Haldane gap in the quasi one-dimensional nonlinear $\sigma$-model

Abstract

This work studies the appearance of a Haldane gap in quasi one-dimensional antiferromagnets in the long wavelength limit, via the nonlinear $\sigma$-model. The mapping from the three-dimensional, integer spin Heisenberg model to the nonlinear $\sigma$-model is explained, taking into account two antiferromagnetic couplings: one along the chain axis ($J$) and one along the perpendicular planes ($J_{\perp }$) of a cubic lattice. An implicit equation for the Haldane gap is derived, as a function of temperature and coupling ratio $J_{\perp }/J$. Solutions to these equations show the existence of a critical coupling ratio beyond which a gap exists only above a transition temperature $T_N$. The cut-off dependence of these results is discussed.

14 pages (RevTeX 3.0), 3 PostScript figures appended (printing instructions included)

References in corpus (1)

• The Mass Gap of the Nonlinear Sigma Model through the Finite Temperature Effective Action

Cited by in corpus (5)

• Semiclassical description of spin ladders
• Low Temperature Dynamics of Magnons in a Spin-1/2 Ladder Compound
• Microscopic model for Bose-Einstein condensation and quasiparticle decay
• Bond Randomness Induced Magnon Decoherence in a Spin-1/2 Ladder Compound
• Magnon bands of N-leg integer-spin antiferromagnetic systems in the weak interchain-coupling regime