Quantum integrability in systems with finite number of levels

TL;DR

This paper explores quantum integrability in finite-level systems by constructing commuting matrix models, demonstrating that parameter-dependent matrices exhibit integrability features like solvability, level crossings, and Poissonian statistics.

Contribution

It introduces new classes of finite-level quantum models based on commuting matrices and proposes a parameter-dependent definition of quantum integrability.

Findings

Exact solvability demonstrated in the models

Presence of level crossings indicating integrability

Poissonian energy level statistics observed

Abstract

We consider the problem of defining quantum integrability in systems with finite number of energy levels starting from commuting matrices and construct new general classes of such matrix models with a given number of commuting partners. We argue that if the matrices depend on a (real) parameter, one can define quantum integrability from this feature alone, leading to specific results such as exact solvability, Poissonian energy level statistics and to level crossings.