Phase Diagram of an Integrable Alternating $U_q[sl(2|1)]$ Superspin Chain

TL;DR

This paper investigates the phase diagram of an integrable superspin chain derived from the quantum group deformation of the Lie superalgebra sl(2|1), analyzing its low energy properties and critical phases.

Contribution

It constructs a new integrable vertex model based on four-dimensional representations of U_q[sl(2|1)] and explores its phase diagram using analytical and numerical methods.

Findings

Identification of different phases as functions of parameters b and gamma

Characterization of critical theories via operator content and symmetries

Discovery of logarithmic corrections in the spectrum due to non-U(1) modes

Abstract

We construct a family of integrable vertex model based on the typical four-dimensional representations of the quantum group deformation of the Lie superalgebra $sl(2|1)$. Upon alternation of such a representation with its dual this model gives rise to a mixed superspin Hamiltonian with local interactions depending on the representation parameter $\pm b$ and the deformation parameter ${\gamma}$. As a subsector this model contains integrable vertex models with ordinary symmetries for twisted boundary conditions. The thermodynamic limit and low energy properties of the mixed superspin chain are studied using a combination of analytical and numerical methods. Based on these results we identify the phases realized in this system as a function of the parameters $b$ and $\gamma$. The different phases are characterized by the operator content of the corresponding critical theory. Only part of the spectrum of this effective theory can be understood in terms of the U(1) symmetries related to the physical degrees of freedom corresponding to spin and charge. The other modes lead to logarithmic finite-size corrections in the spectrum of the theory.