Ground-State Analysis for an Exactly Solvable Coupled-Spin Hamiltonian

TL;DR

This paper analyzes a solvable coupled-spin Hamiltonian using mean-field, Bethe ansatz, and numerical methods to explore its ground-state properties, revealing complex features and connections to $p+ip$ pairing models.

Contribution

It introduces an exactly solvable two-spin Hamiltonian and provides a comprehensive analysis of its ground-state characteristics using multiple theoretical and numerical approaches.

Findings

Rich ground-state features uncovered

Energy gap and fidelity analyzed

Connection to $p+ip$ pairing Hamiltonian established

Abstract

We introduce a Hamiltonian for two interacting $su(2)$ spins. We use a mean-field analysis and exact Bethe ansatz results to investigate the ground-state properties of the system in the classical limit, defined as the limit of infinite spin (or highest weight). Complementary insights are provided through investigation of the energy gap, ground-state fidelity, and ground-state entanglement, which are numerically computed for particular parameter values. Despite the simplicity of the model, a rich array of ground-state features are uncovered. Finally, we discuss how this model may be seen as an analogue of the exactly solvable $p+ip$ pairing Hamiltonian.