Scaling of Berry's Phase Close to the Dicke Quantum Phase Transition

Abstract

We discuss the thermodynamic and finite size scaling properties of the geometric phase in the adiabatic Dicke model, describing the super-radiant 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 order in the 1/N expansion of the Berry phase and its critical exponent.

References in corpus (2)

• Geometric phases and criticality in spin chain systems
• 1/N-expansion for the Dicke model and the decoherence program

Cited by in corpus (9)

• Geometry of quantum phase transitions
• Accurate numerical solution to the finite-size Dicke model
• Critical Property of Geometric Phase in the Dicke Model
• Geometric phases and quantum phase transitions
• Exact solvability, non-integrability, and genuine multipartite entanglement dynamics of the Dicke model
• Optical signatures of quantum phase transitions in a light-matter system
• Berry Phases, Quantum Phase Transitions and Chern Numbers
• Geometric phase and multipartite entanglement of Rydberg atom chains
• Pairwise Entanglement and Geometric Phase in $d=2,3$-Dimensional Free-Fermion Lattice Systems