A comment on free-fermion conditions for lattice models in two and more dimensions

TL;DR

This paper investigates free-fermion conditions in lattice vertex models across multiple dimensions, revealing their connection to symmetry degenerations and proposing a general framework for understanding these conditions.

Contribution

It introduces a unified scheme linking free-fermion conditions to symmetry degenerations in multi-dimensional lattice models.

Findings

Free-fermion conditions correspond to symmetry degenerations.

The paper proposes a general scheme for these conditions in higher dimensions.

Examples include models on square, triangular, and cubic lattices.

Abstract

We analyze free-fermion conditions on vertex models. We show --by examining examples of vertex models on square, triangular, and cubic lattices-- how they amount to degeneration conditions for known symmetries of the Boltzmann weights, and propose a general scheme for such a process in two and more dimensions.