Partial differential equations from integrable vertex models

Abstract

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 $U_q[\widehat{\mathfrak{sl}}(2)]$ invariant six-vertex model and the resulting partial differential equation is studied for particular values of the lattice length.

19 pages. v2: affiliation and references updated, minor changes, accepted for publication in J. Math. Phys

References in corpus (2)

• The ODE/IM Correspondence
• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions

Cited by in corpus (1)

• Off-shell scalar products for the $XXZ$ spin chain with open boundaries