Spin chains and Gustafson’s integrals

DOI10.1088/1751-8121/aa749azbMath1377.82012arXiv1611.09593OpenAlexW3102164678MaRDI QIDQ5348273

Sergey E. Derkachov, Alexander N. Manashov

Publication date: 15 August 2017

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.09593

zbMATH Keywords

Yang-Baxter equationspin chainsGustafson integrals

Mathematics Subject Classification ID

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Basic hypergeometric integrals and functions defined by them (33D60) Yang-Baxter equations (16T25)

Related Items

Integrability in heavy quark effective theory, Gustafson integrals for $SL(2, \mathbb{C})$ spin magnet, Unitarity of the SoV transform for \(\mathrm{SL}(2,\mathbb{C})\) spin chains, On Gustafson integrals for the group \(\mathrm{SL}(2,\mathbb{R} )\), Gamma function solutions to the star-triangle equation, Fishnet four-point integrals: integrable representations and thermodynamic limits, Quantum integrability and quantum groups: a special issue in memory of Petr P Kulish, \(\mathrm{SL}(2,\mathbb{C})\) Gustafson integrals, Completeness of SoV representation for \(\mathrm{SL}(2,\mathbb{R})\) spin chains, Lens elliptic gamma function solution of the Yang–Baxter equation at roots of unity, On complex gamma-function integrals, The \(6j\)-symbols for the \(SL(2,\mathbb{C})\) group

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Elliptic hypergeometry of supersymmetric dualities
• Inversions of integral operators and elliptic beta integrals on root systems
• Quantum inverse problem method. I
• Yang-Baxter equation and representation theory. I
• Unitarity of the SoV transform for the Toda chain
• Short proofs of the elliptic beta integrals
• Transition function for the Toda chain
• Quantum mechanics of null polygonal Wilson loops
• Tensor product spaces
• Iterative construction of eigenfunctions of the monodromy matrix for $SL(2,\mathbb {C})$ magnet
• New solutions of the star–triangle relation with discrete and continuous spin variables
• The importance of the Selberg integral
• Some Hypergeometric Orthogonal Polynomials
• Some q-Beta and Mellin–Barnes Integrals with Many Parameters Associated to the Classical Groups
• Some q-Beta and Mellin-Barnes Integrals on Compact Lie Groups and Lie Algebras
• Some q-Beta Integrals on $SU(n)$ and $Sp(n)$ That Generalize the Askey–Wilson and Nasrallah–Rahman Integrals
• Theta hypergeometric integrals
• Boundary conditions for integrable quantum systems
• Comment on star–star relations in statistical mechanics and elliptic gamma-function identities
• On $BC$ type basic hypergeometric orthogonal polynomials
• Baxter'sQ-operator for the homogeneousXXXspin chain
• Factorization of the transfer matrices for the quantumsell(2) spin chains and Baxter equation
• A new solution of the star–triangle relation
• Noncompact Heisenberg spin magnets from high-energy QCD. I: Baxter Q-operator and separation of variables