Insights into Thermodynamics of Supersymmetric Spin Chains

Recent research by Federico Finkel and Artemio González-López has delved into the thermodynamics and criticality of supersymmetric spin chains of Haldane-Shastry type. The paper, titled "Thermodynamics and criticality of supersymmetric spin chains of Haldane-Shastry type," was submitted to arXiv on August 26, 2024, and is available for review.

The authors analyze four families of su$(m|n)$ supersymmetric spin chains related to classical root systems $A_{N-1}$ and $BC_N$. They utilize a formula that connects the thermodynamic free energy per spin of these models to the Perron eigenvalue of an inhomogeneous transfer matrix. This approach allows them to establish a relationship between the free energy of different models, enabling the evaluation of thermodynamic properties across several infinite families of these spin chains.

A significant finding of the study is the identification of a single marked Schottky peak in the specific heat at constant volume for all examined cases. This peak can be heuristically explained by approximating the model with a multi-level system featuring equally spaced energies. Furthermore, the authors explore the critical behavior of the models, revealing that the low-temperature thermodynamic free energy per spin aligns with that of a $(1+1)$-dimensional conformal field theory characterized by a central charge of $c=m+n/2-1$. However, they conclude that only specific families of chains are truly critical under certain conditions.

This research contributes to the understanding of quantum systems and their thermodynamic behaviors, potentially influencing future studies in condensed matter physics and quantum information science. The full paper can be accessed at arXiv:2408.14444.