We present electron and phonon spectral functions calculated from determinant quantum Monte Carlo simulations of the half-filled two-dimensional Hubbard-Holstein model on a square lattice. By tuning the relative electron-electron ($e$-$e$) and electron-phonon ($e$-$ph$) interaction strengths, we show the electron spectral function evolving between antiferromagnetic insulating, metallic, and charge density wave insulating phases. The phonon spectra concurrently gain a strong momentum dependence and soften in energy upon approaching the charge density wave phase. In particular, we study how the $e$-$e$ and $e$-$ph$ interactions renormalize the spectra, and analyze how the interplay of these interactions influence the spectral renormalizations. We find that the presence of both interactions suppresses the amount of renormalization at low energy, thus allowing the emergence of a metallic phase. These findings demonstrate the importance of considering the influence of multiple interactions in spectroscopically determining any one interaction strength in strongly correlated materials.
Employing the recently developed self-consistent variational basis generation scheme, we have investigated the bipolaron-bipolaron interaction within the purview of Holstein-Hubbard and the extended-Holstein-Hubbard (F2H) model on a discrete one-dimensional lattice. The density-matrix renormalization group (DMRG) method has also been used for the Holstein-Hubbard model. We have shown that there exists no bipolaron-bipolaron attraction in the Holstein-Hubbard model. In contrast, we have obtained clear-cut bipolaron-bipolaron attraction in the F2H model. Composite bipolarons are formed above a c…
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 show that information on the probability density of local fluctuations can be obtained from a numerical renormalisation group calculation of a reduced density matrix. We apply this approach to the Anderson-Holstein impurity model to calculate the ground state probability density $ρ(x)$ for the displacement $x$ of the local oscillator. From this density we can deduce an effective local potential for the oscillator and compare its form with that obtained from a semiclassical approximation as a function of the coupling strength. The method is extended to infinite dimensional Holstein-Hubbard m…
We have studied the influence of nearest-neighbor (NN) repulsion on the low frequency phase diagram of a quarter-filled Hubbard-Holstein chain. The NN repulsion term induces the apparition of two new long range ordered phases (one $4k_F$ CDW for positive $U_{eff} = U-2g^2/ω$ and one $2k_F$ CDW for negative $U_{eff}$) that did not exist in the V=0 phase diagram. These results are put into perspective with the newly observed charge ordered phases in organic conductors and an interpretation of their origin in terms of electron-molecular vibration coupling is suggested.
In order to clarify the physics of the crossover from a spin-density-wave (SDW) Mott insulator to a charge-density-wave (CDW) Peierls insulator in one-dimensional (1D) systems, we investigate the Hubbard-Holstein Hamiltonian at half filling within a density matrix renormalisation group (DMRG) approach. Determining the spin and charge correlation exponents, the momentum distribution function, and various excitation gaps, we confirm that an intervening metallic phase expands the SDW-CDW transition in the weak-coupling regime.
The formation of a finite density multipolaronic state is analyzed in the context of the Holstein model using the Dynamical Mean-Field Theory. The spinless and spinful fermion cases are compared to disentangle the polaron crossover from the bipolaron formation. The exact solution of Dynamical Mean-Field Theory is compared with weak-coupling perturbation theory, non-crossing (Migdal), and vertex correction approximations. We show that polaron formation is not associated to a metal-insulator transition, which is instead due to bipolaron formation.
We study quenches of the interaction and electron-phonon coupling parameter in the Hubbard-Holstein model, using nonequilibrium dynamical mean field theory. The calculations are based on a generalized Lang-Firsov scheme for time-dependent interactions or externally driven phonons, and an approximate strong-coupling impurity solver. The interaction quench calculations reveal the phonon-assisted decay of excess doublons, while the quenches of the electron-phonon coupling lead to persistent oscillations of the phonons and to a phonon-enhanced doublon production.
Using a functional renormalization group method, we obtain the phase diagram of the two-leg ladder system within the Holstein-Hubbard model, which includes both electron-electron and electron-phonon interactions. Our renormalization group technique allows us to analyze the problem for both weak and strong electron-phonon coupling. We show that, in contrast results from conventional weak coupling studies, electron-phonon interactions can dominate electron-electron interactions because of retardation effects.
We extend the weak-coupling diagrammatic determinantal algorithm to projective schemes as well as to the inclusion of phonon degrees of freedom. The projective approach provides a very efficient algorithm to access zero temperature properties. To implement phonons, we integrate them out in favor of a retarded density-density interaction and simulate the resulting purely electronic action with the weak-coupling diagrammatic determinantal algorithm. Both extensions are tested within the dynamical mean field approximation for the Hubbard and Hubbard-Holstein models.
We present the phase diagram and dynamical correlation functions for the Holstein-Hubbard model at half filling and at zero temperature. The calculations are based on the Dynamical Mean Field Theory. The effective impurity model is solved using Exact Diagonalization and the Numerical Renormalization Group. Excluding long-range order, we find three different paramagnetic phases, metallic, bipolaronic and Mott insulating, depending on the Hubbard interaction U and the electron-phonon coupling g. We present the behaviour of the one-electron spectral functions and phonon spectra close to the metal…
We present a method for solving impurity models with electron-phonon coupling, which treats the phonons efficiently and without approximations. The algorithm is applied to the Holstein-Hubbard model in the dynamical mean field approximation, where it allows access to strong interactions, very low temperatures and arbitrary fillings. We show that a renormalized Migdal-Eliashberg theory provides a reasonlable description of the phonon contribution to the electronic self energy in strongly doped systems, but fails if the quasiparticle energy becomes of order of the phonon frequency.
We study a two-dimensional Hubbard-Holstein model with phonons treated in the adiabatic limit. A Hartree-Fock decomposition is employed for the Hubbard term. A range of electronic densities are discussed with special emphasis on the quarter-filling ($n=0.5$). We argue that the quarter-filled system is relevant for the electronic properties observed at the interface between LaAlO$_3$ and SrTiO$_3$, where half-electron per unit cell is transferred to the TiO$_2$ layer as a consequence of the polar discontinuity at the interface. In addition to presenting the overall phase diagrams, we identify a…
We analyze the ground-state properties of strongly-correlated electrons coupled with phonons by means of a generalized Gutzwiller wavefunction which includes phononic degrees of freedom. We study in detail the paramagnetic half-filled Hubbard-Holstein model, where the electron-electron interaction can lead to a Mott transition, and the electron-phonon coupling to a bipolaronic transition. We critically discuss the quality of the proposed wavefunction in describing the various transitions and crossovers that occur as a function of the parameters. Previous variational attempts are recovered as p…
We use continuous-time quantum Monte Carlo simulations to study retardation effects in the metallic, quarter-filled Holstein model in one dimension. Based on results which include the one- and two-particle spectral functions as well as the optical conductivity, we conclude that with increasing phonon frequency the ground state evolves from one with dominant diagonal order---2k_F charge correlations---to one with dominant off-diagonal fluctuations, namely s-wave pairing correlations. In the parameter range of this crossover, our numerical results support the existence of a spin gap for all phon…
We introduce a new type of Gutzwiller variational wavefunction for correlated electrons coupled to phonons, able to treat on equal footing electronic and lattice degrees of freedom. We benchmark the wavefunction in the infinite-$U$ Hubbard-Holstein model away from half-filling on a Bethe lattice, where we can directly compare with exact results by Dynamical Mean-Field Theory. For this model, we find that variational results agree perfectly well with the exact ones. In particular the wavefunction correctly describes the crossover to a heavy polaron gas upon increasing the electron-phonon coupli…
The influence of next-nearest neighbor electron hopping, $t^{\prime}$, on the polaron and bipolaron formation in a square Hubbard-Holstein model is investigated within a variational approach. The results for electron-phonon and electron-electron correlation functions show that a negative value of $t^{\prime}$ induces a strong anisotropy in the lattice distortions favoring the formation of nearest neighbor intersite bipolaron. The role of $t^{\prime}$, electron-phonon and electron-electron interactions is briefly discussed in view of the formation of charged striped domains.
We consider a system of interacting fermions on a chain in a periodic potential incommensurate with the chain spacing. We derive a convergent perturbative expansion, afflicted by a small denominator problem and based on renormalization group, for the two point Schwinger function. We obtain the large distance behavior of the Schwinger function, which is anomalous and described by critical indices, related to the gap and the wave function renormalization.
We re-examine the Peierls insulator to Mott insulator transition scenario in the one-dimensional Holstein-Hubbard model where, at half-filling, electron-phonon and electron-electron interactions compete for establishing charge- and spin-density-wave states, respectively. By means of large-scale density-matrix renormalization group calculations we determine the spin, single-particle and two-particle excitation gaps and prove--in the course of a careful finite-size scaling analysis--recent claims for an intervening metallic phase in the weak-coupling regime. We show that for large phonon frequen…
We reexamine the nature of the metallic phase of the one-dimensional half-filled Holstein model of spinless fermions. To this end we determine the Tomonaga-Luttinger-liquid correlation parameter $K_ρ$ by large-scale density-matrix renormalisation-group (DMRG) calculations, exploiting (i) the leading-order scaling relations between the ground-state energy and the single-particle excitation gap and (ii) the static charge structure factor in the long-wavelength limit. While both approaches give almost identical results for intermediate-to-large phonon frequencies, we find contrasting behaviour in…
We present results on the dynamical correlation functions of the particle-hole symmetric Holstein-Hubbard model at zero temperature, calculated using the dynamical mean field theory which is solved by the numerical renormalization group method. We clarify the competing influences of the electron-electron and electron-phonon interactions particularity at the different metal to insulator transitions. The Coulomb repulsion is found to dominate the behaviour in large parts of the metallic regime. By suppressing charge fluctuations, it effectively decouples electrons from phonons. The phonon propag…
We study the interplay between the electron-phonon (e-ph) and on-site electron-electron (e-e) interactions in a three-orbital Hubbard-Holstein model on an extended one-dimensional lattice using determinant quantum Monte Carlo. For weak e-e and e-ph interactions, we observe a competition between an orbital-selective Mott phase (OSMP) and a (multicomponent) charge-density-wave (CDW) insulating phase, with an intermediate metallic phase located between them. For large e-e and e-ph couplings, the OSMP and CDW phases persist, while the metallic phase develops short-range orbital correlations and be…
A classical analog simulator of the two-site Hubbard-Holstein model, describing the dynamics of two correlated electrons coupled with local phonons, is proposed based on light transport in engineered optical waveguide arrays. Our photonic analog simulator enables to map the temporal dynamics of the quantum system in Fock space into spatial propagation of classical light waves in the evanescently-coupled waveguides of the array. In particular, in the strong correlation regime the periodic temporal dynamics, related to the excitation of Holstein polarons with equal energy spacing, can be visuali…
The density driven Mott transition is studied by means of Dynamical Mean-Field Theory in the Hubbard-Holstein model, where the Hubbard term leading to the Mott transition is supplemented by an electron-phonon (e-ph) term. We show that an intermediate e-ph coupling leads to a first-order transition at T=0, which is accompanied by phase separation between a metal and an insulator. The compressibility in the metallic phase is substantially enhanced. At quite larger values of the coupling a polaronic phase emerges coexisting with a non-polaronic metal.
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…
We study the effect of dynamical Holstein phonons on the physics of the Hubbard model at small doping using the dynamical cluster approximation on a $2\times2$ cluster. Non-local antiferromagnetic correlations are found to significantly enhance the electron-phonon coupling, resulting in polaron formation for moderate coupling strengths. At finite doping, the electron-phonon coupling is found to strongly enhance the non-local spin correlations, indicating a synergistic interplay between the electron-phonon coupling and antiferromagnetic correlations. Although it enhances the pairing interaction…
Single-- and two-particle excitation spectra of the one-dimensional, half-filled Holstein-Hubbard model are calculated using the continuous-time quantum Monte Carlo method. In the metallic phase, the results are consistent with a Luther-Emery liquid that has gapped spin and single-particle excitations but a gapless charge mode. However, given the initially exponential dependence of the spin gap on the backscattering matrix element, the numerical excitation spectra appear gapless in the weak-coupling regime, and therefore resemble those of a Luttinger liquid. The Mott phase has the expected cha…
The effects of quantum lattice fluctuations on the Peierls transition are studied within the one--dimensional Holstein molecular crystal model by means of exact diagonalization methods. Applying a very efficient variational Lanczos technique, the ground--state phase diagram is obtained in excellent agreement with predictions of recent density matrix renormalization group calculations. The transition to the charge--density--wave regime is signaled by a strong increase in the charge structure factor. In the metallic regime, the non--universal Luttinger liquid parameters (charge velocity and coup…
We present a determinant quantum Monte Carlo study of the competition between instantaneous on-site Coulomb repulsion and retarded phonon-mediated attraction between electrons, as described by the two dimensional Hubbard-Holstein model. At half filling, we find a strong competition between antiferromagnetism (AFM) and charge density wave (CDW) order. We demonstrate that a simple picture of AFM-CDW competition that incorporates the phonon mediated attraction into an effective-U Hubbard model requires significant refinement. Specifically, retardation effects slow the onset of charge order, so th…
Several state-of-the-art numerical methods have observed static or fluctuating spin and charge stripes in doped two-dimensional Hubbard models, suggesting that these orders play a significant role in shaping the cuprate phase diagram. Many experiments, however, also indicate that the cuprates have strong electron-phonon ($e$-ph) coupling, and it is unclear how this interaction influences stripe correlations. We study static and fluctuating stripe orders in the doped singleband Hubbard-Holstein model using zero temperature variational Monte Carlo and finite temperature determinant quantum Monte…
We use the continuous-time interaction expansion (CT-INT) quantum Monte Carlo method to calculate the phonon spectral function of the one-dimensional Holstein-Hubbard model at half-filling. Our results are consistent with a soft-mode Peierls transition in the adiabatic regime, and the existence of a central peak related to long-range order in the Peierls phase. We explain a previously observed feature at small momenta in terms of a hybridization of charge and phonon excitations. Tuning the system from a Peierls to a metallic phase with a nonzero Hubbard interaction suppresses the central peak,…
We show that, by an appropriate choice of auxiliary fields and exact integration of the phonon degrees of freedom, it is possible to define a 'sign-free' path integral for the so called Hubbard-Holstein model at half-filling. We use a statistical method, based on an accelerated and efficient Langevin dynamics, for evaluating all relevant correlation functions of the model. Preliminary calculations at $U/t=4$ and $U/t=1$, for $ω_0/t=1$, indicate a quite extended region around $U \simeq {g^2 \over ω_0}$ without either antiferromagnetic or charge-density-wave orders, separating two quantum critic…
We have performed numerical studies of the Hubbard-Holstein model in two dimensions using determinant quantum Monte Carlo (DQMC). Here we present details of the method, emphasizing the treatment of the lattice degrees of freedom, and then study the filling and behavior of the fermion sign as a function of model parameters. We find a region of parameter space with large Holstein coupling where the fermion sign recovers despite large values of the Hubbard interaction. This indicates that studies of correlated polarons at finite carrier concentrations are likely accessible to DQMC simulations. We…
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 …
Charge Order in the half-filled bond-Holstein Model
University of California, Davis（加州大学戴维斯分校）；San José State University（圣何塞州立大学）；The University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校）；Institute for Advanced Materials and Manufacturing, The University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校先进材料与制造研究所）
We investigate metal-insulator transitions in the Holstein-Hubbard model as a function of the on-site electron-electron interaction U and the electron-phonon coupling g. We use several different numerical methods to calculate the phase diagram, the results of which are in excellent agreement. When the electron-electron interaction U is dominant the transition is to a Mott-insulator; when the electron-phonon interaction dominates, the transition is to a localised bipolaronic state. In the former case, the transition is always found to be second order. This is in contrast to the transition to th…
Using a variational numerical method we compute the time-evolution of the Holstein-Hubbard bipolaron from its ground state when at t=0 the constant electric field is switched on. The system is evolved taking into account full quantum effects until it reaches a quasi-stationary state. In the zero-field limit the current shows Bloch oscillations characteristic for the adiabatic regime where the electric field causes the bipolaron to evolve along the quasiparticle band. Bipolaron remains bound and the net current remains zero in this regime. At larger electric fields the system enters the dissipa…
We explore the quantum phase transitions between two ordered states in the infinite dimensional Hubbard-Holstein model at half filling. Our study is based on the dynamical mean field theory (DMFT) combined with the numerical renormalization group (NRG), which allows us to handle both strong electron-electron and strong electron-phonon interactions. The transition line is characterized by an effective electron-electron interaction. Depending on this effective interaction and the phonon frequency $ω_0$ one finds either a continuous transition or discontinuous transition. Here, the analysis focus…
We study the isotope effects arising from the coupling of correlated electrons with dispersionless phonons by considering the Hubbard-Holstein model at half-filling within the dynamical mean-field theory. In particular we calculate the isotope effects on the quasi-particle spectral weight $Z$, the renormalized phonon frequency, and the static charge and spin susceptibilities. In the weakly correlated regime $U/t \lesssim 1.5$, where $U$ is the Hubbard repulsion and $t$ is the bare electron half-bandwidth, the physical properties are qualitatively similar to those characterizing the Holstein mo…
We investigate ordered phases (s-wave superconducting (SC), antiferromagnetic (AF) and charge ordered (CO) phases) of the half-filled Holstein-Hubbard model using the dynamical mean-field theory in combination with a continuous time quantum Monte Carlo impurity solver. We particularly focus on the parameter regime where the electron-electron Coulomb interaction and the phonon mediated retarded attractive interaction are both comparable to the bare electron bandwidth to understand the interplay of these interactions and the retardation effects due to finite phonon frequency ω_0. Results for the…
We use an unbiased, continuous-time quantum Monte Carlo method to address the possibility of a zero-temperature phase without charge-density-wave (CDW) order in the Holstein and, by extension, the Holstein-Hubbard model on the half-filled square lattice. In particular, we present results spanning the whole range of phonon frequencies, allowing us to use the well understood adiabatic and antiadiabatic limits as reference points. For all parameters considered, our data suggest that CDW correlations are stronger than pairing correlations even at very low temperatures. These findings are compatibl…
The one-electron spectral function of the Holstein-Hubbard bipolaron in one dimension is studied using cluster perturbation theory together with the Lanczos method. In contrast to other approaches, this allows one to calculate the spectrum at continuous wave vectors and thereby to study, for the first time, the dispersion and the spectral weight of quasiparticle features. The formation of polarons and bipolarons, and their manifestation in the spectral properties of the system, is studied for the cases of intermediate and large phonon frequencies, with and without Coulomb interaction. A good a…
We investigate polaron formation in a many-electron system in the presence of a local repulsion sufficiently strong to prevent local-bipolaron formation. Specifically, we consider a Hubbard-Holstein model of interacting electrons coupled to dispersionless phonons of frequency $ω_0$. Numerically solving the model in a small one-dimensional cluster, we find that in the nearly adiabatic case $ω_0 < t$, the necessary and sufficient condition for the polaronic regime to occur is that the energy gain in the atomic (i.e., extremely localized) regime ${\cal E}_{pol}$ overcomes the energy of the purely…
We derive an effective electronic Hamiltonian for square lattice Hubbard-Holstein model (HHM) in the strong electron-electron (e-e) and electron-phonon (e-ph) coupling regime and under non-adiabatic conditions ($t/ω_0 \leq 1$), $t$ and $ω_0$ being the electron hopping and phonon frequency respectively. Using Density Matrix Renormalization Group method, we simulate this effective electronic model on $4-$Leg cylinder system at quarter-filling and present a phase diagram in $g-U$ plane where $g$ and $U$ are being the e-ph coupling constant and Hubbard on-site interaction respectively. For larger …
We present a density-matrix embedding theory (DMET) study of the one-dimensional Hubbard-Holstein model, which is paradigmatic for the interplay of electron-electron and electron-phonon interactions. Analyzing the single-particle excitation gap, we find a direct Peierls insulator to Mott insulator phase transition in the adiabatic regime of slow phonons in contrast to a rather large intervening metallic phase in the anti-adiabatic regime of fast phonons. We benchmark the DMET results for both on-site energies and excitation gaps against density-matrix renormalization group (DMRG) results and f…
The spectral response and physical features of the 2D Hubbard-Holstein model are calculated both in equilibrium at zero and low chemical dopings, and after an ultra short powerful light pulse, in undoped systems. At equilibrium and at strong charge-lattice couplings, the optical conductivity reveals a 3-peak structure in agreement with experimental observations. After an ultra short pulse and at nonzero electron-phonon interaction, phonon and spin subsystems oscillate with the phonon period $T_{ph} \approx 80$ fs. The decay time of the phonon oscillations is about 150-200 fs, similar to the re…
We use a recently developed extension of the weak coupling diagrammatic determinantal quantum Monte Carlo method to investigate the spin, charge and single particle spectral functions of the one-dimensional quarter-filled Holstein model with phonon frequency $ω_0 = 0.1 t$. As a function of the dimensionless electron-phonon coupling we observe a transition from a Luttinger to a Luther-Emery liquid with dominant $2k_f$ charge fluctuations. Emphasis is placed on the temperature dependence of the single particle spectral function. At high temperatures and in both phases it is well accounted for wi…
We study the complete extended Hubbard-Holstein Hamiltonian on a four-site chain with equally spaced sites, with spacing-dependent electronic interaction parameters evaluated in terms of Wannier functions built from Gaussian atomic orbitals. By successive application of generalized displacement and squeezing transformations, an effective polaronic Hamiltonian is obtained, containing a purely phonon-induced, long-range intersite charge interaction. The phase diagrams for N=1,2,3,4 electrons have been determined by variational minimization of the sum of the electronic and the phononic energy, pa…
The one-dimensional Holstein model and its generalizations have been studied extensively to understand the effects of electron-phonon interaction. The half-filled case is of particular interest, as it describes a transition from a metallic phase with a spin gap due to attractive backscattering to a Peierls insulator with charge-density-wave (CDW) order. Our quantum Monte Carlo results support the existence of a metallic phase with dominant power-law charge correlations, as described by the Luther-Emery fixed point. We demonstrate that for Holstein and also for purely fermionic models the spin …
We study the interplay between the electron-electron (e-e) and the electron-phonon (e-ph) interactions in the two-orbital Hubbard-Holstein model at half filling using the dynamical mean field theory. We find that the e-ph interaction, even at weak couplings, strongly modifies the phase diagram of this model and introduces an orbital-selective Peierls insulating phase (OSPI) that is analogous to the widely studied orbital-selective Mott phase (OSMP). At small e-e and e-ph coupling, we find a competition between the OSMP and the OSPI, while at large couplings, a competition occurs between Mott a…
Competing interactions are often responsible for intriguing phase diagrams in correlated electron systems. Here we analyze the competition of instantaneous short range Coulomb interaction $U$ with the retarded electron-electron interaction induced by an electron-phonon coupling $g$ as described by the Hubbard-Holstein model. The ground state phase diagram of this model in the limit of large dimensions at half filling is established. The study is based on dynamical mean field theory combined with the numerical renormalization group. Depending on $U$, $g$, and the phonon frequency $ω_0$, the gro…
The Hubbard-Holstein model describes fermions on a discrete lattice, with on-site repulsion between fermions and a coupling to phonons that are localized on sites. Generally, at half-filling, increasing the coupling $g$ to the phonons drives the system towards a Peierls charge density wave state whereas increasing the electron-electron interaction $U$ drives the fermions into a Mott antiferromagnet. At low $g$ and $U$, or when doped, the system is metallic. In one-dimension, using quantum Monte Carlo simulations, we study the case where fermions have a long range coupling to phonons, with char…
We study the effect of strong DC and pulsed electric fields on a Mott insulating system with coupling to optical phonons. A DC field of the order of the gap induces a metallic state characterized by polaronic features in the gap region and a partially inverted population. In this quasi-steady state, the field-induced doublon-hole production is balanced by a phonon-enhanced doublon-hole recombination. The photo-excitation of carriers by a pulsed field leads to similar modifications of the electronic structure in the gap region, and an associated reduction of the doublon life-time. We demonstrat…
We study the Holstein-Hubbard model at half filling to explore ordered phases including su- perconductivity (SC), antiferromagnetism (AF), and charge order (CO) in situations where the electron-electron and electron-phonon interactions are strong (~ electronic bandwidth). The model is solved in the dynamical mean-field approximation using a continuous-time quantum Monte Carlo impurity solver. We determine the superconducting transition temperature (Tc) and the SC order parameter and show that the phonon-induced retardation or the strong Coulomb interaction leads to a significant reduction and …
A variational approach is proposed to determine some properties of the adiabatic Holstein-Hubbard model which describes the interactions between a static atomic lattice and an assembly of fermionic charge carriers. The sum of the electronic energy and the lattice elastic energy is proved to have minima with a polaron structure in a certain domain of the phase diagram. Our analytical work consists in the expansion of these energy minima from the zero electronic transfer limit which remarkably holds for a finite amplitude of the onsite Hubbard repulsion and for an unbounded lattice size.
We derive an effective Hamiltonian for the two-dimensional Hubbard-Holstein model in the regimes of strong electron-electron and strong electron-phonon interactions by using a nonperturbative approach. In the parameter region where the system manifests the existence of a correlated singlet phase, the effective Hamiltonian transforms to a $t_1-V_1-V_2-V_3$ Hamiltonian for hard-core-bosons on a checkerboard lattice. We employ quantum Monte Carlo simulations, involving stochastic-series-expansion technique, to obtain the ground state phase diagram. At filling $1/8$, as the strength of off-site re…
We calculate the spectral function of the one dimensional Hubbard-Holstein model using the time dependent Density Matrix Renormalization Group (tDMRG), focusing on the regime of large local Coulomb repulsion, and away from electronic half-filling. We argue that, from weak to intermediate electron-phonon coupling, phonons interact only with the electronic charge, and not with the spin degrees of freedom. For strong electron-phonon interaction, spinon and holon bands are not discernible anymore and the system is well described by a spinless polaronic liquid. In this regime, we observe multiple p…
The ground state phase diagram of the half-filled one-dimensional Holstein-Hubbard model contains a charge-density-wave (CDW) phase, driven by the electron-phonon (e-ph) coupling, and a spin-density-wave (SDW) phase, driven by the on-site electron-electron (e-e) repulsion. Recently, the existence of a third phase, which is metallic and lies in a finite region of parameter space between these two gapped phases, has been claimed. We study this claim using a renormalization-group method for interacting electrons that has been extended to include also e-ph couplings. Our method treats e-e and e-ph…
