The XXZ spin chain at Δ=−1/2: Bethe roots, symmetric functions, and determinants

DOI10.1063/1.1487445zbMath1060.82012arXivmath-ph/0110011OpenAlexW2168001509MaRDI QIDQ4832712

Bernard Nienhuis, Saibal Mitra, Jan De Gier, Murray T. Batchelor

Publication date: 14 December 2004

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

Full work available at URL: https://arxiv.org/abs/math-ph/0110011

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Exactly solvable models; Bethe ansatz (82B23) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (15)

Exact densities of loops in O(1) dense loop model and of clusters in critical percolation on a cylinder: II. Rotated lattice ⋮ The eight-vertex model and lattice supersymmetry ⋮ Spin chains with dynamical lattice supersymmetry ⋮ Laws of large numbers in the raise and peel model ⋮ Symmetry classes of alternating sign matrices in a nineteen-vertex model ⋮ On Baxter's Q operator of the higher spin XXZ chain at the Razumov-Stroganov point ⋮ New developments in the eight vertex model. II: Chains of odd length ⋮ Exact results for the σ^ztwo-point function of theXXZchain at Δ = 1/2 ⋮ Fully Packed Loop Models on Finite Geometries ⋮ Bethe roots and refined enumeration of alternating-sign matrices ⋮ Free energy of the eight-vertex model with an odd number of lattice sites ⋮ Loops, matchings and alternating-sign matrices ⋮ The open XXZ chain at Δ = −1/2 and the boundary quantum Knizhnik–Zamolodchikov equations ⋮ Open spin chains with dynamic lattice supersymmetry ⋮ Exact densities of loops in O(1) dense loop model and of clusters in critical percolation on a cylinder

Cites Work

• Unnamed Item
• Calculation of norms of Bethe wave functions
• \(O(1)\) loop model with different boundary conditions and symmetry classes of alternating-sign matrices
• Alternating sign matrices and descending plane partitions
• Determinants and alternating sign matrices
• Conformal invariance, the XXZ chain and the operator content of two- dimensional critical systems
• A \textit{Mathematica} version of Zeilberger's algorithm for proving binomial coefficient identities
• Four symmetry classes of plane partitions under one roof
• Combinatorial nature of the ground-state vector of the \(\mathrm{O}(1)\) loop model
• The importance of being odd
• The quantum symmetricXXZchain at Δ = -½, alternating-sign matrices and plane partitions
• Temperley Lieb stochastic processes
• Ground state of the quantum symmetric finite-size XXZ spin chain with anisotropy parameter Delta = ½
• Spin chains and combinatorics
• Spin chains and combinatorics: twisted boundary conditions
• Finite size \(XXZ\) spin chain with anisotropy parameter \(\Delta=\frac 12\)

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