Bosonization and Cluster Updating of Lattice Fermions

TL;DR

This paper introduces a bosonization approach for lattice fermions using Jordan-Wigner representation, enabling local interactions and efficient cluster algorithms for simulation.

Contribution

It formulates a lattice fermion model in Fock space with a novel bosonization method that incorporates Fermi statistics via nonlocal sign factors, facilitating improved computational techniques.

Findings

Path integral expressed as sum over occupation configurations

Nonlocal sign factors encode Fermi statistics

Cluster algorithms enable efficient updates of bosonic variables

Abstract

A lattice fermion model is formulated in Fock space using the Jordan-Wigner representation for the fermion creation and annihilation operators. The resulting path integral is a sum over configurations of lattice site occupation numbers $n(x,t) = 0,1$ which may be viewed as bosonic Ising-like variables. However, as a remnant of Fermi statistics a nonlocal sign factor arises for each configuration. When this factor is included in measured observables the bosonic occupation numbers interact locally, and one can use efficient cluster algorithms to update the bosonized variables.