Quantum Spin Formulation of the Principal Chiral Model

TL;DR

This paper presents a novel quantum spin formulation of the two-dimensional principal chiral model, enabling analysis via quantum operators and revealing a connection to a three-dimensional model through large representation limits and dimensional reduction.

Contribution

It introduces a quantum spin approach to the principal chiral model and demonstrates how classical two-dimensional behavior emerges from a higher-dimensional quantum framework.

Findings

Low energy excitations correspond to a 3D principal chiral model

Dimensional reduction recovers the classical 2D model

Large representation limit simplifies the quantum model

Abstract

We formulate the two-dimensional principal chiral model as a quantum spin model, replacing the classical fields by quantum operators acting in a Hilbert space, and introducing an additional, Euclidean time dimension. Using coherent state path integral techniques, we show that in the limit in which a large representation is chosen for the operators, the low energy excitations of the model describe a principal chiral model in three dimensions. By dimensional reduction, the two-dimensional principal chiral model of classical fields is recovered.