Effective actions for spin ladders

Abstract

We derive a path-integral expression for the effective action in the continuum limit of an AFM Heisenberg spin ladder with an arbitrary number of legs. The map is onto an $O(3)$ nonlinear $\sigma$-model (NL$\sigma$M) with the addition of a topological term that is effective only for odd-legged ladders and half-odd integer spins. We derive the parameters of the effective NL$\sigma$M and the behaviour of the spin gap for the case of even-legged ladders.

Final version, as published in Phys. Rev. Lett

References in corpus (10)

• Correlated Electrons in High Temperature Superconductors
• Surprises on the Way from 1D to 2D Quantum Magnets: the Novel Ladder Materials
• Resonating Valence Bond Theory of Coupled Heisenberg Chains
• The susceptibility and excitation spectrum of (VO)${}_2$P${}_2$O${}_7$ in ladder and dimer chain models
• A Monte Carlo Study of Correlations in Quantum Spin Ladders
• The Non Linear Sigma Model and Spin Ladders
• Singlet pairing in the double chain t-J model
• Semiclassical description of spin ladders
• Renormalization-Group Approach to a Three-Legs Fermionic Ladder
• Correlation functions in the three-chain Hubbard ladder

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