Spin Chains and Chiral Lattice Fermions

TL;DR

This paper explores how Lorentz invariance and chiral structures can be generalized to two-dimensional lattice fermion models using Baxter's corner transfer matrix, leading to a novel formulation differing from traditional methods.

Contribution

It introduces a new approach to lattice fermions that preserves chiral symmetry and Lorentz invariance without relying on Wilson or staggered prescriptions.

Findings

Lattice Hamiltonian and boost operator are fermionized spin chain operators.

Chiral structure is generalized through transformation properties of local fermion operators.

Axial $Q_5$ rotation is sitewise local, unlike vector charge rotation.

Abstract

The generalization of Lorentz invariance to solvable two-dimensional lattice fermion models has been formulated in terms of Baxter's corner transfer matrix. In these models, the lattice Hamiltonian and boost operator are given by fermionized nearest-neighbor Heisenberg spin chain operators. The transformation properties of the local lattice fermion operators under a boost provide a natural and precise way of generalizing the chiral structure of a continuum Dirac field to the lattice. The resulting formulation differs from both the Wilson and staggered (Kogut-Susskind) prescriptions. In particular, an axial $Q_5$ rotation is sitewise local, while the vector charge rotation mixes nearest neighbors on even and odd sublattices.