Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 54, Issue 40, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8121/ac20ef
Keywords
quantum hydrodynamics; quantum coherence; transport; free fermions
Categories
Funding
- Swiss National Science Foundation under division II
- ERC [771536]
- ANR [ANR-17-CE30-0027-01 RaMaTraF]
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In the study of quench dynamics in free fermionic systems, it was found that the higher the correlation in the initial state, the slower the transport speed. This relationship was both qualitatively and quantitatively analyzed using proper measures of correlations and transport 'speed'. Additionally, an exact solution for fermions on a lattice and an explicit solution for a wider class of physically relevant initial states in the continuous case supported this finding.
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 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 et al (2019 J. Stat. Mech. 2019 063105) on the one-dimensional XX spin chain.
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