Finite-size scaling exponents in the Dicke modelJ. Vidal1 and S. Dusuel2
1 Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600 Université Pierre et Marie Curie - 4 Place Jussieu, 75252 Paris Cedex 05, France
2 Institut für Theoretische Physik, Universität zu Köln Zülpicher Str. 77, 50937 Köln, Germany
received 15 February 2006; accepted in final form 12 April 2006
published online 3 May 2006
We consider the finite-size corrections in the Dicke model and determine the scaling exponents at the critical point for several quantities such as the ground-state energy or the gap. Therefore, we use the Holstein-Primakoff representation of the angular momentum and introduce a canonical transformation to diagonalize the Hamiltonian in the normal phase. As already observed in several systems, these corrections turn out to be singular at the transition point and thus lead to nontrivial exponents. We show that for the atomic observables, these exponents are the same as in the Lipkin-Meshkov-Glick model, in agreement with numerical results. We also investigate the behavior of the order parameter related to the radiation mode and show that it is driven by the same scaling variable as the atomic one.
42.50.Fx - Cooperative phenomena in quantum optical systems.
05.30.Jp - Boson systems.
73.43.Nq - Quantum phase transitions.
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