A novel translationally invariant supersymmetric chain with inverse-square interactions: partition function, thermodynamics and criticality

TL;DR

This paper introduces a new family of supersymmetric spin chains with long-range interactions, providing exact partition functions, analyzing thermodynamics, and identifying conditions for criticality and conformal field theory descriptions.

Contribution

The paper presents a novel translationally-invariant supersymmetric spin chain model with explicit partition functions and thermodynamic analysis, including critical behavior and conformal field theory connections.

Findings

Partition function computed in closed form for all parameters.

Thermodynamic properties show a Schottky peak in specific heat.

Critical chains identified with specific supersymmetry parameters.

Abstract

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.