arXiv:1505.06870

Differential approach to on-shell scalar products in six-vertex models

W. Galléas, Jules Lamers

Published May 26, 2015• 4 citations

Abstract

In this work we obtain hierarchies of partial differential equations describing on-shell scalar products for two types of six-vertex models. More precisely, six-vertex models with two different diagonal boundary conditions are considered: the case with boundary twists and the case with open boundary conditions. Solutions and properties of our partial differential equations are also discussed.

DOI: 10.48550/arxiv.1505.06870

Related papers

Properties of eigenstates of the six-vertex model with twisted and open boundary conditions

Heng Fan, Bo-Yu Hou, Kangjie Shi

We use the method proposed by Izergin and Korepin to discuss the Bethe ansatz equations of the six-vertex model with twisted and open boundary conditions. Let two parameters of the Bethe wave functions be equal, then an additional Bethe ansatz equation arises. For the open boundary condition case, we also have discussed the dual pseudovacuum state and have written out the simplest scalar products of the Bethe wave function.

Journal of Mathematical PhysicsJul 1, 19970 citations

The Influence of Boundary Conditions in the Six-Vertex Model

Paul Zinn-Justin

We discuss the influence of boundary conditions on the continuum limit of the six-vertex model by deriving a variational principle for the associated height function with arbitrary fixed boundary conditions. We discuss its consequences using the known phase diagram of the six-vertex model. In some particular cases we compute explicitly the corresponding partial differential equations by means of the Bethe Ansatz.

arXiv:cond-mat/0205192May 9, 200227 citations

Continuous representations of scalar products of Bethe vectors

W. Galléas

We present families of single determinantal representations of on-shell scalar products of Bethe vectors. Our families of representations are parameterized by a continuous complex variable which can be fixed at one’s convenience. Here we consider Bethe vectors in two versions of the six-vertex model: the case with boundary twists and the case with open boundaries.

arXiv:1607.08524Journal of Mathematical PhysicsAug 1, 20174 citations

Partial differential equations from integrable vertex models

W. Galléas

In this work, we propose a mechanism for converting the spectral problem of vertex models transfer matrices into the solution of certain linear partial differential equations. This mechanism is illustrated for the Uq[sl̂(2)] invariant six-vertex model, and the resulting partial differential equation is studied for particular values of the lattice length.

arXiv:1403.0425Journal of Mathematical PhysicsFeb 1, 20157 citations

Boundary K-matrices for the six vertex and the n(2n-1)An-1vertex models

Hector J. de Vega, Amanda Ruiz

Boundary conditions compatible with integrability are obtained for two-dimensional models by solving the factorizability equations for the reflection matrices K +or- ( theta ). For the six vertex model the general solution depending on four arbitrary parameters is found. For the A n-1 models all diagonal solutions are found. The associated integrable magnetic Hamiltonians are explicitly derived.

arXiv:hep-th/9211114Journal of Physics A Mathematical and GeneralJun 21, 1993237 citations

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

Filippo Colomo, Giuseppe Di Giulio, A. G. Pronko

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:2107.13358Nuclear Physics BSep 15, 202110 citations