Dynamics in quantum Ising chain driven by inhomogeneous transverse magnetization

TL;DR

This paper analytically investigates the non-homogeneous dynamics of transverse magnetization in a quantum Ising chain, revealing persistent spatial variations and oscillatory behavior influenced by quantum phase transitions.

Contribution

It provides an analytical solution for the magnetization dynamics starting from special initial states, showing non-homogenization and phase transition signatures in the long-time behavior.

Findings

Magnetization remains spatially non-uniform even after infinite time.

Oscillations in local magnetization have two distinct timescales with algebraic decay.

Frequency of oscillations varies with external field across phases.

Abstract

We study the dynamics caused by transport of transverse magnetization in one dimensional transverse Ising chain at zero temperature. We observe that a class of initial states having product structure in fermionic momentum-space and satisfying certain criteria, produce spatial variation in transverse magnetization. Starting from such a state, we obtain the transverse magnetization analytically and then observe its dynamics in presence of a homogeneous constant field $\Gamma$. In contradiction with general expectation, whatever be the strength of the field, the magnetization of the system does not become homogeneous even after infinite time. At each site, the dynamics is associated with oscillations having two different timescales. The envelope of the larger timescale oscillation decays algebraically with an exponent which is invariant for all such special initial states. The frequency of this oscillation varies differently with external field in ordered and disordered phases. The local magnetization after infinite time also characterizes the quantum phase transition.