An Intersecting Loop Model as a Solvable Super Spin Chain

TL;DR

This paper explores an integrable loop model linked to a supersymmetric spin chain, providing Bethe Ansatz solutions, conjectures on central charge, and insights into low-lying excitations and conformal field theories.

Contribution

It introduces a solvable super spin chain model based on an intersecting loop model and analyzes its properties using Bethe Ansatz, including conjectures on central charge and excitation behavior.

Findings

Conjecture that the central charge c=q-1 for integer q<2.

Evidence of superdiffusive behavior at q=1.

Identification of the model as an example of c ≤ 0 conformal field theories.

Abstract

In this paper we investigate an integrable loop model and its connection with a supersymmetric spin chain. The Bethe Ansatz solution allows us to study some properties of the ground state. When the loop fugacity $q$ lies in the physical regime, we conjecture that the central charge is $c=q-1$ for $q$ integer $< 2$. Low-lying excitations are examined, supporting a superdiffusive behavior for $q=1$. We argue that these systems are interesting examples of integrable lattice models realizing $c \leq 0$ conformal field theories.