Haldane Gap Spin Chains: Behaviour at Finite Temperatures and Fields

Jack A. Tuszyński, J.M. Dixon

Masaki Oshikawa

Ian K. Affleck

One-dimensional antiferromagnets have exotic disordered ground states. As was first argued by Haldane (1983), there is an excitation gap for integer, but not half-integer, spin. The authors review the arguments for this behaviour based on field-theory mappings, the Lieb-Schultz-Mattis theorem, exactly solvable models, finite-chain diagonalisation and real experiments.

Jean‐Philippe Boucher

Robert Konik

We study both the static and dynamic properties of gapped, one-dimensional, Heisenberg, antiferromagnetic, spin chains at finite temperature through an analysis of the O(3) nonlinear sigma model. Exploiting the integrability of this theory, we are able to compute an exact low-temperature expansion of the finite temperature correlators. We do so using a truncated ``form-factor'' expansion and so provide evidence that this technique can be successfully extended to finite temperature. As a direct test, we compute the static zero-field susceptibility and obtain an exact match to the susceptibility derived from the low-temperature expansion of the exact free energy. We also study transport properties, computing both the spin conductance and the NMR-relaxation rate, ${1/T}_{1}.$ We find these quantities to show ballistic behavior. In particular, the computed spin conductance exhibits a nonzero Drude weight at finite temperature and zero applied field. The physics thus described differs from the spin diffusion reported by Takigawa et al. [Phys. Rev. Lett. 76, 2173 (1996)] from experiments on the Haldane gap material, ${\mathrm{AgVP}}_{2}{S}_{6}.$

Fabian H. L. Eßler