Functionally independent conservations laws in a quantum integrable model

TL;DR

This paper investigates a quantum integrable lattice model with Fermions or Bosons, demonstrating it has only N functionally independent conservation laws despite additional conserved quantities, aligning with classical integrability concepts.

Contribution

It identifies higher conservation laws but shows the model's integrability is characterized by only N independent conserved quantities, clarifying its integrable structure.

Findings

The model has 2N parameters and is exactly solvable.

There are additional conservation laws with higher Fermion content.

Only N conservation laws are functionally independent.

Abstract

We study a recently proposed quantum integrable model defined on a lattice with N sites, with Fermions or Bosons populating each site, as a close relative of the well known spin-1/2 Gaudin model. This model has 2N arbitrary parameters, a linear dependence on an interaction type parameter x, and can be solved exactly. It has N known constants of motion that are linear in x. We display further constants of motion with higher Fermion content, that are are linearly independent of the known conservation laws. Our main result is that despite the existence of these higher conservation laws, the model has only N functionally independent conservation laws. Therefore we propose that N can be viewed as the number of degrees of freedom, in parallel to the classical definition of integrability.