Thermodynamics and criticality of supersymmetric spin chains of Haldane-Shastry type

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 A_{N-1} and the BC_{N} 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 multilevel 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 A_{N-1} and the su(m|n) HS chain of BC_{N} type with m=1,2,3 (when the sign ɛ_{B} in the Hamiltonian takes the value -1 in the latter case) are truly critical.