The effect of electron-electron interactions on Dirac fermions, and the possibility of an intervening spin liquid phase between the semi-metal and antiferromagnetic (AF) regimes, has been a focus of intense quantum simulation effort over the last five years. We use determinant quantum Monte Carlo (DQMC) to study the Holstein model on a Honeycomb lattice and explore the role of electron-phonon interactions on Dirac fermions. We show that they give rise to charge density wave (CDW) order, and present evidence that this occurs only above a finite critical interaction strength. We evaluate the temperature for the transition into the CDW which, unlike the AF transition, can occur at finite values owing to the discrete nature of the broken symmetry.
Tuning superconductivity and charge density wave order by next-nearest-neighbor hopping integral in honeycomb Holstein model
School of Physics and Astronomy, Beijing Normal University（北京师范大学物理学院）；Key Laboratory of Multiscale Spin Physics (Beijing Normal University), Ministry of Education（教育部多尺度自旋物理重点实验室（北京师范大学））；School of Physical Science and Technology, Beijing University of Posts and Telecommunications（北京邮电大学理学院）
Disorder Suppression of Charge Density Waves in the Honeycomb Holstein Model
School of Physical Science and Technology, Beijing University of Posts and Telecommunications（北京邮电大学物理科学与技术学院）；School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院）；Key Laboratory of Multiscale Spin Physics (Ministry of Education), Beijing Normal University（北京师范大学多尺度自旋物理教育部重点实验室）
The interplay between electron-electron correlations and disorder has been a central theme of condensed matter physics over the last several decades, with particular interest in the possibility that interactions might cause delocalization of an Anderson insulator into a metallic state, and the disrupting effects of randomness on magnetic order and the Mott phase. Here we extend this physics to explore electron-phonon interactions and show, via exact quantum Monte Carlo simulations, that the suppression of the charge density wave correlations in the half-filled Holstein model by disorder can st…
When performing a Monte Carlo calculation, the running time should in principle be much longer than the autocorrelation time in order to get reliable results. Among different lattice fermion models, the Holstein model is notorious for its particularly long autocorrelation time. In this work, we employ the Wang-Landau algorithm in the determinant quantum Monte Carlo to achieve the flat-histogram sampling in the "configuration weight space", which can greatly reduce the autocorrelation time by sacrificing some sampling efficiency. The proposal is checked in the Holstein model on both square and …
We investigate charge ordering in the Holstein model in the presence of anisotropic hopping, $t_x, t_y=1-δ, 1 + δ$, as a model of the effect of strain on charge density wave (CDW) materials. Using Quantum Monte Carlo simulations, we show that the CDW transition temperature is relatively insensitive to moderate anisotropy $δ\lesssim 0.3$, but begins to decrease more rapidly at $δ\gtrsim 0.4$. However, the density correlations, as well as the kinetic energies parallel and perpendicular to the compressional axis, change significantly for moderate $δ$. Accompanying mean-field theory calculations s…
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）
Over the past several years, reliable Quantum Monte Carlo results for the charge density wave transition temperature $T_{cdw}$ of the half-filled two dimensional Holstein model in square and honeycomb lattices have become available for the first time. Exploiting the further development of numerical methodology, here we present results in three dimensions, which are made possible through the use of Langevin evolution of the quantum phonon degrees of freedom. In addition to determining $T_{cdw}$ from the scaling of the charge correlations, we also examine the nature of charge order at general wa…
The Holstein Hamiltonian describes fermions hopping on a lattice and interacting locally with dispersionless phonon degrees of freedom. In the low density limit, dressed quasiparticles, polarons and bipolarons, propagate with an effective mass. At higher densities, pairs can condense into a low temperature superconducting phase and, at or near commensurate filling on a bipartite lattice, to charge density wave (CDW) order. CDW formation breaks a discrete symmetry and hence occurs via a second order (Ising) transition, and therefore at a finite $T_{\rm cdw}$ in two dimensions. Quantum Monte Car…
We investigate the role of electron-electron and electron-phonon interactions in strongly correlated systems by performing unbiased quantum Monte Carlo simulations in the square lattice Hubbard-Holstein model at half-filling. We study the competition and interplay between antiferromagnetism (AFM) and charge-density wave (CDW), establishing its very rich phase diagram. In the region between AFM and CDW phases, we have found an enhancement of superconducting pairing correlations, favoring (nonlocal) $s$-wave pairs. Our study sheds light over past inconsistencies in the literature, in particular …
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…
Thermal and optical conductivity in the Holstein model at half filling and at finite temperature in the Luttinger-liquid and charge-density-wave regime
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 competition and interplay between charge-density wave and superconductivity have become a central subject for quasi-2D compounds. Some of these materials, such as the transition-metal dichalcogenides, exhibit strong electron-phonon coupling, an interaction that may favor both phases, depending on the external parameters, such as hydrostatic pressure. In view of this, here we analyze the single-band $t$-$t^{\prime}$ Holstein model in the square lattice, adding a next-nearest neighbor hopping $t^{\prime}$ in order to play the role of the external pressure. To this end, we perform unbiased qu…
We report on the observation of a unique honeycomb charge ordering of the cleaved IrTe$_2$ surface by high-resolution scanning tunneling microscopy (STM) and spectroscopy (STS). IrTe$_2$ was recently established to exhibit intriguing stripe charge orderings. Here, we show that the stripe charge order coexists with a metastable honeycomb phase formed locally. The atomic and electronic structures of the honeycomb phase are consistent with the stripe phase indicating unambiguously its charge order nature. A simple model of the honeycomb structure is suggested based on the overlap of three degener…
Despite being relevant to better understand the properties of honeycomb-like systems, as graphene-based compounds, the electron-phonon interaction is commonly disregarded in theoretical approaches. That is, the effects of phonon fields on \textit{interacting} Dirac electrons is an open issue, in particular when investigating long-range ordering. Thus, here we perform unbiased quantum Monte Carlo simulations to examine the Hubbard-Holstein model (HHM) in the half-filled honeycomb lattice. By performing careful finite-size scaling analysis, we identify semimetal-to-insulator quantum critical poi…
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 analyze the quantum phase diagram of the Holstein-Hubbard model using an asymptotically exact strong-coupling expansion. We find all sorts of interesting phases including a pair-density wave (PDW), a charge 4e (and even a charge 6e) superconductor, regimes of phase separation, and a variety of distinct charge-density-wave (CDW), spin-density-wave (SDW) and superconducting regimes. We chart the crossovers that occur as a function of the degree of retardation, i.e. the ratio of characteristic phonon frequency to the strength of interactions.
Tight binding models like the Hubbard Hamiltonian are most often explored in the context of uniform intersite hopping $t$. The electron-electron interactions, if sufficiently large compared to this translationally invariant $t$, can give rise to ordered magnetic phases and Mott insulator transitions, especially at commensurate filling. The more complex situation of non-uniform $t$ has been studied within a number of situations, perhaps most prominently in multi-band geometries where there is a natural distinction of hopping between orbitals of different degree of overlap. In this paper we expl…
The Interplay of Thermal Melting and Pump Driven Melting of Charge Order: A Two-Temperature Study of the Holstein Model
Harish-Chandra Research Institute（哈里什-昌德拉研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Department of Physics, University of Virginia（弗吉尼亚大学物理系）；School of Arts and Sciences, Ahmedabad University（艾哈迈达巴德大学文理学院）
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 …
Transient quantum dynamics in an interacting fermion-phonon system are investigated. In particular, a charge order (CO) melting after a short optical-pulse irradiation and roles of the quantum phonons on the transient dynamics are focused on. A spinless-fermion model in a one-dimensional chain coupled with local phonons is analyzed numerically. The infinite time-evolving block decimation algorithm is adopted as a reliable numerical method for one-dimensional quantum many-body systems. Numerical results for the photoinduced CO melting dynamics without phonons are well interpreted by the soliton…
We propose a numerical method which embeds the variational non-Gaussian wavefunction approach within exact diagonalization, allowing for efficient treatment of correlated systems with both electron-electron and electron-phonon interactions. Using a generalized polaron transformation, we construct a variational wavefunction that absorbs entanglement between electrons and phonons into a variational non-Gaussian transformation; exact diagonalization is then used to treat the electronic part of the wavefunction exactly, thus taking into account high-order correlation effects beyond the Gaussian le…
The electron-phonon (e-ph) interaction remains of great interest in condensed matter physics and plays a vital role in realizing superconductors, charge-density-waves (CDW), and polarons. We study the two-dimensional Holstein model for e-ph coupling using determinant quantum Monte Carlo across a wide range of its phase diagram as a function of temperature, electron density, dimensionless e-ph coupling strength, and the adiabatic ratio of the phonon frequency to the Fermi energy. We describe the behavior of the CDW correlations, the competition between superconducting and CDW orders and polaron…
We consider the extended half-filled Hubbard model on the honeycomb lattice for second nearest neighbors interactions. Using a functional integral approach, we find that collective fluctuations suppress topological states and instead favor charge ordering, in agreement with previous numerical studies. However, we show that the critical point is not of the putative semimetal-Mott insulator variety. Due to the frustrated nature of the interactions, the ground state is described by a novel hidden {\it metallic} charge order with {\it semi-Dirac} excitations. We conjecture that this transition is …
We calculate magnon dispersions and damping in the Kitaev-Heisenberg model with an off-diagonal exchange $Γ$ and isotropic third-nearest-neighbor interaction $J_3$ on a honeycomb lattice. This model is relevant to a description of the magnetic properties of iridium oxides $α$-Li$_2$IrO$_3$ and Na$_2$IrO$_3$, and Ru-based materials such as $α$-RuCl$_3$. We use an unconventional parametrization of the spin-wave expansion, in which each Holstein-Primakoff boson is represented by two conjugate hermitian operators. This approach gives us an advantage over the conventional one in identifying paramet…
When two periodic potentials compete in materials, one may adopt the other, which straightforwardly generates topological defects. Of particular interest are domain walls in charge-, dipole-, and spin-ordered systems, which govern macroscopic properties and important functionality. However, detailed atomic and electronic structures of domain walls have often been uncertain and the microscopic mechanism of their functionality has been elusive. Here, we clarify the complete atomic and electronic structures of the domain wall network, a honeycomb network connected by Z$_{3}$ vortices, in the near…
We study the effects of anharmonicity on the physics of the Holstein model, which describes the coupling of itinerant fermions and localized quantum phonons, by introducing a quartic term in the phonon potential energy. We find that the presence of this anharmonic term reduces the extent of the charge density wave phase (CDW) at half-filling as well as the transition temperature to this phase. Doping away from half-filling, we observe a first order phase transition between the CDW and a homogeneous phase which is also present in the harmonic model. In addition, we study the evolution of the su…
