Bosonization at Finite Temperature and Anyon Condensation

TL;DR

This paper develops an operator formalism for bosonization at finite temperature and density, explicitly constructs correlation functions for anyons, and discovers phenomena like anyon condensation and persistent currents, with applications to the Thirring model.

Contribution

It introduces a novel operator formalism for finite-temperature bosonization with anyon statistics, enabling exact correlation functions and analysis of condensation phenomena.

Findings

Discovery of anyon condensation in certain statistical parameter ranges

Explicit construction of n-point correlation functions satisfying KMS condition

Identification of persistent currents at finite temperature

Abstract

An operator formalism for bosonization at finite temperature and density is developed. We treat the general case of anyon statistics. The exact $n$-point correlation functions, satisfying the Kubo-Martin-Schwinger condition, are explicitly constructed. The invariance under both vector and chiral transformations allows to introduce two chemical potentials. Investigating the exact momentum distribution, we discover anyon condensation in certain range of the statistical parameter. Another interesting feature is the occurrence of a non-vanishing persistent current. As an application of the general formalism, we solve the massless Thirring model at finite temperature, deriving the charge density and the persistent current.