Quantum Spin Chains: Phase Behaviour and Dynamic Excitations

Abstract

Conventional ideas on the phase behavior (at temperature T = 0) of antiferromagnetic (AFM) quantum spin chains have recently been challenged by an interesting conjecture of HALDANE [1]. According to Haldane, half-integer spin chains should behave like the exactly solvable spin-1/2 XXZ model, with a gapless phase for planar anisotropy terminating at an essential singularity at the Heisenberg point, and a phase with long-range order in the ground state together with an excitation energy gap in the case of uniaxial anisotropy. Integer-spin systems, on the other hand, may show an additional phase (subsequently referred to as the “Heisenberg phase”) with a non-ordered ground state together with an excitation energy gap, which encompasses the Heisenberg point. This behavior is shown schematically in Fig. 1, where the parameters are defined through the XXZ AFM Hamiltonian: $$H = J\sum\limits_{i = 1}^N {\left( {S_i^XS_{i + 1}^X + S_i^XS_{i + 1}^X + \lambda _i^XS_{i + 1}^X} \right)} $$ (1) .