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.

arXiv comment7 pages, 3 figures, added new data and discussion

References in corpus (34)

• Ground state overlap and quantum phase transitions
• Chaos and the Quantum Phase Transition in the Dicke Model
• Decay of Loschmidt Echo Enhanced by Quantum Criticality
• Dynamics of Loschmidt echoes and fidelity decay
• Fidelity approach to quantum phase transitions
• Environment-independent decoherence rate in classically chaotic systems
• Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
• Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo
• 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
• Sensitivity of Wave Field Evolution and Manifold Stability in Chaotic Systems
• Quantum fidelity and quantum phase transitions in matrix product states
• Finite-Size Scaling Exponents in the Dicke Model
• Stability of quantum motion and correlation decay
• Quantum phase transitions and quantum fidelity in free fermion graphs
• Quantum fidelity in the thermodynamic limit
• Sensitivity of Quantum Motion for Classically Chaotic Systems
• Detection of quantum critical points by a probe qubit
• Measuring the Lyapunov exponent using quantum mechanics
• Entanglement entropy in collective models
• Direct observation of quantum criticality in Ising spin chains
• Loschmidt Echo and Berry phase of the quantum system coupled to the XY spin chain: Proximity to quantum phase transition
• Semiclassical evaluation of quantum fidelity
• Decay of the Loschmidt Echo for quantum states with sub-Planck scale structures
• Ground state fidelity and quantum phase transitions in free Fermi systems
• Direct equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems: scaling of entanglement
• Hypersensitivity to perturbations of quantum-chaotic wave-packet dynamics
• Stability of Quantum Motion: Beyond Fermi-golden-rule and Lyapunov decay
• Uniform semiclassical approach to fidelity decay in the deep Lyapunov regime
• Uniform Semiclassical Approach to Fidelity Decay: from Weak to Strong Perturbation
• Stability of quantum motion in regular systems: a uniform semiclassical approach
• Semiclassical Approach to Survival Probability at Quantum Phase Transitions

Cited by in corpus (3)

• Dicke coupling by feasible local measurements at the superradiant quantum phase transition
• Revival times at quantum phase transitions
• Complexity and instability of quantum motion near a quantum phase transition