Scaling behavior for a class of quantum phase transitions

Abstract

We show that for quantum phase transitions with a single bosonic zero mode at the critical point, like the Dicke model and the Lipkin-Meshkov-Glick model, metric quantities such as fidelity, that is, the overlap between two ground states corresponding to two values ${\lambda }_1$ and ${\lambda }_2$ of the controlling parameter $\lambda$, only depend on the ratio $\eta =({\lambda }_1-{\lambda }_c)/({\lambda }_2-{\lambda }_c)$, where $\lambda ={\lambda }_c$ at the critical point. Such scaling property is valid also for time-dependent quantities such as the Loschmidt echo, provided time is measured in units of the inverse frequency of the critical mode.

7 pages, 3 figures, added new data and discussion

References in corpus (10)

• Dynamics of Loschmidt echoes and fidelity decay
• Ground-State Fidelity and Bipartite Entanglement in the Bose-Hubbard Model
• Mixed-state fidelity and quantum criticality at finite temperature
• Decoherence induced by interacting quantum spin baths
• Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
• Quantum fidelity and quantum phase transitions in matrix product states
• Quantum phase transitions and quantum fidelity in free fermion graphs
• Detection of quantum critical points by a probe qubit
• Direct observation of quantum criticality in Ising spin chains
• Direct equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems: scaling of entanglement