Phase transitions for a collective coordinate coupled to Luttinger liquids

TL;DR

This paper investigates phase transitions in systems where collective coordinates interact with Luttinger liquids, revealing critical points where the system shifts from delocalized to localized phases with distinct dynamical behaviors.

Contribution

It identifies and characterizes phase transitions for collective coordinates coupled to Luttinger liquids across different interaction regimes, including new critical points at specific Luttinger parameters.

Findings

Phase transition from delocalized to periodic potential phase at 1/2<K<1.

Dissipative dynamics emerge at the transition line.

Localized phase with no diffusion at K=1/2.

Abstract

We study various realizations of collective coordinates, e.g. the position of a particle, the charge of a Coulomb box or the phase of a Bose or a superconducting condensate, coupled to Luttinger liquids (LL) with N flavors. We find that for Luttinger parameter 1/2<K<1 there is a phase transition from a delocalized phase into a phase with a periodic potential at strong coupling. In the delocalized phase the dynamics is dominated by an effective mass, i.e. diffusive in imaginary time, while on the transition line it becomes dissipative. At K=1/2 there is an additional transition into a localized phase with no diffusion at zero temperature.