A Temperley-Lieb quantum chain with two- and three-site interactions

TL;DR

This paper investigates a quantum spin chain with novel two- and three-site interactions, revealing a complex phase diagram with exactly solvable points and extending understanding of anyon models beyond previously studied cases.

Contribution

It introduces a new quantum chain model with combined two- and three-site interactions, providing exact results and exploring its phase diagram for real loop weights.

Findings

Rich phase diagram with gapped and critical phases

Exactly solvable points identified within the model

Extension of anyon model analysis to real loop weights

Abstract

We study a quantum chain of spin-1/2 particles whose world lines form a loop gas. In addition to the usual interaction that projects a pair of neighboring spins onto quantum-group spin 0, we introduce a three-site interaction that projects onto spin 3/2. Changing the relative strengths of these interactions leads to a rich phase diagram containing gapped and critical phases, and exactly solvable points. For loop weight $n=2 \cos [\pi/(p+1)]$, the model corresponds to N=p-3 species of interacting anyons, of which only the Fibonacci case N=1 was studied previously. Our study applies to real n, and provides further exact results which were unnoticed even for the special case N=1.