Exact asymptotic behavior of correlation functions for disordered spin-1/2 XXZ chains

TL;DR

This paper derives the exact asymptotic form of spin-correlation functions in a disordered XXZ spin-1/2 chain at zero temperature, revealing universal power law decay with logarithmic corrections near a phase transition.

Contribution

It provides the first complete asymptotic analysis of correlation functions in disordered XXZ chains, including universal power laws and logarithmic corrections at criticality.

Findings

Correlation functions decay with a universal power law.

Logarithmic corrections due to marginally irrelevant operators.

Results apply at the phase transition between liquid and disordered phases.

Abstract

We consider an XXZ spin-1/2 chain in the presence of several types of disorder that do not break the XY symmetry of the system. We calculate the complete asymptotic form of the spin-correlation functions at zero temperature at the transition between liquid and disordered phase that occurs for a special value of anisotropy in the limit of small disorder. Apart from a universal power law decay of correlations, we find additional logarithmic corrections due to marginally irrelevant operator of disorder.