Six-vertex model and non-linear differential equations I. Spectral problem

Abstract

In this work we relate the spectral problem of the toroidal six-vertex model's transfer matrix with the theory of integrable non-linear differential equations. More precisely, we establish an analogy between the Classical Inverse Scattering Method and previously proposed functional equations originating from the Yang-Baxter algebra. The latter equations are then regarded as an Auxiliary Linear Problem allowing us to show that the six-vertex model's spectrum solves Riccati-type non-linear differential equations. Generating functions of conserved quantities are expressed in terms of determinants and we also discuss a relation between our Riccati equations and a stationary Schrödinger equation.

42 pages, 3 figures

References in corpus (5)

• The ODE/IM Correspondence
• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions
• Baxter Q-operator from quantum K-theory
• The eight-vertex model and Painleve VI
• Partial differential equations from integrable vertex models

Cited by in corpus (2)

• The Functional Method for the Domain-Wall Partition Function
• Domain-wall boundaries through non-diagonal twists in the six-vertex model