Density matrices in integrable face models

TL;DR

This paper develops a method to express local operators and derive functional equations for reduced density matrices in integrable face models, enabling explicit correlation function calculations for complex quantum systems.

Contribution

It introduces a novel approach to relate local operators to transfer matrices and derives functional equations for density matrices in inhomogeneous IRF models, expanding analytical tools for quantum integrable systems.

Findings

Density matrices can be factorized into nearest-neighbour correlators.

Explicit correlation functions are obtained for up to three sites.

Method applies to models with non-Abelian anyons and solid-on-solid types.

Abstract

Using the properties of the local Boltzmann weights of integrable interaction-round-a-face (IRF or face) models we express local operators in terms of generalized transfer matrices. This allows for the derivation of discrete functional equations for the reduced density matrices in inhomogeneous generalizations of these models. We apply these equations to study the density matrices for IRF models of various solid-on-solid type and quantum chains of non-Abelian $\bm{su(2)_3}$ or Fibonacci anyons. Similar as in the six vertex model we find that reduced density matrices for a sequence of consecutive sites can be 'factorized', i.e.\ expressed in terms of nearest-neighbour correlators with coefficients which are independent of the model parameters. Explicit expressions are provided for correlation functions on up to three neighbouring sites.