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.

18 pages, 11 Figures, v2: one typo corrected

Cited by in corpus (26)

• The Green's Function of the Holstein Polaron
• Real-time decay of a highly excited charge carrier in the one-dimensional Holstein model
• 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
• Trapping of three-dimensional Holstein polarons by various impurities
• Spectral and thermodynamic properties of the Holstein polaron: Hierarchical equations of motion approach
• Temperature- and quantum phonon effects on Holstein-Hubbard bipolarons
• Phase diagram of the Holstein polaron in one dimension
• Constrained-Path Auxiliary-Field Quantum Monte Carlo for Coupled Electrons and Phonons
• Spectral functions of the spinless Holstein model
• Quantum simulation of extended polaron models using compound atom-ion systems
• Continuous-time quantum Monte Carlo for fermion-boson lattice models: Improved bosonic estimators and application to the Holstein model
• The two-dimensional $t$-$t^{\prime }$ Holstein model
• Variational wave functions for the spin-Peierls transition in the Su-Schrieffer-Heeger model with quantum phonons
• Holstein polaron in two and three dimensions by quantum Monte Carlo
• Bipolaron formation in 1D-3D quantum dots: A lattice quantum Monte Carlo approach
• The Partition Function Zeroes of Quantum Critical Points
• 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
• Incommensurate charge density wave on multiband intermetallic systems exhibiting competing orders
• Commensurate to Incommensurate Transition of Three Dimensional Charge Density Waves