Long-living prethermalization in nearly integrable spin ladders

TL;DR

This paper demonstrates that in nearly integrable spin ladders, certain observables exhibit extremely slow relaxation due to intersecting integrability lines, leading to long-lived prethermal states with fewer conserved quantities.

Contribution

It reveals a novel relaxation behavior near the intersection of integrability lines, showing a fourth-power dependence and long-lived prethermalization in spin ladder systems.

Findings

Relaxation rates can be significantly smaller near the intersection of integrability lines.

Certain observables show relaxation rates scaling with the fourth power of the distance from the intersection.

Long-lived prethermalization occurs with fewer nearly conserved operators.

Abstract

Relaxation rates in nearly integrable systems usually increase quadratically with the strength of the perturbation that breaks integrability. We show that the relaxation rates can be significantly smaller in systems that are integrable along two intersecting lines in the parameter space. In the vicinity of the intersection point, the relaxation rates of certain observables increase with the fourth power of the distance from this point, whereas for other observables one observes standard quadratic dependence on the perturbation. As a result, one obtains exceedingly long-living prethermalization but with a reduced number of the nearly conserved operators. We show also that such a scenario can be realized in spin ladders.