Low temperature dynamics of nonlinear Luttinger liquids

TL;DR

This paper extends nonlinear Luttinger liquid theory to low-temperature quantum critical systems, providing new insights into spin diffusion and the effects of irrelevant interactions, validated by numerical simulations.

Contribution

It introduces a generalized nonlinear Luttinger liquid framework for low-temperature dynamics and demonstrates its accuracy through comparison with DMRG results.

Findings

Evidence for spin diffusion in the XXZ chain.

Renormalization of oscillatory frequencies and exponents.

Excellent agreement between theory and numerical data.

Abstract

We generalize nonlinear Luttinger liquid theory to describe the dynamics of one-dimensional quantum critical systems at low temperatures. Analyzing density-matrix renormalization group results for the spin autocorrelation function in the XXZ chain we provide, in particular, direct evidence for spin diffusion in sharp contrast to the exponential decay in time predicted by conventional Luttinger liquid theory. Furthermore, we discuss how the frequencies and exponents of the oscillatory contributions from the band edges are renormalized by irrelevant interactions and obtain excellent agreement between our finite temperature nonlinear Luttinger liquid theory and the numerical data.