Six-vertex model on a finite lattice: integral representations for nonlocal correlation functions

Abstract

We consider the problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions. To this aim, we formulate the model as a scalar product of off-shell Bethe states, and, by applying the quantum inverse scattering method, we derive three different integral representations for these states. By suitably combining such representations, and using certain antisymmetrization relation in two sets of variables, it is possible to derive integral representations for various correlation functions. In particular, focusing on the emptiness formation probability, besides reproducing the known result, obtained by other means elsewhere, we provide a new one. By construction, the two representations differ in the number of integrations and their equivalence is related to a hierarchy of highly nontrivial identities.

arXiv comment42 pages, 4 figures

References in corpus (47)

• Quantum Inverse Scattering Method and Correlation Functions
• Form factors of the XXZ Heisenberg spin-1/2 finite chain
• Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field
• Analytic solution of the Domain Wall non-equilibrium stationary state
• Integral representations for correlation functions of the XXZ chain at finite temperature
• Spin-spin correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field
• Thermodynamic limit of the Six-Vertex Model with Domain Wall Boundary Conditions
• Integral Formulas for the Asymmetric Simple Exclusion Process
• Thermalization with a chemical potential from AdS spaces
• Inhomogeneous field theory inside the arctic circle
• Six-Vertex Model with Domain Wall Boundary Conditions and One-Matrix Model
• Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions
• The arctic curve of the domain-wall six-vertex model
• Hidden Grassmann Structure in the XXZ Model III: Introducing Matsubara direction
• Emptiness Formation Probability and Quantum Knizhnik-Zamolodchikov Equation
• Boundary correlation functions of the six-vertex model
• Arctic curves of the six-vertex model on generic domains: the Tangent Method
• Algebraic representation of correlation functions in integrable spin chains
• Directed-loop Monte Carlo simulations of vertex models
• Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain
• N=4 SYM structure constants as determinants
• Emptiness formation probability in the domain-wall six-vertex model
• Quantum Correlations and Number Theory
• Influence of charges on the behavior of polyelectrolyte microgels confined to oil-water interfaces
• The hexagon in the mirror: the three-point function in the SoV representation
• Refined Cauchy and Littlewood identities, plane partitions and symmetry classes of alternating sign matrices
• On two-point boundary correlations in the six-vertex model with DWBC
• The arctic curve of the domain-wall six-vertex model in its anti-ferroelectric regime
• The limit shape of large alternating sign matrices
• Boundary polarization in the six-vertex model
• Three-point function of semiclassical states at weak coupling
• Extreme boundary conditions and random tilings
• On the correlation functions of the domain wall six vertex model
• New exact results on density matrix for XXX spin chain
• On the problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions
• Phase separation in the six-vertex model with a variety of boundary conditions
• Long-distance and large-time asymptotic behaviour of dynamic correlation functions in the massless regime of the XXZ spin-1/2 chain
• The role of orthogonal polynomials in the six-vertex model and its combinatorial applications
• The 6-vertex model with fixed boundary conditions
• A numerical study of the F-model with domain-wall boundaries
• Generalized emptiness formation probability in the six-vertex model
• Bisymmetric functions, Macdonald polynomials and sl_3 basic hypergeometric series
• Boundary correlation functions of the six and nineteen vertex models with domain wall boundary conditions
• Combinatorial properties of symmetric polynomials from integrable vertex models in finite lattice
• Integral formulas and antisymmetrization relations for the six-vertex model
• Asymptotic shapes with free boundaries
• Integrability of Limit Shapes of the Inhomogeneous Six Vertex Model

Cited by in corpus (7)

• The frustration-free fully packed loop model
• Exact time evolution formulae in the XXZ spin chain with domain wall initial state
• Arctic curves of the four-vertex model
• Construction of determinants for the six-vertex model with domain wall boundary conditions
• Evaluation of integrals for the emptiness formation probability in the square-ice model
• Boundary one-point function of the rational six-vertex model with partial domain wall boundary conditions: explicit formulas and scaling properties
• Scaling limit of domino tilings on a pentagonal domain