The open Haldane-Shastry chain: thermodynamics and criticality
- URL: http://arxiv.org/abs/2206.02651v1
- Date: Mon, 6 Jun 2022 14:41:06 GMT
- Title: The open Haldane-Shastry chain: thermodynamics and criticality
- Authors: Federico Finkel, Artemio Gonz\'alez-L\'opez
- Abstract summary: We study the thermodynamics and criticality of the su($m|n$) Haldane-Shastry chain of $BC_N$ type.
We identify the critical intervals in chemical potential space and compute their corresponding Fermi velocities.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We study the thermodynamics and criticality of the su($m|n$) Haldane-Shastry
chain of $BC_N$ type with a general chemical potential term. We first derive a
complete description of the spectrum of this model in terms of $BC_N$-type
motifs, from which we deduce a representation for the partition function as the
trace of a product of site-dependent transfer matrices. In the thermodynamic
limit, this formula yields a simple expression for the free energy per spin in
terms of the Perron-Frobenius eigenvalue of the continuum limit of the transfer
matrix. Evaluating this eigenvalue we obtain closed-form expressions for the
thermodynamic functions of the chains with $m,n\le2$. Using the motif-based
description of the spectrum derived here, we study in detail the ground state
of these models and their low energy excitations. In this way we identify the
critical intervals in chemical potential space and compute their corresponding
Fermi velocities. By contrast with previously studied models of this type, we
find in some cases two types of low energy excitations with linear
energy-quasimomentum relation. Finally, we determine the central charge of all
the critical phases by analyzing the low-temperature behavior of the expression
for the free energy per spin.
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