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

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 $1\le m,n\le 2$, 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.

44 pages, 10 figures. Minor corrections, references added

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Cited by in corpus (5)

• The open Haldane-Shastry chain: thermodynamics and criticality
• A novel class of translationally invariant spin chains with long-range interactions
• Thermodynamics and criticality of su($m$) spin chains of Haldane-Shastry type
• Supersymmetric $t$-$J$ models with long-range interactions: thermodynamics and criticality
• Supersymmetric $t$-$J$ models with long-range interactions: partition function and spectrum