2024/07/18 by B. Basu-Mallick, Basu-Mallick, Bireswar, Federico Finkel +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Protein Structure and Dynamics #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2407.13827
openalex publication_date 2024/07/18 · openalex created_date 2025/01/05 · openalex updated_date 2026/07/28
We introduce a novel family of translationally-invariant su(m|n) supersymmetric spin chains with long-range interaction not directly associated to a root system. We study the symmetries of these models, establishing in particular the existence of a boson-fermion duality characteristic of this type of systems. Taking advantage of the relation of the new chains with an associated many-body supersymmetric spin dynamical model, we are able to compute their partition function in closed form for all values of m and n and for an arbitrary number of spins. When both m and n are even, we show that the partition function factorizes as the product of the partition functions of two supersymmetric Haldane-Shastry spin chains, which in turn leads to a simple expression for the thermodynamic free energy per spin in terms of the Perron eigenvalue of a suitable transfer matrix. We use this expression to study the thermodynamics of a large class of these chains, showing in particular that the specific heat presents a single Schottky peak at approximately the same temperature as a suitable k-level model. We also analyze the critical behavior of the new chains, and in particular the ground state degeneracy and the existence of low energy excitations with a linear energy-momentum dispersion relation. In this way we are able to show that the only possible critical chains are the ones with m=0,1,2. In addition, using the explicit formula for the partition function we are able to establish the criticality of the su(0|n) and su(2|n) chains with even n, and to evaluate the central charge of their associated conformal field theory.