Density matrix renormalization group study of the polaron problem in the Holstein model

TL;DR

This paper introduces a novel DMRG method using pseudo-sites to study the polaron problem in the Holstein model, enabling analysis of large lattices with high phonon states and revealing a crossover from free electrons to polarons.

Contribution

A new pseudo-site DMRG approach for bosonic systems that efficiently handles large lattices and high phonon states in the Holstein model.

Findings

Identified a smooth crossover from free electron to polaronic states.

Achieved ground state calculations on large 1D and 2D lattices.

Results agree with previous studies on polaron behavior.

Abstract

We propose a new density matrix renormalization group (DMRG) approach to study lattices including bosons. The key to the new approach is an exact mapping of a boson site containing 2^N states to N pseudo-sites, each with 2 states. The pseudo-sites can be viewed as the binary digits of a boson level. We apply the pseudo-site DMRG method to the polaron problem in the one- and two-dimensional Holstein models. Ground state results are presented for a wide range of electron-phonon coupling strengths and phonon frequencies on lattices large enough (up to 80 sites in one dimension and up to 20x20 sites in two dimensions) to eliminate finite size effects, with up to 128 phonon states per phonon mode. We find a smooth but quite abrupt crossover from a quasi-free electron ground state with a slightly renormalized mass at weak electron-phonon coupling to a polaronic ground state with a large effective mass at strong coupling, in agreement with previous studies.