Sensitivity to perturbations and quantum phase transitions

Abstract

The local density of states or its Fourier transform, usually called fidelity amplitude, are important measures of quantum irreversibility due to imperfect evolution. In this Rapid Communication we study both quantities in a paradigmatic many body system, the Dicke Hamiltonian, where a single-mode bosonic field interacts with an ensemble of N two-level atoms. This model exhibits a quantum phase transition in the thermodynamic limit, while for finite instances the system undergoes a transition from quasi-integrability to quantum chaotic. We show that the width of the local density of states clearly points out the imprints of the transition from integrability to chaos but no trace remains of the quantum phase transition. The connection with the decay of the fidelity amplitude is also established.

5 pages, 4 figures, accepted for publication PRE rapid communication

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Cited by in corpus (7)

• Nonexponential fidelity decay in isolated interacting quantum systems
• Non-ergodicity in the Anisotropic Dicke model
• Quantum diffusion and thermalization at resonant tunneling
• Proliferation of effective interactions: decoherence-induced equilibration in a closed many-body system
• Relaxation of isolated quantum systems beyond chaos
• The role of quantum work statistics in many-body physics
• Quantum Geometric Tensor and Critical Metrology in the Anisotropic Dicke Model