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Six-Vertex Model and Non-linear Differential Equations. I: Spectral Problem

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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.

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  1. Institut für Theoretische Physik, Eidgenössische Technische Hochschule Zürich, Wolfgang-Pauli-Strasse 27, 8093, Zurich, Switzerland

    W. Galleas

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  1. W. Galleas
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Communicated by C. Schweigert

The work of W.G. is partially supported by the Swiss National Science Foundation through the NCCR SwissMAP.

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Galleas, W. Six-Vertex Model and Non-linear Differential Equations. I: Spectral Problem. Commun. Math. Phys. 363, 59–96 (2018). https://doi.org/10.1007/s00220-018-3232-7

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