# Spectral flow for an integrable staggered superspin chain

## TL;DR

This paper investigates how the low energy states of a superspin chain with alternating representations evolve as boundary conditions change, revealing a flow between continuous and discrete spectrum levels.

## Contribution

It introduces a detailed analysis of spectral flow in an integrable superspin chain with mixed representations, highlighting the impact of boundary condition variations.

## Key findings

- Levels from the continuous spectrum flow into discrete levels when boundary conditions change.
- Finite size data extrapolation reveals spectrum restructuring under boundary condition variation.
- The study characterizes the spectrum using scaling dimensions and quasi momenta for two transfer matrix families.

## Abstract

The flow of the low energy eigenstates of a $U_q[sl(2|1)]$ superspin chain with alternating fundamental ($3$) and dual ($\bar{3}$) representations is studied as function of a twist angle determining the boundary conditions. The finite size spectrum is characterized in terms of scaling dimensions and quasi momenta representing the two families of commuting transfer matrices for the model which are even and odd under the interchange $3\leftrightarrow \bar{3}$, respectively. Based on the extrapolation of our finite size data we find that under a variation of the boundary conditions from periodic to antiperiodic for the fermionic degrees of freedom levels from the continuous part of the spectrum flow into discrete levels and vice versa.