Non-equilibrium dynamics of superconductivity in the Hatsugai-Kohmoto model

TL;DR

This paper investigates the non-equilibrium dynamics of superconductivity in the Hatsugai-Kohmoto model, revealing complex phase behavior, dynamical quantum phase transitions, and the surprising resilience of momentum space entanglement during quenches.

Contribution

It provides the first detailed analysis of the non-equilibrium superconducting dynamics in the HK model, including phase diagram mapping and entanglement behavior.

Findings

Identified three dynamical phases with different long-time behaviors of the order parameter.

Discovered that Loschmidt echo's non-analyticities do not precisely match superconductivity vanishing.

Found that momentum space entanglement remains large despite the decay of superconductivity.

Abstract

We study the non-equilibrium dynamics of the superconducting order parameter in the Hatsugai-Kohmoto (HK) model. In the absence of superconductivity, its ground state is a non-Fermi liquid, whose properties are controlled by the HK interaction. Our protocol involves quantum quenching the HK interaction but leaving the interaction responsible for superconductivity unchanged. We map out the non-equilibrium dynamical phase diagram of the interacting model which contains three phases where, at long times, the order parameter amplitude vanishes, approaches a constant value or persistently oscillates. We also investigate the Loschmidt echo in searching for dynamical quantum phase transition, and find that its non-analytic temporal behaviour is close but does not match exactly the vanishing of the order parameter. The momentum space entanglement entropy between positive and negative momentum modes, relevant for Cooper pairing, is calculated. Counterintuitively, this momentum space entanglement does not change significantly during the quench dynamics and its value remains reasonably large even for vanishing superconducting order parameter. Nevertheless, its derivative with respect to the HK interaction signals the dynamical phase transition associated to the late time vanishing of superconductivity.