Floquet Engineering in Quantum Chains

TL;DR

This paper investigates how periodic driving affects a one-dimensional interacting fermion system, revealing different thermalization behaviors and defect formation near quantum critical points using advanced numerical methods.

Contribution

It introduces a DMRG-based approach to study large-time dynamics of driven quantum chains, highlighting the effects of ramp speed and drive frequency on phase transitions and defect formation.

Findings

Power law correlations in gapless phases regardless of ramp speed

Effective temperature depends on ramp rate in gapped phases

Quantum defects form when crossing the quantum critical point

Abstract

We consider a one-dimensional interacting spinless fermion model, which displays the well-known Luttinger liquid (LL) to charge density wave (CDW) transition as a function of the ratio between the strength of the interaction, $U$, and the hopping, $J$. We subject this system to a spatially uniform drive which is ramped up over a finite time interval and becomes time-periodic in the long time limit. We show that by using a density matrix renormalization group (DMRG) approach formulated for infinite system sizes, we can access the large-time limit even when the drive induces finite heating. When both the initial and long-time states are in the gapless (LL) phase, the final state has power law correlations for all ramp speeds. However, when the initial and final state are gapped (CDW phase), we find a pseudothermal state with an effective temperature that depends on the ramp rate, both for the Magnus regime in which the drive frequency is very large compared to other scales in the system and in the opposite limit where the drive frequency is less than the gap. Remarkably, quantum defects (instantons) appear when the drive tunes the system through the quantum critical point, in a realization of the Kibble-Zurek mechanism.