Berry phase and fidelity susceptibility of the three-qubit Lipkin-Meshkov-Glick ground state

TL;DR

This paper investigates Berry phases and fidelity susceptibilities in a three-qubit Lipkin-Meshkov-Glick model, revealing a magnetic monopole structure and providing explicit formulas for ground state properties.

Contribution

It provides the first detailed analysis of Berry phases and fidelities for a finite three-qubit LMG model, including subsystem properties and monopole structures.

Findings

Explicit formulas for Berry phase and fidelity susceptibility of the three-qubit ground state.

Identification of a nontrivial magnetic monopole structure in the system.

Analysis of local and global quantum geometric properties.

Abstract

Berry phases and quantum fidelities for interacting spins have attracted considerable attention, in particular in relation to entanglement properties of spin systems and quantum phase transitions. These efforts mainly focus either on spin pairs or the thermodynamic infinite spin limit, while studies of the multipartite case of a finite number of spins are rare. Here, we analyze Berry phases and quantum fidelities of the energetic ground state of a Lipkin-Meshkov-Glick (LMG) model consisting of three spin-1/2 particles (qubits). We find explicit expressions for the Berry phase and fidelity susceptibility of the full system as well as the mixed state Berry phase and partial-state fidelity susceptibility of its one- and two-qubit subsystems. We demonstrate a realization of a nontrivial magnetic monopole structure associated with local, coordinated rotations of the three-qubit system around the external magnetic field.