Interplay between transport and quantum coherences in free fermionic systems

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 spatial correlations 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 a byproduct, 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.

Exact entanglement growth of a one-dimensional hard-core quantum gas during a free expansion

“…Moreover, the particles spreading is bounded by the propagation velocity of the fastest modes k = ±π/2, |v(±π/2)| = 1, which define the light-cone region |x/τ | 1, outside of which the system keeps its initial configuration. Close to the light-cone, there is a boundary layer of width x/τ ± 1 ∼ τ −2/3 which allows the matching of the physics of the bulk of the light-cone with the one outside of it [76,85,86]. We mention that within our hydrodynamic approach it is possible to establish the correct behavior also in this layer, see e.g.…”

“…This setup has been studied intensively in the past and the exact expressions for the conserved charges and current profiles have been found for a spin-1/2 xxz model both in the free [65,75] and interacting [72] cases. Very recently, it was also shown that initial quantum correlations can suppress particle transport [76]. On the other hand, so far the exact evolution of the entanglement entropy has been only conjectured on the basis of heuristic arguments and numerical results [67,68,72].…”

Generalized-hydrodynamic approach to inhomogeneous quenches: correlations, entanglement and quantum effects

“…where the initial state is composed by the junction of two different homogeneous pieces, have been extensively studied in the literature. Of particular interest have been the sudden junction of two half chains prepared at different temperatures [38,39, and at different chemical potentials (or fillings) [38,44,50,, but more general initial states have also been considered [38,[111][112][113][114][115][116][117], particularly in relation to studies on the entanglement growth (see section 4 for references). Here we will refer to inhomogeneous quenches of this kind as 'bipartitioning protocols'.…”

Exact entanglement growth of a one-dimensional hard-core quantum gas during a free expansion

“…Moreover, the particles spreading is bounded by the propagation velocity of the fastest modes k = ±π/2, |v(±π/2)| = 1, which define the light-cone region |x/τ | 1, outside of which the system keeps its initial configuration. Close to the light-cone, there is a boundary layer of width x/τ ± 1 ∼ τ −2/3 which allows the matching of the physics of the bulk of the light-cone with the one outside of it [74,83,84]. We mention that within our hydrodynamic approach it is possible to establish the correct behavior also in this layer, see e.g.…”

“…This setup has been studied intensively in the past and the exact expressions for the conserved charges and current profiles have been found for a spin-1/2 xxz model both in the free [68,73] and interacting [67] cases. Very recently, it was also shown that initial quantum correlations can suppress particle transport [74]. On the other hand, so far the exact evolution of the entanglement entropy has been only conjectured on the basis of heuristic arguments and numerical results [64,65,67].…”