A study of the Haldane gap and constraints on the low-energy physics of quantum spin chains. The manuscript follows spin coherent-state path integrals and antiferromagnetic Heisenberg chains, develops the nonlinear sigma model and its topological term, and discusses original and generalized Lieb–Schultz–Mattis theorems.
Contents
- Quantization of spin: spin coherent states and spinor path integrals.
- Spin chain models: ferromagnetic and antiferromagnetic Heisenberg chains.
- Renormalization group analysis: the SO(3) nonlinear sigma model, large-N limit, and the role of the topological term.
- The Lieb–Schultz–Mattis theorem: original theorem and generalizations.
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