Quantum phase transitions, entanglement, and geometric phases of two qubits

TL;DR

This paper explores the relationship between quantum phase transitions, entanglement, and geometric phases in a two-qubit XY model, revealing complex behaviors and counterexamples to common assumptions about entanglement as an indicator.

Contribution

It demonstrates that entanglement may not always signal quantum phase transitions and links geometric phases to parameter space topology in a two-qubit system.

Findings

Entanglement changes abruptly across a circle in parameter space.

Ground state acquires geometric phase outside a monopole-like sphere.

Counterexample showing entanglement isn't always a reliable phase transition indicator.

Abstract

The relation between quantum phase transitions, entanglement, and geometric phases is investigated with a system of two qubits with XY type interaction. A seam of level crossings of the system is a circle in parameter space of the anisotropic coupling and the transverse magnetic field, which is identical to the disorder line of an one-dimensional XY model. The entanglement of the ground state changes abruptly as the parameters vary across the circle except specific points crossing to the straight line of the zero magnetic field. At those points the entanglement does not change but the ground state changes suddenly. This is an counter example that the entanglement is not alway a good indicator to quantum phase transitions. The rotation of the circle about an axis of the parameter space produces the magnetic monopole sphere like a conducting sphere of electrical charges. The ground state evolving adiabatically outside the sphere acquires a geometric phase, whereas the ground state traveling inside the sphere gets no geometric phase. The system also has the Renner-Teller intersection which gives no geometric phases.