Thermodynamics and criticality of supersymmetric spin chains with long-range interactions

TL;DR

This paper analyzes the thermodynamics and critical phenomena of supersymmetric long-range spin chains, deriving exact formulas for their partition functions and free energy, and identifying phase transitions and critical regions.

Contribution

It provides a closed-form partition function and an analytic free energy expression for supersymmetric spin chains, revealing new phase transition behaviors.

Findings

Exact partition function derived for supersymmetric chains

Identification of critical regions and central charges

Discovery of first-order phase transitions at zero temperature

Abstract

We study the thermodynamics and critical behavior of su($m|n$) supersymmetric spin chains of Haldane-Shastry type with a chemical potential term. We obtain a closed-form expression for the partition function and deduce a description of the spectrum in terms of the supersymmetric version of Haldane's motifs, which we apply to obtain an analytic expression for the free energy per site in the thermodynamic limit. By studying the low-temperature behavior of the free energy, we characterize the critical behavior of the chains with $1\le m,n\le2$, determining the critical regions and the corresponding central charge. We also show that in the su($2|1$), su($1|2$) and su($2|2$) chains the bosonic or fermionic densities can undergo first-order (discontinuous) phase transitions at $T=0$, in contrast with the previously studied su(2) case.