Steady-state entanglement scaling in open quantum systems: A comparison between several master equations

TL;DR

This paper compares different master equations to analyze how fermionic logarithmic negativity scales in the steady state of a driven-dissipative quantum chain, revealing regimes of logarithmic and superlogarithmic growth.

Contribution

It provides a comparative analysis of three master equations, highlighting their predictions for entanglement scaling in open quantum systems.

Findings

Nonlocal Lindblad predicts logarithmic FLN growth for all couplings.

Redfield and ULE show logarithmic growth in weak coupling, superlogarithmic beyond.

FLN scaling behavior depends on coupling strength and subsystem size.

Abstract

We investigate the scaling of the fermionic logarithmic negativity (FLN) between complementary intervals in the steady state of a driven-dissipative tight-binding critical chain, coupled to two thermal reservoirs at its edges. We compare the predictions of three different master equations, namely a nonlocal Lindblad equation, the Redfield equation, and the recently proposed universal Lindblad equation (ULE). Within the nonlocal Lindblad equation approach, the FLN grows logarithmically with the subsystem size $\ell$, for any value of the system-bath coupling and of the bath parameters. This is consistent with the logarithmic scaling of the mutual information analytically demonstrated in [Phys. Rev. B 106, 235149 (2022)]. In the ultraweak-coupling regime, the Redfield equation and the ULE exhibit the same logarithmic increase; such behavior holds even when moving to moderately weak coupling and intermediate values of $\ell$. However, when venturing beyond this regime, the FLN crosses over to superlogarithmic scaling for both equations.