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

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Cited by in corpus (6)

• Reflection algebra and functional equations
• Off-shell scalar products for the $XXZ$ spin chain with open boundaries
• Differential approach to on-shell scalar products in six-vertex models
• Six-vertex model and non-linear differential equations I. Spectral problem
• On the elliptic ${\mathfrak{gl}}_2$ solid-on-solid model: functional relations and determinants
• Six-vertex model and non-linear differential equations II. Continuous symmetries