Thermodynamics and criticality of su($m$) spin chains of Haldane-Shastry type

• URL: http://arxiv.org/abs/2208.04014v1
• Date: Mon, 8 Aug 2022 09:52:37 GMT
• Title: Thermodynamics and criticality of su($m$) spin chains of Haldane-Shastry type
• Authors: Federico Finkel and Artemio Gonz\'alez-L\'opez
• Abstract summary: We study the thermodynamics and critical behavior of su($m$) spin chains of Haldane-Shastry type at zero chemical potential. We derive explicit formulas for the energy, entropy and specific heat per spin.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the thermodynamics and critical behavior of su($m$) spin chains of Haldane-Shastry type at zero chemical potential, both in the $A_{N-1}$ and $BC_N$ cases. We evaluate in closed form the free energy per spin for arbitrary values of $m$, from which we derive explicit formulas for the energy, entropy and specific heat per spin. In particular, we find that the specific heat features a single Schottky peak, whose temperature is well approximated for $m\lesssim10$ by the corresponding temperature for an $m$-level system with uniformly spaced levels. We show that at low temperatures the free energy per spin of the models under study behaves as that of a one-dimensional conformal field theory with central charge $c=m-1$ (with the only exception of the Frahm-Inozemtsev chain with zero value of its parameter). However, from a detailed study of the ground state degeneracy and the low-energy excitations, we conclude that these models are only critical in the antiferromagnetic case, with a few exceptions that we fully specify.

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