Burnett coefficients in quantum many-body systems

TL;DR

This paper investigates the Burnett coefficient in quantum many-body systems, revealing different growth behaviors in integrable and non-integrable chains, and providing insights into transport properties.

Contribution

It provides the first detailed numerical analysis of the Burnett coefficient in quantum spin chains, distinguishing behaviors in integrable and non-integrable regimes.

Findings

Non-integrable chains show linear growth of B(t) with time.

Integrable chains exhibit cubic growth of B(t) with time.

Results are supported by studies in non-interacting and classical large-spin chains.

Abstract

The Burnett coefficient B is investigated for transport in one-dimensional quantum many-body systems. Extensive numerical computations in spin-1/2 chains suggest a linear growth with time, B(t) \sim t, for non-integrable chains exhibiting diffusive transport. For integrable spin chains in the metallic regime, on the other hand, we find a cubic growth with time, B(t) \sim -D_m^2 t^3, with the proportionality constant being simply a square of the Drude weight D_m. The results are corroborated with additional studies in non-interacting quantum chains and in the classical limit of large-spin chains.