Anomalous thermodynamics of a quantum spin system with large residual entropy

Abstract

In contrast to strongly frustrated classical systems, their quantum counterparts typically have a non-degenerate ground state. A counterexample is the celebrated Heisenberg sawtooth spin chain with ferromagnetic zigzag bonds J_1 and competing antiferromagnetic basal bonds J_2. At a quantum phase transition point |J_2/J_1|=1/2, this model exhibits a flat one-magnon excitation band leading to a massively degenerate ground-state manifold which results in a large residual entropy. Thus, for the spin-half model, the residual entropy amounts to exactly one half of its maximum value lim_{T→ ∞} S(T)/N = ln2. In the present paper we study in detail the role of the spin quantum number s and the magnetic field H in the parameter region around the transition (flat-band) point. For that we use full exact diagonalization up to N = 20 lattice sites and the finite-temperature Lanczos method up to N = 36 sites to calculate the density of states as well as the temperature dependence of the specific heat, the entropy and the susceptibility. The study of chain lengths up to N = 36 allows a careful finite-size analysis. At the flat-band point we find extremely small finite-size effects for spin s = 1/2, i.e., the numerical data virtually correspond to the thermodynamic limit. In all other cases the finite-size effects are still small and become visible at very low temperatures. In a sizeable parameter region around the flat-band point the former massively degenerate ground-state manifold acts as a large manifold of low-lying excitations leading to extraordinary thermodynamic properties at the transition point as well as in its vicinity such as an additional low-temperature maximum in the specific heat. Moreover, there is a very strong influence of the magnetic field on the low-temperature thermodynamics including an enhanced magnetocaloric effect.

Keywords

• quantum heisenberg model
• frustration
• sawtooth chain
• residual entropy