Dynamical quantum phase transitions in the axial next-nearest-neighbour Ising chain

TL;DR

This paper studies how non-integrable perturbations affect dynamical quantum phase transitions in the transverse field Ising chain after a sudden quench, showing these phenomena are robust and generic.

Contribution

It derives analytical expressions for the Loschmidt amplitude in a perturbed Ising model and demonstrates the robustness of dynamical quantum phase transitions against non-integrable interactions.

Findings

Non-analyticities in the rate function occur at critical times.

Perturbations shift and reshape the non-analyticities.

Dynamical quantum phase transitions are robust to non-integrable perturbations.

Abstract

We investigate sudden quenches across the critical point in the transverse field Ising chain with a perturbing non-integrable next-nearest-neighbour interaction. Expressions for the return (Loschmidt) amplitude and associated rate function are derived to linear order in the next-nearest-neighbour coupling. In the thermodynamic limit these quantities exhibit non-analytic behaviour at a set of critical times, a phenomenon referred to as a dynamical quantum phase transition. We quantify the effect of the integrability breaking perturbation on the location and shape of these non-analyticities. Our results agree with those of earlier numerical studies and offer further support for the assertion that the dynamical quantum phase transitions exhibited by this model are a generic feature of its post-quench dynamics and is robust with respect to the inclusion of non-integrable perturbations.