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

Francesco Plastina·Giuseppe Liberti·Angelo Carollo
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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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Francesco Plastina, Giuseppe Liberti, Angelo Carollo. 2006-04-04. Scaling of Berry's Phase Close to the Dicke Quantum Phase Transition. https://doi.org/10.1209/epl%2Fi2006-10270-x

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