Quantum Monte Carlo and variational approaches to the Holstein model

Abstract

Based on the canonical Lang-Firsov transformation of the Hamiltonian we develop a very efficient quantum Monte Carlo algorithm for the Holstein model with one electron. Separation of the fermionic degrees of freedom by a reweighting of the probability distribution leads to a dramatic reduction in computational effort. A principal component representation of the phonon degrees of freedom allows to sample completely uncorrelated phonon configurations. The combination of these elements enables us to perform efficient simulations for a wide range of temperature, phonon frequency and electron-phonon coupling on clusters large enough to avoid finite-size effects. The algorithm is tested in one dimension and the data are compared with exact-diagonalization results and with existing work. Moreover, the ideas presented here can also be applied to the many-electron case. In the one-electron case considered here, the physics of the Holstein model can be described by a simple variational approach.

arXiv comment18 pages, 11 Figures, v2: one typo corrected

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Cited by in corpus (57)

• Froehlich Polaron and Bipolaron: Recent Developments
• The Green's Function of the Holstein Polaron
• Variational Study of Fermionic and Bosonic Systems with Non-Gaussian States: Theory and Applications
• Quantum Monte Carlo Simulations of the 2D Su-Schrieffer-Heeger Model
• Charge Order in the Holstein Model on a Honeycomb Lattice
• Real-time decay of a highly excited charge carrier in the one-dimensional Holstein model
• Superconductivity and charge density wave order in the 2D Holstein model
• Symmetry Enforced Self-Learning Monte Carlo Method Applied to the Holstein Model
• Langevin Simulations of a Long Range Electron Phonon Model
• Effect of electron-phonon interaction range on lattice polaron dynamics: a continuous-time quantum Monte Carlo study
• Effects of lattice geometry and interaction range on polaron dynamics
• Charge-density-wave melting in the one-dimensional Holstein model
• Photoemission spectra of many-polaron systems
• Electron motion in a Holstein molecular chain in an electric field
• Finite-temperature density-matrix renormalization group method for electron-phonon systems: Thermodynamics and Holstein-polaron spectral functions
• Momentum average approximation for models with boson-modulated hopping: Role of closed loops in the dynamical generation of a finite quasiparticle mass
• Temperature-filling phase diagram of the two-dimensional Holstein model in the thermodynamic limit by self-consistent Migdal approximation
• Electron-Phonon Interactions in Flat Band Systems
• Trapping of three-dimensional Holstein polarons by various impurities
• Langevin Simulations of the Half-Filled Cubic Holstein Model
• Single polaron properties of the breathing-mode Hamiltonian
• Temperature- and quantum phonon effects on Holstein-Hubbard bipolarons
• Variational Monte Carlo Method for Electron-Phonon Coupled Systems
• Spectral and thermodynamic properties of the Holstein polaron: Hierarchical equations of motion approach
• Comparative Study of State-of-the-Art Matrix-Product-State Methods for Lattice Models with Large Local Hilbert Spaces
• Properties of the non-linear Holstein polaron at finite doping and temperature
• Magnetism and charge order in the honeycomb lattice
• Phase diagram of the Holstein polaron in one dimension
• Constrained-Path Auxiliary-Field Quantum Monte Carlo for Coupled Electrons and Phonons
• Single-particle spectral function of the Holstein-Hubbard bipolaron
• Superconductivity in the presence of strong electron-phonon interactions and frustrated charge order
• Spectral functions of the spinless Holstein model
• Polaronic effects in one- and two-band quantum systems
• Charge-Density Wave Order on a $\pi$-flux Square Lattice
• The two-dimensional $t$-$t^{\prime }$ Holstein model
• Continuous-time quantum Monte Carlo for fermion-boson lattice models: Improved bosonic estimators and application to the Holstein model
• Quantum simulation of extended polaron models using compound atom-ion systems
• Quantum Monte Carlo study of an anharmonic Holstein model
• Variational wave functions for the spin-Peierls transition in the Su-Schrieffer-Heeger model with quantum phonons
• Polaron action for multimode dispersive phonon systems
• Holstein polaron in two and three dimensions by quantum Monte Carlo
• An approach for studying the influence of uniaxial strain (pressure) on the temperature of the Bose-Einstein condensation of intersite bipolarons: possible implementation for RBa${}_2$Cu${}_3$O${}_{7-\delta }$ cuprates
• Effect of screening of the electron-phonon interaction on mass renormalization and optical conductivity of the Extended Holstein model polarons
• The Partition Function Zeroes of Quantum Critical Points
• Bipolaron formation in 1D-3D quantum dots: A lattice quantum Monte Carlo approach
• Mass of a lattice polaron from extended Holstein model using Yukawa potential
• The Holstein Polaron Problem Revisited
• Thermodynamic properties of Holstein polarons and the effects of disorder
• Enhancement of Charge Density Wave Correlations in a Holstein Model with an Anharmonic Phonon Potential
• Particularities of polaron formation in the extended Holstein model with next nearest neighbor transfer
• Light bipolarons in a system of electrons coupled to dispersive optical phonons
• Magnetic impurities in a charge-ordered background
• Beyond-quasiparticle transport with vertex correction: self-consistent ladder formalism for electron-phonon interactions
• Periodically driven small polarons
• Incommensurate charge density wave on multiband intermetallic systems exhibiting competing orders
• Commensurate to Incommensurate Transition of Three Dimensional Charge Density Waves
• Diagrammatic quantum Monte Carlo study of an acoustic lattice polaron