Finite size properties of staggered $U_q[sl(2|1)]$ superspin chains

TL;DR

This paper analyzes the finite size properties of a superspin chain derived from the $U_q[sl(2|1)]$ algebra, revealing critical behaviors, conformal dimensions, and effective theories across different regimes of the deformation parameter.

Contribution

It provides an exact solution for the superspin chain's eigenvalues and explores its critical properties, including central charge and conformal dimensions, across various deformation regimes.

Findings

Critical line with $c=0$ and conformal dimensions depending on $ ext{gamma}$.

In the ferromagnetic regime, the model exhibits $c=-1$ with continuously varying exponents.

Finite size spectrum shows spin-charge separation and matches the $U_q[osp(2|2)]$ spin chain.

Abstract

Based on the exact solution of the eigenvalue problem for the $U_q[sl(2|1)]$ vertex model built from alternating 3-dimensional fundamental and dual representations by means of the algebraic Bethe ansatz we investigate the ground state and low energy excitations of the corresponding mixed superspin chain for deformation parameter $q=\exp(-i\gamma/2)$. The model has a line of critical points with central charge $c=0$ and continua of conformal dimensions grouped into sectors with $\gamma$-dependent lower edges for $0\le\gamma<\pi/2$. The finite size scaling behaviour is consistent with a low energy effective theory consisting of one compact and one non-compact bosonic degree of freedom. In the 'ferromagnetic' regime $\pi<\gamma\le2\pi$ the critical theory has $c=-1$ with exponents varying continuously with the deformation parameter. Spin and charge degrees of freedom are separated in the finite size spectrum which coincides with that of the $U_q[osp(2|2)]$ spin chain. In the intermediate regime $\pi/2<\gamma<\pi$ the finite size scaling of the ground state energy depends on the deformation parameter.