Interplay between transport and quantum coherences in free fermionic systems

TL;DR

This paper investigates how initial quantum correlations affect transport in free fermionic systems, revealing that higher correlations lead to slower transport, supported by exact solutions in both lattice and continuous models.

Contribution

It introduces a quantitative framework linking quantum correlations and transport speed, including a novel 'transition map' function and exact solutions for correlated initial states.

Findings

More correlated initial states slow down transport.

A 'transition map' relates stationary current to correlations.

Extended full counting statistics for correlated domain walls.

Abstract

We study the quench dynamics in free fermionic systems in the prototypical bipartitioning protocol obtained by joining two semi-infinite subsystems prepared in different states, aiming at understanding the interplay between quantum coherences in space in the initial state and transport properties. Our findings reveal that, under reasonable assumptions, the more correlated the initial state, the slower the transport is. Such statement is first discussed at qualitative level, and then made quantitative by introducing proper measures of correlations and transport ``speed''. Moreover, it is supported for fermions on a lattice by an exact solution starting from specific initial conditions, and in the continuous case by the explicit solution for a wider class of physically relevant initial states. In particular, for this class of states, we identify a function, that we dub \emph{transition map}, which takes the value of the stationary current as input and gives the value of correlation as output, in a protocol-independent way. As an aside technical result, in the discrete case, we give an expression of the full counting statistics in terms of a continuous kernel for a general correlated domain wall initial state, thus extending the recent results in [Moriya, Nagao and Sasamoto, JSTAT 2019(6):063105] on the one-dimensional XX spin chain.