Steady state entanglement beyond the thermodynamic limit

Shinji Mukohyama A

Xu Feng, Shu Chen

The skin effect, characterized by the tendency of particles to accumulate at the boundaries, has been extensively studied in non-Hermitian systems. In this paper, we propose an intuitive Lindbladian composed of two chains with reversed skin localization. The skin steady state is gradually delocalized as the interchain coupling increases. In the single-body scenario, it corresponds to a shift in the scaling of the Liouvillian gap $\mathrm{\ensuremath{\Delta}}$ from $\mathrm{\ensuremath{\Delta}}\ensuremath{\propto}{N}^{0}$ to $\mathrm{\ensuremath{\Delta}}\ensuremath{\propto}{N}^{\ensuremath{-}2}$. Notably, exact diagonalization results reveal a system-size sensitivity of the single-particle Liouvillian spectrum, inherited from the system-size sensitivity of the non-Hermitian effective Hamiltonian. We predict that even an arbitrarily small coupling will induce dramatic changes in the Liouvillian spectrum and steady state in the thermodynamic limit, a phenomenon we term the critical Liouvillian skin effect. Additionally, in the many-body scenario, by employing the stochastic Schr\"odinger equation to unravel the Lindblad master equation, it is revealed that the scaling behavior of steady-state entanglement changes from the area law to the logarithmic law. In this paper, we demonstrate the delocalization of both single- and many-body skin steady states, introducing a mechanism for inducing entanglement transitions beyond the quantum Zeno effect.

Fernando G. S. L. Brandão, Martin Bodo Plenio

Kai Müller, Walter T. Strunz

We investigate the occurrence of genuine quantum effects and beyond mean-field physics in the balanced and unbalanced open Dicke models with a large yet finite number of atoms N. Such driven and dissipative quantum many-body systems have recently been realized in experiments involving ultracold gases inside optical cavities and are known to obey mean-field predictions in the thermodynamic limit N→∞. Here we show quantum effects that survive for large but finite N, by employing a novel open-system dynamics method that allows us to obtain numerically exact quantum dynamical results for atom numbers up to a mesoscopic N≈1000. While we find that beyond-mean-field effects vanish quickly with increasing N in the balanced Dicke model, we are able to identify parameter regimes in the unbalanced Dicke model that allow genuine quantum effects to persist even for mesoscopic N. They manifest themselves in a strong squeezing of the steady state and a modification of the steady-state phase diagram that cannot be seen in a mean-field description. This is due to the fact that the steady-state limit t→∞ and thermodynamic limit N→∞ do not commute.

Rui-Jing Guo, Ji-Yao Chen, Zhi-Yuan Wei

A common view in monitored quantum dynamics is that local measurements suppress entanglement growth. We show that this intuition can fail in a one-dimensional spinful fermionic chain governed by a BCS Hamiltonian with pairing strength $Δ$ and subject to continuous, on-site, spin-resolved charge measurements at rate $γ$. Using free-fermion simulations and quasiparticle analysis, we show that pairing suppresses entanglement growth, while measurements suppress pairing. Their competition yields measurement-enhanced entanglement: for $Δ>0$, the steady-state entanglement $\mathcal{S}_s$ increases with $γ$ over a finite interval $0<γ<γ_{\mathrm{peak}}$. This occurs because stronger measurements suppress pairing correlations, which would otherwise suppress entanglement growth. Using a nonlinear sigma-model calculation and free-fermion simulations, we provide evidence that for $Δ>0$ and small but finite $γ$, the steady-state entanglement scales as $\mathcal{S}_s(L)\sim \ln^2 L$. This implies that, in this setting, measurement-enhanced entanglement does not persist in the thermodynamic limit.

Pasquale Calabrese