Exact Bethe ansatz solution for a quantum field model of interacting scalar fields in quasi-two dimensions

TL;DR

This paper introduces a new integrable quantum field model in quasi-two dimensions, constructed using multi-time concepts and higher-order Lax matrices, and solves it exactly via algebraic Bethe ansatz.

Contribution

It develops a novel quantum field model in quasi-two dimensions with proven Yang-Baxter integrability and exact solutions, expanding the scope of integrable systems beyond one dimension.

Findings

Constructed a new quasi-two-dimensional integrable quantum field model.

Proved Yang-Baxter integrability using a novel commutation rule.

Solved the model exactly with algebraic Bethe ansatz.

Abstract

Integrable quantum field models are known to exist mostly in one space-dimension. Exploiting the concept of multi-time in integrable systems and a Lax matrix of higher scaling order, we construct a novel quantum field model in quasi-two dimensions involving interacting fields. The Yang-Baxter integrability is proved for the model by finding a new kind of commutation rule for its basic fields, representing nonstandard scalar fields along the transverse direction. In spite of a close link with the quantum Landau-Lifshitz equation, the present model differs widely from it, in its content and the result obtained. Using further the algebraic Bethe ansatz we solve exactly the eigenvalue problem of this quantum field model for all its higher conserved operators. The idea presented here should instigate the construction of a novel class of integrable field and lattice models and exploration of a new type of underlying algebras.