Non-Abelian ${SU}{(3)}_{k}$ anyons: inversion identities for higher rank face models

DOI10.1088/1751-8113/48/48/484001zbMath1334.82068arXiv1506.00822OpenAlexW2207621864MaRDI QIDQ3458723

Nikos Karaiskos, Holger Frahm

Publication date: 21 December 2015

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

Full work available at URL: https://arxiv.org/abs/1506.00822

zbMATH Keywords

integrable modelsIRF modelstransfer matrix identities

Mathematics Subject Classification ID

PDEs in connection with quantum mechanics (35Q40) Statistical mechanics of solids (82D20) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) PDEs in connection with statistical mechanics (35Q82)

Related Items

Exactly solved models and beyond: a special issue in honour of R J Baxter’s 75th birthday, New construction of eigenstates and separation of variables for SU(\(N\)) quantum spin chains, Condensation of non-Abelian ${SU(3)_{N_f}}$ anyons in a one-dimensional fermion model

Cites Work

• Unnamed Item
• Unnamed Item
• Inversion identities for inhomogeneous face models
• Integrable anyon chains: from fusion rules to face models to effective field theories
• Separation of variables in the open \(XXX\) chain
• Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities
• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• Etiology of IRF models
• The \(A_ n^{(1)}\) face models
• Yang-Baxter equation and representation theory. I
• Separation of variables in the quantum integrable models related to the Yangian \(\mathcal Y [sl (3)\)]
• Solution of functional equations of restricted \(A^{(1)}_{n-1}\) fused lattice models
• Dynamical symmetry of integrable quantum systems
• Off-diagonal Bethe ansatz solution of the XXX spin chain with arbitrary boundary conditions
• Off-diagonal Bethe ansatz solutions of the anisotropic spin-\(\frac{1}{2}\) chains with arbitrary boundary fields
• Partition function of the eight-vertex lattice model
• Families of solutions of the nested Bethe ansatz for theA₂spin chain
• Diagonalisation of GL(N) invariant transfer matrices and quantum N-wave system (Lee model)
• Restricted solid-on-solid models connected with simply laced algebras and conformal field theory
• Bosonization of vertex operators for the face model
• From spin to anyon notation: the XXZ Heisenberg model as aD₃(orsu(2)₄) anyon chain
• Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction
• Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain. I: Some fundamental eigenvectors.
• Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain. III: Eigenvectors of the transfer matrix and Hamiltonian.
• Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain. II: Equivalence to a generalized ice-type lattice model.