Dissipative Luttinger liquids

TL;DR

This paper studies a dissipative quantum fluid modeled as a Luttinger liquid coupled to an Ohmic bath, showing that dissipation destroys perfect conductivity and enhances localization, with exact correlation functions computed at finite temperature.

Contribution

It provides an exact analysis of a dissipative Luttinger liquid, revealing how dissipation affects conductivity and localization, which was not previously understood in detail.

Findings

Dissipation destroys perfect conductivity via Zeno localization.

Open Luttinger liquids are more prone to localization by potentials.

Correlation functions are computed exactly at finite temperature.

Abstract

We investigate a one dimensional quantum fluid coupled to a dissipative bath. The quantum fluid is captured by the canonical Luttinger liquid; the bath is given by the model of Caldeira and Leggett, i.e. a tower of oscillators coupled linearly to the fluid density, $\rho$. The bath can be integrated out exactly, producing an effective interaction for the fluid that is nonlocal in time; we argue that the form corresponding to Ohmic dissipation is generic. Compared to previous works, we compute correlation functions for this minimal model without approximation, including at finite temperature $T>0$. From these and a Kubo calculation, we conclude that arbitrary dissipation destroys the perfect conductivity of the Luttinger liquid via Zeno localization, even in the absence of a spatial potential; from RG analysis of harmonic terms, we also find that the open Luttinger liquid is significantly more prone to localization by such potentials, in contrast to the usual intuition that baths make systems less localized.