Geometric phases and quantum phase transitions in open systems

TL;DR

This paper explores how geometric phases relate to quantum phase transitions in open quantum systems, specifically analyzing a dissipative Ising model and identifying a first-order transition through geometric phase behavior.

Contribution

It establishes a connection between geometric phases and quantum phase transitions in open systems governed by non-Hermitian Hamiltonians, with a focus on the dissipative Ising model.

Findings

Geometric phase associated with the ground state signals quantum phase transitions.

The quantum phase transition in the studied model is of the first order.

The relationship between eigenvalue crossings and geometric phases is demonstrated.

Abstract

The relationship between quantum phase transition and complex geometric phase for open quantum system governed by the non-Hermitian effective Hamiltonian with the accidental crossing of the eigenvalues is established. In particular, the geometric phase associated with the ground state of the one-dimensional dissipative Ising model in a transverse magnetic field is evaluated, and it is demonstrated that related quantum phase transition is of the first order.