Ferromagnetic ordering of energy levels for \(\mathrm{U}_q(\mathfrak{sl}_2)\) symmetric spin chains

DOI10.1007/s11005-011-0538-1zbMath1251.82011arXiv1105.5264OpenAlexW3122449526MaRDI QIDQ454338

Shannon Starr, Stephen Ng, Bruno Nachtergaele

Publication date: 1 October 2012

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

Full work available at URL: https://arxiv.org/abs/1105.5264

zbMATH Keywords

Temperley-Lieb algebraasymmetric simple exclusion processordering of energy levelsXXZ Heisenberg chain

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Quantum equilibrium statistical mechanics (general) (82B10) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items

Riordan trees and the homotopy \(sl_{2}\) weight system, A generalized asymmetric exclusion process with \(U_q(\mathfrak {sl}_2)\) stochastic duality

Cites Work

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• Categorifying fractional Euler characteristics, Jones-Wenzl projectors and \(3j\)-symbols
• 2-block Springer fibers: convolution algebras and coherent sheaves
• Proof of the Razumov-Stroganov conjecture
• The ordering of energy levels for \(\text{su}(n)\) symmetric antiferromagnetic chains
• Ordering of energy levels for extended \(SU(N)\) Hubbard chain
• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• A q-analogue of Young symmetrizer
• Reaction-diffusion processes, critical dynamics, and quantum chains
• 3-valent graphs and the Kauffman bracket
• Geometric aspects of quantum spin states
• The spectral gap of the ferromagnetic \(XXZ\) chain
• Canonical bases in tensor products and graphical calculus for \(U_ q(sl_ 2)\)
• Symmetry classes of alternating-sign matrices under one roof
• The representation theory of the Temperley-Lieb algebras
• Ferromagnetic ordering of energy levels
• Duality and hidden symmetries in interacting particle systems
• Jones-Wenzl idempotents for rank 2 simple Lie algebras
• Quantum Heisenberg models and their probabilistic representations
• Ordering Energy Levels of Interacting Spin Systems
• Proof of Aldous’ spectral gap conjecture
• Quantum Heisenberg ferromagnets and stochastic exclusion processes
• Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134)
• Ordering of Energy Levels in Heisenberg Models and Applications
• Quantum invariants of knots and 3-manifolds