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.

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• Exact solvability, non-integrability, and genuine multipartite entanglement dynamics of the Dicke model
• On the finite size behavior of quantum collective spin systems
• Optical signatures of quantum phase transitions in a light-matter system
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• A binary mixture of Bose-Einstein-condensates in a double-well potential: Berry phase and two-mode entanglement
• Dynamically generated darkness in the Dicke model
• Berry Phase and Fidelity in the Dicke model with $A^2$ term
• Pairwise Entanglement and Geometric Phase in $d=2,3$-Dimensional Free-Fermion Lattice Systems
• Geometric phase and multipartite entanglement of Rydberg atom chains