2024/08/26 by Federico Finkel, Artemio González-López, Finkel, Federico +1
Physics and Astronomy · Materials Science · #Quantum many-body systems #Magnetism in coordination complexes #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2408.14444
We analyze the thermodynamics and criticality properties of four families of su(m|n) supersymmetric spin chains of Haldane-Shastry (HS) type, related to both the AN-1 and the BCN classical root systems. Using a known formula expressing the thermodynamic free energy per spin of these models in terms of the Perron (largest in modulus) eigenvalue of a suitable inhomogeneous transfer matrix, we prove a general result relating the su(kp|kq) free energy with arbitrary k=1,2,… to the su(p|q) free energy. In this way we are able to evaluate the thermodynamic free energy per spin of several infinite families of supersymmetric HS-type chains, and study their thermodynamics. In particular, we show that in all cases the specific heat at constant volume features a single marked Schottky peak, which in some cases can be heuristically explained by approximating the model with a suitable multi-level system with equally spaced energies. We also study the critical behavior of the models under consideration, showing that the low-temperature behavior of their thermodynamic free energy per spin is the same as that of a (1+1)-dimensional conformal field theory with central charge c=m+n/2-1. However, using a motif-based description of the spectrum we prove that only the three families of su(1|n) chains of type AN-1 and the su(m|n) HS chain of BCN type with m=1,2,3 (when the sign εB in the Hamiltonian takes the value -1 in the latter case) are truly critical.