Relaño Pérez, ArmandoPérez Fernández, P.Arias, J. M.Dukelsky, J.García Ramos, J. E.2023-06-202023-06-202009-091050-294710.1103/PhysRevA.80.032111https://hdl.handle.net/20.500.14352/44423©2009 The American Physical Society. This work has been partially supported by the Spanish Ministerio de Educacion y Ciencia and by the European regional development fund (FEDER) under Projects No. FIS2008-04189, No. FIS2006-12783-C03-01, No. FPA2006-13807-C02-02, and No. FPA2007-63074, by CPAN-Ingenio, by Comunidad de Madrid under Project No. 200650M012, CSIC, and by Junta de Analucia a under Projects No. FQM160, No. FQM318, No. P05-FQM437, and No. P07-FQM-02962. A. R. is supported by the Spanish program "Juan de la Cierva" and P. P- F. is supported by a FPU grant of the Spanish Ministerio de Educacion y Ciencia.The decoherence induced on a single qubit by its interaction with the environment is studied. The environment is modeled as a scalar two-level boson system that can go through either first-order or continuous-excited-state quantum phase transitions, depending on the values of the control parameters. A mean-field method based on the Tamm-Damkoff approximation is worked out in order to understand the observed behavior of the decoherence. Only the continuous-excited-state phase transition produces a noticeable effect in the decoherence of the qubit. This is maximal when the system-environment coupling brings the environment to the critical point for the continuous phase transition. In this situation, the decoherence factor (or the fidelity) goes to zero with a finite-size scaling power law.engjournal articlehttp://dx.doi.org/10.1103/PhysRevA.80.032111http://journals.aps.org/open access536Lipkin ModelSystemsTermodinámica2213 Termodinámica