Scaling of Berry's phase close to the Dicke quantum phase transition

¹ Dipartimento di Fisica, Università della Calabria and Istituto Nazionale di Fisica Nucleare, Gruppo collegato di Cosenza I-87036 Arcavacata di Rende, Cosenza, Italy
² Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences - A-6020 Innsbruck, Austria

Received: 26 June 2006
Accepted: 31 August 2006

Abstract

We discuss the thermodynamic and finite-size scaling properties of the geometric phase in the adiabatic Dicke model, describing a quantum phase transition for an N qubit register coupled to a slow oscillator mode. We show that, in the thermodynamic limit, a non-zero Berry phase is obtained only if a path in parameter space is followed that encircles the critical point. Furthermore, we investigate the precursors of this critical behavior for a system with finite size and obtain the leading orders in the expansion of the Berry phase and its critical exponent.