Information transport and transport-induced entanglement in open fermion chains

TL;DR

This work addresses how information and entanglement propagate in nonequilibrium open quantum many-body systems by introducing the information lattice, a local, scale-resolved description of information flow tied to a solvable model of noninteracting fermions driven by Lindblad reservoirs. The authors derive explicit local information currents, connect them to both unitary dynamics and environmental dissipation, and show that particle-hole symmetry induces a shielding effect that limits information flow into the bulk, while impurities or symmetry breaking create an information pillar that establishes long-range correlations. They link the information lattice to experimentally accessible noise measurements via a noise lattice and the Klich–Levitov correspondence, enabling practical probes of information transport and transport-induced entanglement quantified by fermionic negativity. The results reveal impurity- and symmetry-driven control of information and entanglement spread in nonequilibrium steady states, offering a path toward a hydrodynamic-like theory of entanglement in open quantum matter with potential experimental verification in quantum-dot arrays and ultracold fermionic systems. The study lays groundwork for extensions to interacting systems, heat transport, and measurement-induced dynamics, aiming to unify microscopic information scrambling with macroscopic transport laws.

Abstract

Understanding the entanglement dynamics in quantum many-body systems under steady-state transport conditions is an actively pursued challenging topic. Hydrodynamic equations, akin to transport equations for charge or heat, would be of great interest but face severe challenges because of the inherent nonlocality of entanglement and the difficulty of identifying conservation laws. We show that progress is facilitated by using information as key quantity related to - but distinct from - entanglement. Employing the recently developed "information lattice" framework, we characterize spatially and scale-resolved information currents in nonequilibrium open quantum systems. Specifically, using Lindblad master equations, we consider noninteracting fermion chains coupled to dissipative reservoirs. By relating the information lattice to a noise lattice constructed from particle-number fluctuations, we show that information is experimentally accessible via noise easurements. Similarly, local information currents can be obtained by measuring particle currents, onsite occupations, and covariances of particle numbers and/or particle currents. Using the fermionic negativity to quantify bipartite entanglement, we also study transport-induced entanglement and its relation to information currents. For a clean particle-hole symmetric chain, we find that information currents are shielded from entering the information lattice. Impurities or particle-hole asymmetry break this effect, causing information current flow and entanglement between end segments of the chain. Our work opens the door to systematic investigations of information transport and entanglement generation in driven open quantum systems far from equilibrium.

Figures (19)

• Figure 1: Schematic of a spinless fermion chain with $N$ sites, connected at its ends to fermionic reservoirs with single-particle injection (removal) rates $\Gamma_1$ and $\Gamma_N$ ($\gamma_1$ and $\gamma_N$), respectively. A possible partition into a subsystem $A$ (red sites) with complement $\bar{A}={\bar{A}}_L \cup {\bar{A}}_R$ (blue sites) is indicated.
• Figure 2: Information lattice and information currents for system size $N=2$. Circles indicate the possible subsystems $A=(\ell, n)$. Filled circles on the bottom layer $\ell=0$ correspond to physical sites $(n=1,2)$ representing information in the single-site density matrices. a) Triangle representation of the information lattice using $I_{(\ell,n)}$ in Eq. \ref{['eq:von_neumann_entropy']}. b) Site representation using $i_{(\ell,n)}$ in Eq. \ref{['eq:triangles-to-sites']}. c) Information currents in the site representation, see Eq. \ref{['eq:info-currents']}, with the unitary terms \ref{['unitarycurr2']} shown as blue arrows and the dissipative terms \ref{['disscurr2']} as wavy orange arrows. Dotted lines refer to the interpretations discussed in the text.
• Figure 3: Information lattice and information currents for $N=3$. Circles indicate all possible subsystems $A=(\ell, n)$. Filled circles on the bottom layer correspond to physical sites. a) Triangular representation of the information lattice. b) Effective information currents $\tilde{\cal I}_{(\ell,n),R/L/E}$ in site representation from Eqs. \ref{['conservN3']} and \ref{['effcurrent']}, distinguishing unitary (blue arrows) and dissipative terms (wavy orange arrows). For the bottom layer $\ell=0$, one finds $\tilde{\cal I}_{(0,n),R/L/E}= {\cal I}_{(0,n),R/L/E}$.
• Figure 4: Information currents for arbitrary $N$ at a generic site $(\ell,n)$ of the information lattice, see Eq. \ref{['fig4formula']}. Unitary (dissipative) terms are shown as blue (wavy orange) arrows.
• Figure 5: Average occupation number $\bar{n}_j$ vs site index $j$ under large-bias conditions in the NESS for $N=21$, $g=J=1$, and $\epsilon=0$. Dashed lines are guides to the eye only. (a) Impurity-free case for different particle-hole asymmetry parameters $\delta$. (b) Results for $\delta=0$ and a site defect at $j_0=11$ with different values of $\epsilon_{j_0}$.