Mixing of Ground States in Vertex Models

TL;DR

This paper analyzes a generalized vertex model combining different spin lines, diagonalizes the transfer matrix, and derives explicit formulas for local correlations and ground state mixing ratios using advanced algebraic methods.

Contribution

It introduces a novel mixed-spin vertex model, identifies its transfer matrix via quantum group representation theory, and computes exact mixing ratios and correlation functions.

Findings

Transfer matrix diagonalization for mixed-spin vertex models.

Explicit formulas for local correlation functions.

Exact calculation of ground state mixing ratios.

Abstract

We consider the analogue of the 6-vertex model constructed from alternating spin n/2 and spin m/2 lines, where $1\leq n<m$. We identify the transfer matrix and the space on which it acts in terms of the representation theory of $U_q(sl_2)$. We diagonalise the transfer matrix and compute the S-matrix. We give a trace formula for local correlation functions. When n=1, the 1-point function of a spin m/2 local variable for the alternating lattice with a particular ground state is given as a linear combination of the 1-point functions of the pure spin m/2 model with different ground states. The mixing ratios are calculated exactly and are expressed in terms of irreducible characters of $U_q(sl_2)$ and the deformed Virasoro algebra.