3 research outputs found
Quantum Monte Carlo and variational approaches to the Holstein model
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.Comment: 18 pages, 11 Figures, v2: one typo correcte