The geometry of antiferromagnetic spin chains

DOI10.1007/s00220-013-1702-5zbMath1278.81133arXiv1206.2777OpenAlexW3101362961MaRDI QIDQ358801

Dmitri Bykov

Publication date: 9 August 2013

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.2777

zbMATH Keywords

spin chain\(\sigma\)-modelantiferromagnetic vacuasympletic geometry

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Quantum field theory on curved space or space-time backgrounds (81T20) Continuum limits in quantum field theory (81T27) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Statistical mechanics of magnetic materials (82D40)

Related Items (9)

Flag manifold sigma models from \(\mathrm{SU}(n)\) chains ⋮ Flag manifold sigma models. Spin chains and integrable theories ⋮ Generalization of the Haldane conjecture to \(\operatorname{SU}(3)\) chains ⋮ Ricci-flat metrics on vector bundles over flag manifolds ⋮ Winding \(\theta\) and destructive interference of instantons ⋮ Flag manifold $\sigma$-models: the $\frac{1}{N}$-expansion and the anomaly two-form ⋮ Generalization of the Haldane conjecture to \(\mathrm{SU}(n)\) chains ⋮ Dual simulation of the 2d \(\operatorname{U}(1)\) gauge Higgs model at topological angle \(\theta = \pi\): Critical endpoint behavior ⋮ Grassmannian and flag sigma models on interval: phase structure and L-dependence

Cites Work

• General concept of quantization
• Haldane limits via Lagrangian embeddings
• On the topology of Lagrangian submanifolds examples and counter-examples
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