Probing the Possibilities of Ergodicity in the 1D Spin-1/2 XY Chain with Quench Dynamics

Abstract

Ergodicity sits at the heart of the connection between statistical mechanics and dynamics of a physical system. By fixing the initial state of the system into the ground state of the Hamiltonian at zero temperature and tuning a control parameter, we consider the occurrence of the ergodicity with quench dynamics in the one-dimensional (1D) spin-1/2 XY model in a transverse magnetic field. The ground-state phase diagram consists of two ferromagnetic and paramagnetic phases. It is known the magnetization in this spin system is non-ergodic. We set up two different experiments as we call them single and double quenches and test the dynamics of the magnetization along the Z-axis and the spin-spin correlation function along the X-axis which are the order parameters of the zero-temperature phases . Our exact results reveal that for single quenches at zero-temperature, the ergodicity depends on the initial state and the order parameter. In single quenches for a given order parameter, ergodicity will be observed with an ergodic-region for quenches from another phase, non-correspond to the phase of the order parameter, into itself. In addition, a quench from a ground-state phase point corresponding to the order parameter into or very close to the quantum critical point, h c = 1.0, discloses an ergodic behavior. Otherwise, for all other single quenches, the system behaves non-ergodic. Interestingly on the other setup, a double quench on a cyclic path, ergodicity is completely broken for starting from the phase corresponding to the order parameter.Otherwise, it depends on the first quenched point, and the quench time T when the model spent before a second quench in the way back which gives an ability to controlling the ergodicity in the system. Therefore, and contrary to expectations, in the mentioned model the ergodicity can be observed with probing quench dynamics at zero-temperature. Our results provide further insight into the zero-temperature dynamical behavior of quantum systems and their connections to the ergodicity phenomenon. arXiv:2003.09462v1 [quant-ph]

Achieving spin-squeezed states by quench dynamics in a quantum chain

“…For related results, see Refs. [60,61,79]. Note, however, that in the present case a nonanalyticity appears only when the ground state of the post-quench Hamiltonian itself is critical.…”

Constant-depth circuits for dynamic simulations of materials on quantum computers

“…This is illustrated by the ubiquity of these models in current research on near-term quantum computers (Zhukov et al 2018;Lamm and Lawrence 2018;Zhu et al 2020;Yeter-Aydeniz et al 2021;Sun et al 2021;Neill et al 2021). Indeed, systems like the TFIM are quintessential in the study of quantum phase transitions (Suzuki et al 2012;Gómez-Ruiz et al 2016;Yang et al 2019), ergodicity (Cheraghi and Mahdavifar 2020), critical behavior (Granato 1992), as well as myriad condensed matter systems, such as ferroelectrics (Blinc et al 1979) and magnetic spin glasses (Wu et al 1991). When these models are made time-dependent, non-equilibrium effects such as dynamic phase transitions and quantum hysteresis can be studied (Tomé and de Oliveira 1990;Acharyya and Chakrabarti 1995;Acharyya 1998;Sides et al 1998).…”

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“…Now to make an imprint on our JW‐MF results coming out of the rate function, we look at the long‐time average of the rate function where it was displayed it can determine the nonequilibrium quantum phase transitions exactly at the QCPs, [ 47 ] a phenomenon similar to the long‐time average of order parameters. [ 48 ] The long‐time average of the rate function is where the dynamics of the rate function goes to or fluctuates quietly around a stable situation. Defining and thus Figure 2(c) portrays for quenches from to desired anisotropy parameter and constant values of the TF as .…”

“…Now to make an imprint on our JW-MF results coming out of the rate function, we look at the long-time average of the rate function where it was displayed it can determine the nonequilibrium quantum phase transitions exactly at the QCPs, [47] a phenomenon similar to the long-time average of order parameters. [48] The long-time average of the rate function r lta is where the dynamics of the rate function goes to or fluctuates quietly around a stable situation. Defining = lim 2c the signatures of r lta exactly coincide with the quantum critical line h c .…”