Loschmidt Echo and Berry phase of the quantum system coupled to the XY spin chain: Proximity to quantum phase transition

Abstract

We study the Loschmidt echo (LE) of a coupled system consisting of a central spin and its surrounding environment described by a general XY spin-chain model. The quantum dynamics of the LE is shown to be remarkably influenced by the quantum criticality of the spin chain. In particular, the decaying behavior of the LE is found to be controlled by the anisotropy parameter of the spin chain. Furthermore, we show that due to the coupling to the spin chain, the ground-state Berry phase for the central spin becomes nonanalytical and its derivative with respect to the magnetic parameter $\lambda$ in spin chain diverges along the critical line $\lambda =1$, which suggests an alternative measurement of the quantum criticality of the spin chain.

15 pages, 5 figures

References in corpus (6)

• Decay of Loschmidt Echo Enhanced by Quantum Criticality
• Quantum Phase Transitions and Bipartite Entanglement
• Scaling of geometric phases close to quantum phase transition in the XY chain
• Geometric phases and criticality in spin chain systems
• Entanglement and Quantum Phase Transition in Low Dimensional Spin Systems
• Metamagnetic quantum criticality in Sr3Ru2O7 studied by thermal expansion

Cited by in corpus (38)

• Fidelity approach to quantum phase transitions
• Geometry of quantum phase transitions
• Loschmidt Echo Revivals: Critical and Noncritical
• Detection of quantum critical points by a probe qubit
• Direct observation of quantum criticality in Ising spin chains
• Coherent and dissipative dynamics at quantum phase transitions
• Disentanglement of two qubits coupled to an XY spin chain: Role of quantum phase transition
• Decoherence due to an excited state quantum phase transition in a two-level boson model
• Dynamical signature of localization-delocalization transition in one-dimensional incommensurate lattice
• High-harmonic generation approaching the quantum critical point of strongly correlated systems
• Loschmidt echo with a non-equilibrium initial state: early time scaling and enhanced decoherence
• Disordered Kitaev chain with long-range pairing: Loschmidt echo revivals and dynamical phase transitions
• Dynamical Topological Phase Transition in a Bose-Einstein Condensate
• Dynamical quantum phase transition in a system of non-interacting bosons
• Geometric phases and quantum phase transitions
• Study of Loschmidt Echo for a qubit coupled to an XY-spin chain environment
• Disentanglement dynamics of interacting two qubits and two qutrits in an XY spin-chain environment with the Dzyaloshinsky-Moriya interaction
• Decoherence from spin environments: Loschmidt echo and quasiparticle excitations
• On the possibility of complete revivals after quantum quenches to a critical point
• Probing the quantum phase transition in the Dicke model through mechanical vibrations
• Probing the out-of-equilibrium dynamics of two interacting atoms
• Quenching Dynamics and Quantum Information
• Return amplitude after a quantum quench in the XY chain
• Odd thermodynamic limit for the Loschmidt echo
• Achieving spin-squeezed states by quench dynamics in a quantum chain
• Semiclassical Approach to Survival Probability at Quantum Phase Transitions
• Landau-Zener transition of a two-level system driven by spin chains near their critical points
• Complexity and instability of quantum motion near a quantum phase transition
• Scaling behavior for a class of quantum phase transitions
• Berry Phases, Quantum Phase Transitions and Chern Numbers
• Reduced fidelities for free fermions out of equilibrium: From dynamical quantum phase transitions to Mpemba effect
• Semiclassical approach to the quantum Loschmidt echo in deep quantum regions: from validity to breakdown
• Probing Quantum Phase Transitions on a Spin Chain with a Double Quantum Dot
• Quench field sensitivity of two-particle correlation in a Hubbard model
• Relaxation of antiferromagnetic order and growth of Rényi entropy in a generalized Heisenberg star
• Decoherence of a quantum memory coupled to a collective spin bath
• Stacked quantum Ising systems and quantum Ashkin-Teller model
• Loschmidt echo and Momentum Distribution in a Kitaev Spin Chain