Long-time asymptotics and conservation laws in integrable systems

TL;DR

This paper investigates the slow decay of currents in one-dimensional integrable systems, revealing that certain non-analytic combinations of conservation laws explain this phenomenon.

Contribution

It identifies a non-analytic conservation law in integrable models like the Heisenberg model, clarifying the origin of slow current decay.

Findings

Conservation laws can be non-analytic combinations.

Slow current decay is linked to these hidden conservation laws.

Analytical and numerical methods confirm the existence of these laws.

Abstract

One dimensional systems sometimes show pathologically slow decay of currents. This robustness can be traced to the fact that an integrable model is nearby in parameter space. In integrable models some part of the current can be conserved, explaining this slow decay. Unfortunately, although this conservation law is formally anticipated, in practice it has been difficult to find in concrete cases, such as the Heisenberg model. We investigate this issue both analytically and numerically and find that the appropriate conservation law can be a non-analytic combination of the known local conservation laws and hence is invisible to elementary assumptions.