Ineffectiveness of the Dzyaloshinskii-Moriya interaction in the dynamical quantum phase transition in the ITF model

TL;DR

This study investigates the effect of Dzyaloshinskii-Moriya interaction on dynamical quantum phase transitions in the 1D transverse field Ising model, finding that DMI does not influence DQPT occurrence.

Contribution

It demonstrates that Dzyaloshinskii-Moriya interaction does not affect dynamical quantum phase transitions in the ITF model, challenging previous assumptions about their relationship.

Findings

DMI induces chiral phases in the ground state.

DMI does not impact the rate function of the return probability.

Ramping across the critical point is not necessary for DQPT.

Abstract

Quantum phase transition occurs at a quantum critical value of a control parameter such as the magnetic field in the Ising model in a transverse magnetic field (ITF). Recently, it is shown that ramping across the quantum critical point generates non-analytic behaviors in the time evolution of a closed quantum system in the thermodynamic limit at zero temperature. The mentioned phenomenon is called the dynamical quantum phase transition (DQPT). Here, we consider the one-dimensional (1D) ITF model with added the Dzyaloshinskii-Moriya interaction (DMI). Using the fermionization technique, the Hamiltonian is exactly diagonalized. Although the DM interaction induces chiral phase in the ground state phase diagram of the model, the study of the rate function of the return probability has proven that the DMI does not affect in the DQPT. We conclude accordingly that the ramping across the quantum critical point is not a necessary and sufficient condition for DQPT.