Quantum spin chains and the Haldane gap

1989/05/15 by Ian Affleck · 6 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Computer science #Condensed matter physics #Excitation #Field (mathematics) #Integer (computer science) #Mathematics #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum #Quantum mechanics #Spin (aerodynamics) #Theoretical and Computational Physics #Theoretical physics

paper · doi:10.1088/0953-8984/1/19/001

openalex publication_date 1989/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

One-dimensional antiferromagnets have exotic disordered ground states. As was first argued by Haldane (1983), there is an excitation gap for integer, but not half-integer, spin. The authors review the arguments for this behaviour based on field-theory mappings, the Lieb-Schultz-Mattis theorem, exactly solvable models, finite-chain diagonalisation and real experiments.

Citations

• Critical theory of quantum spin chains
• Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State
• On Next-Nearest-Neighbor Interaction in Linear Chain. I
• The critical properties of the two-dimensional xy model
• Ordering, metastability and phase transitions in two-dimensional systems
• Two soluble models of an antiferromagnetic chain
• Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models
• Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model

Cited by

• Magnetization Transport and Quantized Spin Conductance
• Cluster-Based Haldane State in an Edge-Shared Tetrahedral Spin-Cluster Chain: Fedotovite K2Cu3O(SO4)3
• Self-consistent large-N analytical solutions of inhomogeneous condensates in quantum ℂPN − 1 model
• Renormalization of the vacuum angle for a particle on a ring
• Integrable models and quantum spin ladders: comparison between theory and experiment for the strong coupling ladder compounds
• Topological order [wikipedia]