Probing the Possibilities of Ergodicity in the 1D Spin-1/2 XY Chain with
Quench Dynamics
- URL: http://arxiv.org/abs/2003.09462v2
- Date: Tue, 14 Apr 2020 06:47:36 GMT
- Title: Probing the Possibilities of Ergodicity in the 1D Spin-1/2 XY Chain with
Quench Dynamics
- Abstract summary: Ergodicity sits at the heart of the connection between statistical mechanics and dynamics of a physical system.
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.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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. 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.
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