Low temperature dynamics of nonlinear Luttinger liquids

C Karrasch,J Sirker,R G Pereira

doi:10.1088/1367-2630/17/10/103003

Abstract

We develop a general nonlinear Luttinger liquid theory to describe the dynamics of one-dimensional quantum critical systems at low temperatures. To demonstrate the predictive power of our theory we compare results for the autocorrelation G(t) in the XXZ chain with numerical density-matrix renormalization group data and obtain excellent agreement. Our calculations provide, in particular, direct evidence that G(t) shows a diffusion-like decay, in sharp contrast to the exponential decay in time predicted by conventional Luttinger liquid theory.

Highlights

The dynamics of quantum critical systems at finite temperatures is an outstanding challenge in many-body physics [1]
Studies of ground state dynamical correlations have recently forced us to revise our understanding of quasiparticles in critical 1D systems [12,13,14,15,16,17,18,19,20], culminating with the development of the nonlinear Luttinger liquid (NLL) theory [21]
Rather than exploring the full space–time dependence of the spin–spin correlation function, here we focus on the autocorrelation since our main goal is to analyze the asymptotic long-time behavior where conventional Luttinger liquid theory breaks down. (More generally, for correlations at finite distance r the high-energy contributions associated with band edge modes are observed inside the light cone for times t r v.) Non-zero temperatures are incorporated via a purification of the density matrix

Summary

September 2015

Any further distribution of We develop a general nonlinear Luttinger liquid theory to describe the dynamics of one-dimensional this work must maintain quantum critical systems at low temperatures. To demonstrate the predictive power of our theory we attribution to the author(s) and the title of compare results for the autocorrelation G(t) in the XXZ chain with numerical density-matrix the work, journal citation and DOI. Renormalization group data and obtain excellent agreement. In particular, direct evidence that G(t) shows a diffusion-like decay, G (t ) ~ 1 t , in sharp contrast to the exponential decay in time predicted by conventional Luttinger liquid theory

Introduction

Noninteracting case

Interacting case

Diffusive decay

Numerical results

Conclusion