Torus partition function of the six-vertex model from algebraic geometry


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Date

2019-03

Publication Type

Journal Article

ETH Bibliography

yes

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Abstract

We develop an efficient method to compute the torus partition function of the six-vertex model exactly for finite lattice size. The method is based on the algebro-geometric approach to the resolution of Bethe ansatz equations initiated in a previous work, and on further ingredients introduced in the present paper. The latter include rational Q-system, primary decomposition, algebraic extension and Galois theory. Using this approach, we probe new structures in the solution space of the Bethe ansatz equations which enable us to boost the efficiency of the computation. As an application, we study the zeros of the partition function in a partial thermodynamic limit of M × N tori with N ≫ M. We observe that for N → ∞ the zeros accumulate on some curves and give a numerical method to generate the curves of accumulation points.

Publication status

published

Editor

Book title

Volume

2019 (3)

Pages / Article No.

152

Publisher

Springer

Event

Edition / version

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Subject

Bethe Ansatz; Differential and Algebraic Geometry; Lattice Integrable Models

Organisational unit

03896 - Beisert, Niklas / Beisert, Niklas check_circle

Notes

Funding

161341 - Multi-loop Scattering Amplitudes via Algebraic Geometry (SNF)

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