NUMERICAL INVESTIGATION OF CORRELATION FUNCTIONS FOR THE U_qSU(2) INVARIANT SPIN-1/2 HEISENBERG CHAIN

TL;DR

This paper numerically investigates correlation functions in the U_qSU(2) invariant spin-1/2 XXZ quantum spin chain at roots of unity, revealing connections to conformal field theory and critical exponents.

Contribution

It provides a numerical analysis of correlation functions for chains up to 28 sites, linking lattice operators to conformal fields in minimal models.

Findings

Correlation functions differ with q and finite size.

Identified critical exponent -1/5 for Lee-Yang edge singularity.

Operators relate to conformal fields with spin (m-1)/(m+1).

Abstract

We consider the U_qSU(2) invariant spin-1/2 XXZ quantum spin chain at roots of unity q=exp(i*pi/(m+1)), corresponding to different minimal models of conformal field theory. We conduct a numerical investigation of correlation functions of U_qSU(2) scalar two-point operators in order to find which operators in the minimal models they correspond to. Using graphical representations of the Temperley--Lieb algebra we are able to deal with chains of up to 28 sites. Depending on q the correlation functions show different characteristics and finite size behaviour. For m=2/3, which corresponds to the Lee--Yang edge singularity, we find the surface and bulk critical exponent -1/5. Together with the known result in the case m=3 (Ising model) this indicates that in the continuum limit the two-point operators involve conformal fields of spin (m-1)/(m+1). For other roots of unity q the chains are too short to determine surface and bulk critical exponents.