Dynamical Phase diagram of the Quantum Ising model with Cluster Interaction Under Noisy and Noiseless Driven field

TL;DR

This paper investigates the dynamical quantum phase transitions in a transverse field Ising model with cluster interaction, revealing how noise influences the critical sweep velocity and induces multi-critical modes in the dynamical phase diagram.

Contribution

It demonstrates how noise modifies the dynamical phase diagram, including the critical sweep velocity and the emergence of multi-critical modes, in a model with tunable gap closing points.

Findings

DQPTs occur when quench points are between two critical points.

Critical sweep velocity decreases with increasing noise intensity.

Noise induces multi-critical modes in the dynamical phase diagram.

Abstract

In most lattice models, gap closing typically occurs at high-symmetry points in the Brillouin zone. In the transverse field Ising model with cluster interaction, besides the gap closing at high-symmetry points, the gap closing at the quantum phase transition between paramagnetic and cluster phases of the model can be moved by tuning the strength of the cluster interaction. We take advantage of this property to examine the nonequilibrium dynamics of the model in the framework of dynamical quantum phase transitions (DQPTs) after a noiseless and noisy ramp of the transverse magnetic field. The numerical results show that DQPTs always happen if the starting or ending point of the quench field is restricted between two critical points. In other ways, there is always critical sweep velocity above which DQPTs disappear. Our finding reveals that noise modifies drastically the dynamical phase diagram of the model. We find that the critical sweep velocity decreases by enhancing the noise intensity and scales linearly with the square of noise intensity for weak and strong noise. Moreover, the region with multi-critical modes induced in the dynamical phase diagram by noise. The sweep velocity under which the system enters the multi-critical modes (MCMs) region increases by enhancing the noise and scales linearly with the square of noise intensity