Spin Hamiltonian with large fourth order terms: Triple well potentials and Bloch sphere visualization

TL;DR

This paper investigates a complex spin Hamiltonian with fourth order terms, revealing multiple quantum phase transitions and visualizing ground state localization on the Bloch sphere using semiclassical and catastrophe theory methods.

Contribution

It introduces a detailed analysis of a high-order spin Hamiltonian, demonstrating multiple phase transitions and ground state localization visualization.

Findings

Presence of three-well semiclassical potentials for large fourth order parameters

Multiple ground state quantum phase transitions due to parameter space crossings

Visualization of ground state localization on the Bloch sphere

Abstract

We present a study of a general spin Hamiltonian with terms up to fourth order. With the coherent states the semiclassical potential is obtained and with catastrophe theory its parameter space is constructed. When the fourth order parameters are large enough the parameter space has regions where the semiclassical potential has three wells. By applying an oscillating magnetic field a trajectory in parameter space crosses the Maxwell set multiple times resulting in many ground state quantum phase transitions. Using the coherent states we are able to visualize the localization of the ground state on the Bloch sphere as the magnetic field is varied.