The geometry of antiferromagnetic spin chains

Abstract

We construct spin chains that describe relativistic sigma-models in the continuum limit, using symplectic geometry as a main tool. The target space can be an arbitrary complex flag manifold, and we find universal expressions for the metric and theta-term.

31 pages, 3 figures

References in corpus (1)

• Haldane limits via Lagrangian embeddings

Cited by in corpus (22)

• Anomaly and global inconsistency matching: $\theta$-angles, $SU(3)/U(1{)}^2$ nonlinear sigma model, $SU(3)$ chains and its generalizations
• Generalization of the Haldane conjecture to SU(3) chains
• Dual simulation of the 2d U(1) gauge Higgs model at topological angle $\theta =\pi$: Critical endpoint behavior
• Sigma Models on Flags
• Flag manifold sigma models: spin chains and integrable theories
• Generalization of the Haldane conjecture to SU($n$) chains
• Flag manifold sigma-models: the 1/N-expansion and the anomaly two-form
• Anomalies and unnatural stability of multi-component Luttinger liquids in ${\mathbb{Z}}_n\times {\mathbb{Z}}_n$ spin chains
• Haldane Gap of the Three-Box Symmetric $\mathrm{SU}(3)$ Chain
• Mass generation by fractional instantons in SU($n$) chains
• Topological terms of (2+1)d flag-manifold sigma models
• Symmetry-protected topological phases in the SU(N) Heisenberg spin chain: a Majorana-fermion approach
• Flag manifold sigma models from SU($n$) chains
• An Index for Quantum Integrability
• The classical and quantum particle on a flag manifold
• Winding theta and destructive interference of instantons
• Ricci-flat metrics on vector bundles over flag manifolds
• Grassmannian and Flag sigma models on interval: phase structure and L-dependence
• Sigma-model analysis of $SU(3)$ antiferromagnetic spins on the triangular lattice
• Density Matrix Renormalization Group simulations of the SU(N) Fermi-Hubbard chain implementing the full SU(N) symmetry via Semi-Standard Young Tableaux and Unitary Group Subduction Coefficients
• Oscillator Calculus on Coadjoint Orbits and Index Theorems
• Edge states and universality class of the critical two-box symmetric SU(3) chain