The Haldane phase at finite temperatures: a defect approach

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Abstract
The authors investigate a one-dimensional, spin s=1 Heisenberg antiferromagnet with exchange and single-ion anisotropy. A self-consistent approach using defects, which was recently proposed by Gomez-Santos (1989), is applied to determine the phase diagram at T=0 K and is generalised to finite temperatures. The phase diagram for exchange anisotropy constant epsilon >or=1 is in reasonable agreement with earlier numerical results; the three different phases (Neel, Haldane and large-D phases) can be characterised by the defect concentration. It is shown that the ground state and the excitations are BCS-like. The Haldane phase can be interpreted as a BCS phase in particular, and the lowest excitations, as a break-up of 'Cooper pairs'. The specific heat C exhibits a maximum. Its position Tmax increases with increasing gap energy Eg; below Tmax, there exists a regime with linear temperature dependence.