Bath induced phase transition in a Luttinger liquid

TL;DR

This paper investigates how coupling a Luttinger liquid to an ohmic bath induces a phase transition from a conducting Luttinger liquid to a dissipative, localized phase, revealing the bath's role as annealed disorder.

Contribution

It demonstrates the existence of a bath-induced Kosterlitz-Thouless transition in a Luttinger liquid using bosonization and numerical methods, highlighting the bath's impact on transport and localization.

Findings

Identifies a KT transition driven by bath coupling

Shows the Luttinger liquid remains conductive below critical coupling

Reveals the dissipative phase exhibits finite resistivity

Abstract

We study an XXZ spin chain, where each spin is coupled to an independent ohmic bath of harmonic oscillators at zero temperature. Using bosonization and numerical techniques, we show the existence of two phases separated by an Kosterlitz-Thouless (KT) transition. At low coupling with the bath, the chain remains in a Luttinger liquid phase with a reduced but finite spin stiffness, while above a critical coupling the system is in a dissipative phase characterized by a vanishing spin stiffness. We argue that the transport properties are also inhibited: the Luttinger liquid is a perfect conductor while the dissipative phase displays finite resistivity. Our results show that the effect of the bath can be interpreted as annealed disorder inducing signatures of localization.