Influence of thermal fluctuations on quantum phase transitions in one-dimensional disordered systems: Charge density waves and Luttinger liquids

TL;DR

This paper investigates how thermal fluctuations affect quantum phase transitions in one-dimensional disordered systems like charge density waves and Luttinger liquids, revealing a complex phase diagram with multiple scaling regions.

Contribution

It provides a comprehensive finite temperature RG analysis of disordered 1D quantum systems, including exact solutions for strong disorder and mapping to Burgers equation for weak disorder, extending understanding of phase transitions.

Findings

Thermal fluctuations suppress localization transitions at finite temperature.

Four distinct scaling regions identified: classical disordered, quantum disordered, quantum critical, thermal.

Zero temperature transition persists, shaping the crossover phase diagram.

Abstract

The low temperature phase diagram of 1D weakly disordered quantum systems like charge or spin density waves and Luttinger liquids is studied by a \emph{full finite temperature} renormalization group (RG) calculation. For vanishing quantum fluctuations this approach is amended by an \emph{exact} solution in the case of strong disorder and by a mapping onto the \emph{Burgers equation with noise} in the case of weak disorder, respectively. At \emph{zero} temperature we reproduce the quantum phase transition between a pinned (localized) and an unpinned (delocalized) phase for weak and strong quantum fluctuations, respectively, as found previously by Fukuyama or Giamarchi and Schulz. At \emph{finite} temperatures the localization transition is suppressed: the random potential is wiped out by thermal fluctuations on length scales larger than the thermal de Broglie wave length of the phason excitations. The existence of a zero temperature transition is reflected in a rich cross-over phase diagram of the correlation functions. In particular we find four different scaling regions: a \emph{classical disordered}, a \emph{quantum disordered}, a \emph{quantum critical} and a \emph{thermal} region. The results can be transferred directly to the discussion of the influence of disorder in superfluids. Finally we extend the RG calculation to the treatment of a commensurate lattice potential. Applications to related systems are discussed as well.