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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 vertical bar J(2)/J(1)vertical bar = 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)(->infinity) S(T)/N = ln 2. 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.