The quantum symmetricXXZchain at Δ = -½, alternating-sign matrices and plane partitions

2001/01/25 by Murray T. Batchelor, M. T. Batchelor, Jan de Gier +3 · 4 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Antiferromagnetism #Boundary (topology) #Boundary value problem #Chain (unit) #Geometry #Ground state #Mathematical analysis #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Plane (geometry) #Quantum #Quantum many-body systems #Quantum mechanics #Sign (mathematics) #Symmetry (geometry) #Wave function #cond-mat.stat-mech #math.CO

paper · pdf · doi:10.1088/0305-4470/34/19/101

published as J.Phys.A 34 (2001) L265-L270 · 7 pages, Latex

arxiv created 2001/01/25 · openalex publication_date 2001/05/02 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We consider the ground-state wavefunction of the quantum symmetric antiferromagnetic XXZ chain with open and twisted boundary conditions at Δ = -½, along with the ground-state wavefunction of the corresponding O( n ) loop model at n = 1. Based on exact results for finite-size systems, sums involving the wavefunction components, and in some cases the largest component itself, are conjectured to be directly related to the total number of alternating-sign matrices and plane partitions in certain symmetry classes.

Citations

• Spin chains and combinatorics
• Critical behaviour and conformal anomaly of the O(n) model on the square lattice

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