The quantum (non-Abelian) Potts model and its exact solution

TL;DR

This paper introduces a quantum generalization of the classical non-Abelian Potts model, providing an exact solution for its energy spectrum, degeneracies, partition function, and entanglement properties of ground states.

Contribution

It presents the first exact solution for the quantum non-Abelian Potts model, including spectrum, degeneracies, partition function, and entanglement analysis.

Findings

Complete energy spectrum and degeneracy structure determined.

Partition function calculated via algebraic and combinatorial methods.

Entanglement properties of ground states characterized.

Abstract

We generalize the classical one dimensional Potts model to the case where the symmetry group is a non-Abelian finite group. It turns out that this new model has a quantum nature in that its spectrum of energy eigenstates consists of entangled states. We determine the complete energy spectrum, i.e. the ground states and all the excited states with their degeneracy structure. We calculate the partition function by two different algebraic and combinatorial methods. We also determine the entanglement properties of its ground states.