Emptiness formation probability in the domain-wall six-vertex model

2007/12/10 by Filippo Colomo, F. Colomo, A. G. Pronko
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Boundary (topology) #Combinatorics #Domain (mathematical analysis) #Emptiness #Geometry #Graph #Homogeneous #Inverse #Inverse problem #Inverse scattering problem #Limit (mathematics) #Mathematical analysis #Mathematics #Physics #Quantum inverse scattering method #Quantum many-body systems #Representation (politics) #Statistical physics #Theoretical and Computational Physics #Vertex (graph theory) #Vertex model #cond-mat.stat-mech #math-ph #math.MP

paper · pdf · doi:10.1016/j.nuclphysb.2007.12.016

published as Nucl. Phys. B 798 (2008) 340-362 · 22 pages, no figures

arxiv created 2007/12/10 · openalex publication_date 2007/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08

Abstract

The emptiness formation probability in the six-vertex model with domain wall boundary conditions is considered. This correlation function allows one to address the problem of limit shapes in the model. We apply the quantum inverse scattering method to calculate the emptiness formation probability for the inhomogeneous model. For the homogeneous model, the result is given both in terms of certain determinant and as a multiple integral representation.

Citations

• Quantum Inverse Scattering Method and Correlation Functions
• The Influence of Boundary Conditions in the Six-Vertex Model
• Algebraic Representation of Correlation Functions in Integrable Spin Chains
• Directed-loop Monte Carlo simulations of vertex models
• THE QUANTUM METHOD OF THE INVERSE PROBLEM AND THE HEISENBERG XYZ MODEL
• Calculation of norms of Bethe wave functions