the gauge field theory of the nonlinear representation of a superconformal group.
We investigate the competition between charge-density-wave (CDW) states and a Coulomb interaction-driven topological Mott insulator (TMI) in the honeycomb extended Hubbard model. For the spinful model with on-site ($U$) and next-nearest-neighbor ($V_2$) Coulomb interactions at half filling, we find two peculiar six-sublattice charge-density-wave insulating states by using variational Monte Carlo simulations as well as the Hartree-Fock approximation. We observe that conventional ordered states always win with respect to the TMI. The ground state is given in the large-$V_2$ region by a CDW chara…
The extended Bose-Hubbard model in a quadratic trap potential is studied using a finite-size density-matrix renormalization group method (DMRG). We compute the boson density profiles, the local compressibility and the hopping correlation functions. We observed the phase separation induced by the trap in all the quantities studied and conclude that the local density approximation is valid in the extended Bose-Hubbard model. From the plateaus obtained in the local compressibility it was possible to obtain the phase diagram of the homogeneous system which is in agreement with previous results.
BCS theory accounts for the pairing instability in the weak coupling limit, but fails to describe pairing fluctuations above $T_c$. One possibility for describing these fluctuations in the dilute limit is the T-matrix approximation. We critically examine various degrees of self-consistency in the T-matrix formalism, along with a non-diagrammatic two-particle self-consistent (TPSC) formulation, in the strong coupling regime, where an exact solution is readily available. We find that one particular degree of self-consistency is quite accurate, particularly at low temperature as evidenced by exam…
We study the effects of intersite RKKY-like interactions in the mixed valence regime of a two-band extended Hubbard model. This model is known to display a metallic non-Fermi liquid state with spin-charge separation in the standard $D=\infty$ limit (where interactions lead to purely on-site fluctuations only). Using an extended $D=\infty$ approach, we find that the spin-charge separation survives the quantum fluctuations associated with arbitrary intersite density-density interactions and a finite range of intersite spin-exchange interactions. We determine the qualitative behavior of the spin,…
An extended Hubbard model (including nearest-neighbor repulsion and antiferromagnetic spin exchange) is investigated on the frustrated checkerboard lattice, a two-dimensional analog of the pyrochlore lattice. Combining Gutzwiller renormalized mean-field (MF) calculations, exact diagonalization (ED) techniques, and a weak-coupling renormalization group (RG) analysis we provide strong evidence for a crystalline valence bond plaquette phase at quarter-filling. The ground state is twofold degenerate and breaks translation symmetry. The bond energies show a staggering while the charge distribution …
The papaer shows how the known, exact results for the two electron bound states can modify the ground state phase diagram of extended Hubbard model (EHM) for on-site attraction, intersite repulsion and arbitrary electron density. The main result is suppression of the superconducting state in favor of normal phase for small charge densities.
Using finite-temperature determinantal quantum Monte Carlo simulations, we examine the thermodynamic properties of the extended Hubbard model on the half-filled square lattice in the Slater regime at intermediate coupling. We consider both the case of nearest-neighbor interactions and long-range Coulomb interactions, for coupling strengths in which the presence of non-local interactions still allows us to perform sign-problem free quantum Monte Carlo simulations. In particular, we assess a recently proposed scenario from variational calculations in terms of a first-order metal-insulator transi…
We study the ground state of the one-dimensional extended Hubbard model at half-filling using the entanglement entropy calculated by Density Matrix Renormalization Group (DMRG) techniques. We apply a novel curve fitting and scaling method to accurately identify a $2^{nd}$ order critical point as well as a Berezinskii-Kosterlitz-Thouless (BKT) critical point. Using open boundary conditions and medium-sized lattices with very small truncation errors, we are able to achieve similar accuracy to previous authors. We also report observations of finite-size and boundary effects that can be remedied w…
We extend our previous approach (Eur. Phys. J. B, \textbf{74}, 63(2010)) to modeling correlated electronic states and the metal-insulator transition by applying the so-called \emph{statistically consistent Gutzwiller approximation} (SGA) to carry out self-consistent calculations of the renormalized single-particle Wannier functions in the correlated state. The transition to the Mott-Hubbard insulating state at temperature T=0 is of weak first order even if antiferromagnetism is disregarded. The magnitude of the introduced self-consistent magnetic correlation field is calculated and shown to le…
We demonstrate a robust frustration-driven charge-order to superconductivity transition in the half-filled negative-U extended Hubbard model. Superconductivity extends over a broad region of the parameter space. We argue that the model provides the correct insight to understanding unconventional superconductivity in the organic charge-transfer solids and other quarter-filled systems.
We perform a detailed study of the phase transitions and mechanisms of electron localization in the extended Hubbard model using the dynamical cluster approximation on a $2\times 2$ cluster. We explore the interplay of charge order and Mott physics. We find that a nearest-neighbor Coulomb interaction $V$ causes "screening" effects close to the Mott phase transition, pushing the phase boundary to larger values of $U$. We also demonstrate the different effects of $V$ on correlations in metallic and insulating regimes and document the different correlation aspects of charge order and Mott states.
We present a comprehensive numerical study on the ground state phase diagram of the two-dimensional hardcore boson extended Hubbard model with nearest ($V_1$) and next nearest neighbor ($V_2$) repulsions. In addition to the quantum solid and superfluid phases, we report the existence of striped supersolid and three-quarter (quarter) filled supersolid at commensurate density $ρ=0.75$ (0.25) due to the interplay of $V_1$ and $V_2$ interactions. The nature of three-quarter filled supersolid and the associated quantum solid will be discussed. Quantum phase transition between the two supersolids of…
Using quantum Monte Carlo simulations, results of a strong-coupling expansion, and Luttinger liquid theory, we determine quantitatively the ground state phase diagram of the one-dimensional extended Hubbard model with on-site and nearest-neighbor repulsions U and V. We show that spin frustration stabilizes a bond-ordered (dimerized) state for U appr. V/2 up to U/t appr. 9, where t is the nearest-neighbor hopping. The transition from the dimerized state to the staggered charge-density-wave state for large V/U is continuous for U up to appr. 5.5 and first-order for higher U.
We study charge ordering in the extended Hubbard model with both on-site and nearest neighbor Coulomb repulsion (U and V, respectively) within the Coherent potential approximation (CPA). The phase boundary between the homogeneous and charge ordered phase for the square lattice is obtained for different values of U. It is shown that at quarter filling for all values of U the charge ordering exists only if the inter-site Coulomb repulsion V exceeds certain critical value which is of the order of the kinetic energy t. At finite temperature a reentrant transition is found in some region of V.
