Correlation functions at the topological quantum phase transition in the S=1 XXZ chain with single-ion anisotropy

TL;DR

This paper analyzes the correlation functions at the quantum critical point of the S=1 XXZ chain with single-ion anisotropy, combining bosonization theory and DMRG simulations to reveal their asymptotic behavior and effects of bond alternation.

Contribution

It provides a detailed theoretical and numerical study of correlation functions at the topological quantum phase transition in the S=1 XXZ chain, highlighting the impact of bond alternation.

Findings

Correlation functions decay algebraically in specific sectors at criticality.

Bosonization accurately predicts the asymptotic forms of correlations.

Bond alternation introduces missing power-law components in correlations.

Abstract

We study the one-dimensional S=1 XXZ spin model with single-ion anisotropy. It is known that at the transition points between the Haldane and large-D phases, the model exhibits a quantum criticality described by the Gaussian theory, i.e., a conformal field theory with the central charge c=1. Using the bosonization approach, we investigate various correlation functions at the phase transition and derive their asymptotic forms. This allows us to clarify their peculiar behavior: the longitudinal (transverse) two-point spin correlation function has components that decay algebraically only in the uniform (staggered) sector. These theoretical predictions are verified by the numerical calculations using the density-matrix renormalization group method. The effect of weak bond alternation on the critical ground state at the phase transition is also discussed. It is shown that the bond alternation induces the missing power-law components in the correlation functions.