Dynamical mean-field theory computations of the electron self energy of the Hubbard-Holstein model as a function of electron-phonon and electron-electron interactions are analyzed to gain insight into the dependence of electron-phonon couplings on correlation strength in quantum materials. We find that the electron-phonon interaction is strongly suppressed by electronic correlations, while electron-electron correlation effects at Fermi liquid scales are only weakly modified by coupling to phonons, with phonon-induced modifications most evident at high frequencies on the order of the electronic bandwidth. Implications for beyond-density functional theories of the electron-phonon interaction are discussed.
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…
The effect of dispersive optical phonons on the behaviour of a Holstein polaron
本文利用无近似的Bold Diagrammatic Monte Carlo方法研究了光学声子模的有限色散对Holstein极化子性质，特别是其有效质量的影响。对于弱的电子-声子耦合，这种影响很小，但对于中等和大的电子-声子耦合，它变得显著。有效质量被发现增加（减少），如果声子色散有一个负（正）曲率在中心的布里渊区。
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,…
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 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 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 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 …
The Holstein model with dispersionless Einstein phonons is one of the simplest models describing electron-phonon interactions in condensed matter. A naive extrapolation of perturbation theory in powers of the relevant dimensionless electron-phonon coupling $λ_0$ suggests that at zero temperature the model exhibits a Pomeranchuk instability characterized by a divergent uniform compressibility at a critical value of $λ_0$ of order unity. In this work, we re-examine this problem using modern functional renormalization group (RG) methods. For dimensions $d > 3$ we find that the RG flow of the Hols…
Recent experiments have suggested that the electron-phonon coupling may play an important role in the $γ\rightarrow α$ volume collapse transition in Cerium. A minimal model for the description of such transition is the periodic Anderson model. In order to better understand the effect of the electron-phonon interaction on the volume collapse transition, we study the periodic Anderson model with coupling between Holstein phonons and electrons in the conduction band. We find that the electron-phonon coupling enhances the volume collapse, which is consistent with experiments in Cerium. While we st…
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 …
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 and symmetry breaking in the Hubbard-Holstein model
在相关电子系统中，相互竞争的相互作用常常是引起有趣的相图的原因。本文分析了瞬时短程库仑相互作用$U$与Hubbard-Holstein模型描述的电子-声子耦合$g$引起的延迟电子-电子相互作用的竞争。建立了该模型在大尺寸极限下的半填充状态下的基态相图。研究是基于动力学平均场理论结合数值重整化群。根据$U$、$g$和声子频率$ω_0$，基态是反铁磁的（AFM）或电荷有序的（CO）。我们发现当$U-λ\simeq 0$，其中$λ$表征声子诱导的有效吸引力时，从AFM到CO态的量子相变发生。对于小的耦合和大的声子频率$ω_0$，跃迁是连续的，而对于大的耦合和小的$ω_0$值，跃迁变得不连续。我们评论这项工作可能的相关性Ba ${}_{1-x}$ K ${}_x$生物${}_3$。
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 use the Momentum Average approximation together with perturbative approaches, in the appropriate limits, to study the single polaron physics on a perovskite lattice inspired by BaBiO3. We investigate electron-phonon coupling of the Peierls type whereby the motion of ions modulates the values of the hopping integrals between sites, and show that it cannot be mapped onto the simpler one-band Holstein model in the whole parameter space. This is because the dispersion of the Peierls polaron has sharp transitions where the ground-state momentum jumps between high-symmetry points in the Brillouin…
