We show that backflow correlations in the variational wave function for the Hubbard model greatly improve the previous results given by the Slater-Jastrow state, usually considered in this context. We provide evidence that, within this approach, it is possible to have a satisfactory connection with the strong-coupling regime. Moreover, we show that, for the Hubbard model on the lattice, backflow correlations are essentially short range, inducing an effective attraction between empty (holons) and doubly occupied sites (doublons). In presence of frustration, we report the evidence that the metal to Mott-insulator transition is marked by a discontinuity of the double occupancy, together with a similar discontinuity of the kinetic term that does not change the number of holons and doublons, while the other kinetic terms are continuous across the transition. Finally, we show the estimation of the charge gap, obtained by particle-hole excitations {\it à la Feynman} over the ground-state wave function.
We introduce an efficient way to improve the accuracy of projected wave functions, widely used to study the two-dimensional Hubbard model. Taking the clue from the backflow contribution, whose relevance has been emphasized for various interacting systems on the continuum, we consider many-body correlations to construct a suitable approximation for the ground state at intermediate and strong couplings. In particular, we study the phase diagram of the frustrated $t{-}t^\prime$ Hubbard model on the square lattice and show that, thanks to backflow correlations, an insulating and non-magnetic phase…
We investigate the nature of the interaction-driven Mott-Hubbard transition of the half-filled $t_1{-}t_2$ Hubbard model in one dimension, using a full-fledged variational Monte Carlo approach including a distance-dependent Jastrow factor and backflow correlations. We present data for the evolution of the magnetic properties across the Mott-Hubbard transition and on the commensurate to incommensurate transition in the insulating state. Analyzing renormalized excitation spectra, we find that the Fermi surface renormalizes to perfect nesting right at the Mott-Hubbard transition in the insulating…
We study the Hubbard-Holstein model, which includes both the electron-electron and electron-phonon interactions characterized by $U$ and $g$, respectively, employing the dynamical mean-field theory combined with Wilson's numerical renormalization group technique. A zero temperature phase diagram of metal-insulator and insulator-insulator transitions at half-filling is mapped out which exhibits the interplay between $U$ and $g$. As $U$ ($g$) is increased, a metal to Mott-Hubbard insulator (bipolaron insulator) transition occurs, and the two insulating states are distinct and can not be adiabati…
I investigate band and Mott insulating states in a two-band Hubbard model, with the aim of understanding the differences between the idealised one-orbital model and the more realistic multi-band case. Using a projection ansatz I show that additional orbitals suppress the metal-insulator transition, leading to a critical coupling of approximately eight times the bare band-width. I also demonstrate the effects of orbital ordering, which hinder Mott-Hubbard states and open a band gap. Since multi-band correlations are common in real materials, this work suggests that the existence of very strongl…
We obtain exact numerical solutions of the degenerate Hubbard model in the limit of large dimensions (or large lattice connectivity). Successive Mott-Hubbard metal insulator transitions at integer fillings occur at intermediate values of the interaction and low enough temperature in the paramagnetic phase. The results are relevant for transition metal oxides with partially filled narrow degenerate bands.
The zero temperature transition from a paramagnetic metal to a paramagnetic insulator is investigated in the Dynamical Mean Field Theory for the Hubbard model. The self-energy of the effective impurity Anderson model (on which the Hubbard model is mapped) is calculated using Wilson's Numerical Renormalization Group method. Results for quasiparticle weight, spectral function and self-energy are discussed for Bethe and hypercubic lattice. In both cases, the metal-insulator transition is found to occur via the vanishing of a quasiparticle resonance which appears to be isolated from the Hubbard ba…
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 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 derived a simple metal-insulator criterion in analytical form for the doped Mott-Hubbard materials. Its readings closely related to the orbital and spin nature of the ground states of the unit cell. The available criterion readings (metal or insulator) in the paramagnetic phase points to the possibility of the insulator state of doped materials with the forbidden first removal electron states. According to its physical meaning the result is similar to Wilsons criterion in the itinerant electron systems. An application of the criterion to the high-Tc cuprates discussed.
By comparing the responses to an in-plane magnetic field near the metal-insulator transition (MIT), we find that the observed MIT in Si MOSFETs can be described by the non-perturbative Mott-Hubbard scenario. Interrelations between independent measurables are uncovered and confirmed by replotting the experimental data. A universal critical energy scale vanishing at the MIT is extracted from the experimental data and the critical exponent found.
We calculate the one-particle density of states for the Mott-Hubbard insulating phase of the Hubbard model on a Bethe lattice in the limit of infinite coordination number. We employ the Kato-Takahashi perturbation theory around the strong-coupling limit to derive the Green function. We show that the Green function for the lower Hubbard band can be expressed in terms of polynomials in the bare hole-hopping operator. We check our technique against the exact solution of the Falicov-Kimball model and give explicit results up to and including second order in the inverse Hubbard interaction. Our res…
We study the low energy behavior of the one dimensional Hubbard model across the Mott metal-insulator phase transition in an external magnetic field. In particular we calculate elements of the dressed charge matrix at the critical point of the Mott transition for arbitrary Hubbard repulsion and magnetization numerically and, in certain limiting cases, analytically. These results are combined with a non-perturbative effective field theory approach to reveal how the breaking of time reversal symmetry influences the Mott transition.
We investigate the neutral-to-ionic insulator-insulator transition in one-dimensional materials by treating a strong-coupling effective model based on the ionic Hubbard model using the density-matrix renormalization group and finite-size scaling. The effective model, formulated in a spin-one representation, contains a single parameter. We carry out an extensive finite-size scaling analysis of the relevant gaps and susceptibilities to characterize the two zero-temperature transitions. We find that the transition from the ionic band-insulating phase to an intermediate spontaneously dimerized pha…
Determining the nature of band gaps in transition-metal compounds remains challenging. We present a first-principles study on electronic and optical properties of CoO using hybrid functional pseudopotentials. We show that optical absorption spectrum can provide a clear fingerprint to distinguish between Mott-Hubbard, intermediate and charge-transfer insulators. This discrimination is reflected by the qualitative difference in peak satellites due to unique interplay between $d$-$d$ and $p$-$d$ excitations, thus allowing identification from experimental data alone, unlike the existing methods th…
We present a calculation of the recombination rate of the excited holon-doublon pairs based on the two-dimensional model relevant for undoped cuprates which shows that fast processes, observed in pump-probe experiments on Mott-Hubbard insulators in picosecond range, can be explained even quantitatively with the multi-magnon emission. The precondition is the existence of the Mott-Hubbard bound exciton of the s-type. We find that its decay is exponentially dependent on the Mott-Hubbard gap and on the magnon energy, with a small prefactor which can be traced back to strong correlations and conseq…
Employing extensive cellular dynamical mean-field theory (CDMFT) calculations with exact diagonalization impurity solver, we investigate the ground state phase diagrams and non-magnetic metal-insulator transitions of the half-filled Hubbard model on two plaquette -- the 1/5 depleted and checkerboard -- square lattices. We identify three different insulators in the phase diagrams: dimer insulator, antiferromagnetic insulator, and plaquette insulator. And we demonstrate that the plaquette insulator is a novel fragile Mott insulator (FMI) which features a nontrivial one-dimensional irreducible re…
The Mott-Hubbard metal-insulator transition is one of the most important problems in correlated electron systems. In the past decade, much progress has been made on examining a particle-hole symmetric form of the transition in the Hubbard model with dynamical mean field theory where it was found that the electronic self energy develops a pole at the transition. We examine the particle-hole asymmetric metal-insulator transition in the Falicov-Kimball model, and find that a number of features change when the noninteracting density of states has a finite bandwidth. Since, generically particle-hol…
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 electron spectrum structure in the half-filled Hubbard model is considered in terms of the one-particle Green's functions within many-electron representation. A simple analytical generalization of the single-site Hubbard-III approximation is obtained, which takes into account the Fermi excitations (Kondo terms). The problem of the metal-insulator transition is investigated. The occurrence of a three-peak density-of-states structure including the "Kondo" peak at the Fermi level is discussed. A comparison with large-d calculations is performed.
In the present paper metal-insulator transition is studied in a generalized Hubbard model with correlated hopping at half-filling and zero temperature. Single-particle Green function and energy spectrum of electron system are calculated. The expressions for energy gap width and the concentration of polar states (holes or doublons) are obtained. The conditions for metallic and insulating states are found.
We study the superfluid-insulator transition in Bose-Hubbard models in one-, two-, and three-dimensional cubic lattices by means of a recently proposed variational wave function. In one dimension, the variational results agree with the expected Berezinskii-Kosterlitz-Thouless scenario of the interaction-driven Mott transition. In two and three dimensions, we find evidences that, across the transition,most of the spectral weight is concentrated at high energies, suggestive of pre-formed Mott-Hubbard side-bands. This result is compatible with the experimental data by Stoferle et al. [Phys. Rev. …
We study the effect of disorder and doping on the metal-insulator transition in a repulsive Hubbard model on a square lattice using the determinant quantum Monte Carlo method. First, with the aim of making our results reliable, we compute the sign problem with various parameters such as temperature, disorder, on-site interactions, and lattice size. We show that in the presence of randomness in the hopping elements, the metal-insulator transition occurs and the critical disorder strength differs at different fillings. We also demonstrate that doping is a driving force behind the metal-insulator…
We study the optical response of a strongly correlated electron system near the metal-insulator transition using a mapping to the sine-Gordon model. With semiclassical quantization, the spectral weight is distributed between a Drude peak and absorption lines due to breathers. We calculate the Drude weight, the optical gap, and the lineshape of breather absorption.
The interaction-driven insulator-to-metal transition has been reported in the ionic Hubbard model (IHM) for moderate interaction $U$, while its metallic phase only occupies a narrow region in the phase diagram. To explore the enlargement of the metallic regime, we extend the ionic Hubbard model to two coupled layers and study the interplay of interlayer hybridization $V$ and two types of intralayer staggered potentials $Δ$: one with the same (in-phase) and the other with a $π$-phase shift (anti-phase) potential between layers. Our determinant Quantum Monte Carlo (DQMC) simulations at lowest ac…
We study the interplay of strong electron correlations and intra-triangle spin exchange at two-thirds filling of the single-orbital Hubbard model on the decorated honeycomb lattice using rotationally invariant slave bosons. We find that the spin exchange tunes between a spin-$1$ Mott insulator, a metal, and a spin-$0$ Mott insulator when the exchange is antiferromagnetic. The Mott insulators occur from effective intra-triangle multi-orbital interactions and are adiabatically connected to the ground state of an isolated triangle. An antiferromagnetic spin exchange, as determined by the Goodenou…
The Mott-Hubbard metal-insulator transition is investigated in a two-band Hubbard model within dynamical mean-field theory. To this end, we use a suitable extension of Wilson's numerical renormalization group for the solution of the effective two-band single-impurity Anderson model. This method is non-perturbative and, in particular, allows to take into account the full exchange part of the Hund's rule coupling between the two orbitals. We discuss in detail the influence of the various Coulomb interactions on thermodynamic and dynamic properties, for both the impurity and the lattice model. Th…
Metal-insulator transitions in the paramagnetic phase of the two dimensional square lattice Hubbard model are studied using the dynamical cluster approximation with eight momentum cells. We show that both the interaction-driven and the doping-driven transition are multi-stage and momentum-sector specific, with Fermi liquid metal and fully gapped insulator phases separated by an intermediate phase in which some regions of the Brillouin zone are gapped while others sustain gapless quasiparticles. We argue that this is the coarse-grained version of a gradually shrinking arc or pocket. A pronounce…
We investigate the local moment formation in the half-filled SU($N$) Hubbard model under a staggered ionic potential. As the Hubbard $U$ increases, the charge fluctuations are suppressed and eventually frozen when $U$ is above a critical value $U_c$, marking the development of well-defined local moment with integer $m$ fermions on the A-sublattice and $(N-m)$ fermions on the B-sublattice, respectively. We obtain an analytical solution for $U_c$ for the paramagnetic ground state within the variational Gutzwiller approximation and renormalized mean field theory. For large $N$, $U_c$ is found to …
Using the determinant quantum Monte Carlo method, we investigate the metal-insulator transition in the interacting disordered Hubbard model of a Lieb lattice, in which the system characterizes the flat band centered at the Fermi level. By choosing suitable electron densities, we ensure the weak interaction sign problem to improve the reliability of our results. It is found that disorder and on-site Coulomb repulsive interaction produce interesting effects that induce the metal-insulator transition which is impossible in the half-filled case. The density of states at the Fermi energy is still f…
We use determinant Quantum Monte Carlo simulations and exact diagonalization to explore insulating behavior in the Hubbard model with a bimodal distribution of randomly positioned local site energies. From the temperature dependence of the compressibility and conductivity, we show that gapped, incompressible Mott insulating phases exist away from half filling when the variance of the local site energies is sufficiently large. The compressible regions around this Mott phase are metallic only if the density of sites with the corresponding energy exceeds the percolation threshold, but are Anderso…
The iterative perturbation theory of the dynamical mean field theory is generalized to arbitrary electron occupation in case of multi-orbital Hubbard bands. We present numerical results of doubly degenerate Eg bands in a simple cubic lattice. The spectrum shows the electron ionization and affinity levels of different electron occupations. For sufficiently large Coulomb integral, a gap opens in the spectrum at integer filling of electrons and the system becomes insulator. The present scheme is easy to combine with the LSDA electronic structure theory.
We use an exact holon and spinon Landau-liquid functional which describes the holon - spinon interactions at all scattering orders, to study correlation functions of integrable multicomponent many-particle problems showing both linear and non-linear energy bands. We consider specific cases when the dominant non-linear band terms are quadratic and apply our results to the evaluation of the 1D Hubbard model correlation functions beyond conformal-field theory.
Obtaining an accurate ground state wave function is one of the great challenges in the quantum many-body problem. In this paper, we propose a new class of wave functions, neural network backflow (NNB). The backflow approach, pioneered originally by Feynman, adds correlation to a mean-field ground state by transforming the single-particle orbitals in a configuration-dependent way. NNB uses a feed-forward neural network to find the optimal transformation. NNB directly dresses a mean-field state, can be systematically improved and directly alters the sign structure of the wave-function. It genera…
The Mott-Hubbard metal-insulator transition in the paramagnetic phase of the one-band Hubbard model has long been used to describe similar features in real materials like V$_2$O$_3$. Here we show that this transition is hidden inside a rather robust antiferromagnetic insulator even in the presence of comparatively strong magnetic frustration. This result raises the question of the relevance of the Mott-Hubbard metal-insulator transition for the generic phase diagram of the one-band Hubbard model.
We solve the Periodic Anderson model in the Mott-Hubbard regime, using Dynamical Mean Field Theory. Upon electron doping of the Mott insulator, a metal-insulator transition occurs which is qualitatively similar to that of the single band Hubbard model, namely with a divergent effective mass and a first order character at finite temperatures. Surprisingly, upon hole doping, the metal-insulator transition is not first order and does not show a divergent mass. Thus, the transition scenario of the single band Hubbard model is not generic for the Periodic Anderson model, even in the Mott-Hubbard re…
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 calculate the Hubbard bands for the half-filled Hubbard model on a Bethe lattice with infinite coordination number up to and including third order in the inverse Hubbard interaction. We employ the Kato--Takahashi perturbation theory to solve the self-consistency equation of the Dynamical Mean-Field Theory analytically for the single-impurity Anderson model in multi-chain geometry. The weight of the secondary Hubbard sub-bands is of fourth order so that the two-chain geometry is sufficient for our study. Even close to the Mott--Hubbard transition, our results for the Mott--Hubbard gap agree …
The metal-insulator transition of the quarter-filled Hubbard model on triangular lattice is studied at the mean field level. We find a quasi-one dimensional metallic state with a collinear magnetic order competes closely with an insulating state with a non-coplanar magnetic order for both signs of the hopping integral $t$. In the strong correlation regime($U/|t|\gg1$), it is found that the metal-insulator transition of the system occurs in a two-step manner. The quasi-one dimensional metallic state with collinear magnetic order is found to be stable in an intermediate temperature region betwee…
The ground state of the Hubbard model is studied within the single-site approximation (SSA) and beyond the SSA. Within the SSA, the ground state is a typical Mott insulator at the critical point n=1 and U/W=+infty, with n being the electron density per unit cell, W the bandwidth of electrons, and U the on-site repulsion, and is a normal Fermi liquid except for the critical point. Beyond the SSA, the normal Fermi liquid is unstable against a non-normal Fermi liquid state except for a trivial case of U=0 such as a magnetic or superconducting state in two and higher dimensions. In order to explai…
The nature of the Mott-Hubbard metal-insulator transition in the infinite-dimensional Hubbard model is investigated by Quantum Monte Carlo simulations down to temperature T=W/140 (W=bandwidth). Calculating with significantly higher precision than in previous work, we show that the hysteresis below T_{IPT}\simeq 0.022W, reported in earlier studies, disappears. Hence the transition is found to be continuous rather than discontinuous down to at least T=0.325T_{IPT}. We also study the changes in the density of states across the transition, which illustrate that the Fermi liquid breaks down before …
We have made an angle-resolved photoemission study of a one-dimensional (1D) Mott-Hubbard insulator Na_{0.96}V_{2}O_{5} and found that the spectra of the V 3d lower Hubbard band are strongly dependent on the temperature. We have calculated the one-particle spectral function of the one-dimensional t-J model at finite temperatures by exact diagonalization and compared them with the experimental results. Good overall agreement is obtained between experiment and theory. The strong finite temperature effects are discussed in terms of the existence of the ``Fermi surface'' of the spinon band.
The single-particle dynamics close to a metal-to-insulator transition induced by strong repulsive interaction between the electrons is investigated. The system is described by a half-filled Hubbard model which is treated by dynamic mean-field theory evaluated by high-resolution dynamic density-matrix renormalization. We provide theoretical spectra with momentum resolution which facilitate the comparison to photoelectron spectroscopy.
The validity of the Luttinger sum rule is investigated within the prototype tight-binding model of interacting fermions in one dimension, i.e., the t-V model including the next-nearest neighbor hopping t' in order to break the particle-hole symmetry. Scaling analysis of finite-system results at half-filling reveals evident breakdown of the sum rule in the regime of large gap at V >> t, while the sum rule appears to recover together with vanishing of the Mott-Hubbard gap.
We investigate the infinite-dimensional two-orbital Hubbard model at arbitrary band fillings. By means of the self-energy functional approach, we discuss the stability of the metallic state in the systems with same and different bandwidths. It is found that the Mott insulating phases are realized at commensurate band fillings. Furthermore, it is clarified that the orbital selective Mott phase with one orbital localized and the other itinerant is stabilized even at fractional band fillings in the system with different bandwidths.
We study the phase diagram of the frustrated $t{-}t^\prime$ Hubbard model on the square lattice by using a novel variational wave function. Taking the clue from the backflow correlations that have been introduced long-time ago by Feynman and Cohen and have been used for describing various interacting systems on the continuum (like liquid $^3$He, the electron jellium, and metallic Hydrogen), we consider many-body correlations to construct a suitable approximation for the ground state of this correlated model on the lattice. In this way, a very accurate {\it ansatz} can be achieved both at weak …
In order to clarify the physics of the crossover from a Peierls band insulator to a correlated Mott-Hubbard insulator, we analyze ground-state and spectral properties of the one-dimensional half-filled Holstein-Hubbard model using quasi-exact numerical techniques. In the adiabatic limit the transition is connected to the band to Mott insulator transition of the ionic Hubbard model. Depending on the strengths of the electron-phonon coupling and the Hubbard interaction the transition is either first order or evolves continuously across an intermediate phase with finite spin, charge, and optical …
The Mott metal-insulator transition in the two-band Hubbard model in infinite dimensions is studied by using the linearized dynamical mean-field theory. The discontinuity in the chemical potential for the change from hole to electron doping is calculated analytically as a function of the on-site Coulomb interaction $U$ at the $d$-orbital and the charge-transfer energy $Δ$ between the $d$- and $p$-orbitals. Critical behaviour of the quasiparticle weight is also obtained analytically as a function of $U$ and $Δ$. The analytic results are in good agreement with the numerical results of the exact …
We study how the electron hopping reduces the Mott-Hubbard band gap in the limit of a large Coulomb interaction U and as a function of the orbital degeneracy N. The results support the conclusion that the hopping contribution grows as roughly \sqrt{N}W, where W is the one-particle band width, but in certain models a crossover to a \sim NW behavior is found for a sufficiently large N.
In this work we study the two-orbital Hubbard model on a square lattice in the presence of hybridization between nearest-neighbor orbitals and a crystal-field splitting. We use a highly reliable numerical technique based on the density matrix renormalization group to solve the dynamical mean field theory self-consistent impurity problem. We find that the orbital mixing always leads to a finite local density states at the Fermi energy in both orbitals when at least one band is metallic. When one band is doped, and the chemical potential lies between the Hubbard bands in the other band, the cohe…
We study the electronic structure of the doped paramagnetic insulator by finite temperature Quantum Monte-Carlo simulations for the 2D Hubbard model. Throughout we use the moderately high temperature T=0.33t, where the spin correlation length has dropped to < 1.5 lattice spacings, and study the evolution of the band structure with hole doping. The effect of doping can be best described as a rigid shift of the chemical potential into the lower Hubbard band, accompanied by some transfer of spectral weight. For hole dopings <20% the Luttinger theorem is violated, and the Fermi surface volume, inf…
Motivated by the current interest in the understanding of the Mott insulators away from half filling, observed in many perovskite oxides, we study the Mott metal-insulator transition (MIT) in the doped Hubbard-Holstein model using the Hatree-Fock mean field theory. The Hubbard-Holstein model is the simplest model containing both the Coulomb and the electron-lattice interactions, which are important ingredients in the physics of the perovskite oxides. In contrast to the half-filled Hubbard model, which always results in a single phase (either metallic or insulating), our results show that away …
We study the electronic state of the doped Mott-Hubbard insulator within Dynamical Mean Field Theory. The evolution of the finite temperature spectral functions as a function of doping show large redistributions of spectral weight in both antiferromagnetic and paramagnetic phases. In particular, a metallic antiferromagnetic state is obtained with a low frequency Slater-splitted quasiparticle peak coexisting with Hubbard bands. In the high temperature paramagnetic metallic phase, upon reducing doping, the system has a crossover through a ``bad metal'' state characterized by an anomalous shift o…
The frequency-dependent conductivity is studied for the one-dimensional Hubbard model, using a selection rule, the Bethe ansatz, and symmetries associated with conservation laws. For densities where the system is metallic the absorption spectrum has two contributions, a Drude peak at $ω= 0$ separated by a pseudogap from a broad absorption band whose lower edge is characterized by a non-classical critical exponent. Our findings shed new light on the ``far infrared puzzle'' and other optical properties of metallic organic chain compounds.
