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

We study the temporal evolution of a central spin-1/2 (qubit) coupled to the environment which is chosen to be a spin-1/2 transverse XY spin chain. We explore the entire phase diagram of the spin-Hamiltonian and investigate the behavior of Loschmidt echo(LE) close to critical and multicritical point(MCP). To achieve this, the qubit is coupled to the spin chain through the anisotropy term as well as one of the interaction terms. Our study reveals that the echo has a faster dec...

We study the transition of a quantum system $S $ from a pure state to a mixed one, which is induced by the quantum criticality of the surrounding system $E$ coupled to it. To characterize this transition quantitatively, we carefully examine the behavior of the Loschmidt echo (LE) of $E$ modelled as an Ising model in a transverse field, which behaves as a measuring apparatus in quantum measurement. It is found that the quantum critical behavior of $E$ strongly affects its capa...

We establish a relation between Hahn spin-echo of a spin-$\frac 1 2 $ particle and quantum phase transition in a spin-chain, which couples to the particle. The Hahn echo is calculated and discussed at zero as well as at finite temperatures. On the example of XY model, we show that the critical points of the chain are marked by the extremal values in the Hahn echo, and influence the Hahn echo in surprising high temperature. An explanation for the relation between the echo and ...

In this paper, we study the Loschmidt Echo (LE) of a two-dimensional Kitaev model residing on a honeycomb lattice which is chosen to be an environment that is coupled globally to a central spin. The decay of LE is highly influenced by the quantum criticality of the environmental spin model e.g., it shows a sharp dip close to the anisotropic quantum critical point (AQCP) of its phase diagram. The early time decay and the collapse and revival as a function of time at AQCP do al...

We revisit the problem of decoherence of a qubit centrally coupled to an interacting spin environment, here modeled by a quantum compass chain or an extended XY model in a staggered magnetic field. These two models both support distinct spin liquid phases, adding a new element to the problem. By analyzing their Loschmidt echoes when perturbed by the qubit we find that a fast decoherence of the qubit is conditioned on the presence of propagating quasiparticles which couple to ...

The equilibration dynamics of a closed quantum system is encoded in the long-time distribution function of generic observables. In this paper we consider the Loschmidt echo generalized to finite temperature, and show that we can obtain an exact expression for its long-time distribution for a closed system described by a quantum XY chain following a sudden quench. In the thermodynamic limit the logarithm of the Loschmidt echo becomes normally distributed, whereas for small que...

A critically enhanced decay of the Loschmidt echo is characteristic of sudden quench dynamics near a quantum phase transition. Here, we demonstrate that the decay and revival of the Loschmidt echo follows power-law scaling in the system size and the distance from a critical point with equilibrium critical exponents. We reveal such dynamical scaling laws by analyzing relevant perturbations to the Loschmidt echo cast in a scaling invariant form. We confirm the validity and the ...

We study the Loschmidt echo (LE) in a central spin model in which a central spin is globally coupled to an environment (E) which is subjected to a small and sudden quench at $t=0$ so that its state at $t=0^+$, remains the same as the ground state of the initial environmental Hamiltonian before the quench; this leads to a non-equilibrium situation. This state now evolves with two Hamiltonians, the final Hamiltonian following the quench and its modified version which incorporat...

We study the Loschmidt echo and Berry phase in a nonlinear system transported around a double and triple degeneracy. The nonlinearity of the system makes the Berry phase different from that in linear systems. We propose a witness of nonlinearity for the nonlinear system and show its dependence on the parameters of the system, taking the standard Landau-Zener model as an example. We calculate the Loschmidt echo(LE) or quantum fidelity in the quantum dynamics under perturbation...

We study the non-equilibrium evolution of concurrence of a Bell pair constituted of two qubits, through the measurement of Loschmidt echo (LE) under the scope of generalized central spin model. Having detected the Griffiths phase via derivative of LE in equilibrium, we show that in the non-equilibrium situation, the spin chain requires a temporal window to realize the effect of disorder. We show that within this timescale, LE falls off exponentially and this decay is maximall...