1,721,180 research outputs found
Diffusion and operator entanglement spreading
No full textUnderstanding the spreading of the operator space entanglement entropy (OSEE) is key in order to explore out-of-equilibrium quantum many-body systems. Here we argue that for integrable models the dynamics of the OSEE is related to the diffusion of the operator front. We derive the logarithmic bound 1/2ln(t) for the OSEE of some simple, i.e., low-rank, diagonal local operators. We numerically check that the bound is saturated in the rule 54 chain, which is representative of interacting integrable systems. Remarkably, the same bound is saturated in the spin-1/2 Heisenberg XXZ chain. Away from the isotropic point and from the free-fermion point, the OSEE grows as 1/2ln(t), irrespective of the chain anisotropy, suggesting universality. Finally, we discuss the effect of integrability breaking. We show that strong finite-time effects are present, which prevent us from probing the asymptotic behavior of the OSEE
Towards a Generalized Hydrodynamics description of Rényi entropies in integrable systems
No full text
Noninteracting fermionic systems with localized losses: Exact results in the hydrodynamic limit
No full textWe investigate the interplay between unitary and nonunitary dynamics after a quantum quench in a noninteracting fermionic chain. In particular, we consider the effect of localized loss processes, for which fermions are added and removed incoherently at the center of the chain. We focus on the hydrodynamic limit of large distances from the localized losses and of long times, with their ratio being fixed. In this limit, the localized losses gives rise to an effective imaginary delta potential (nonunitary impurity), and the time-evolution of the local correlation functions admits a simple hydrodynamic description in terms of the fermionic occupations in the initial state and the reflection and transmission amplitudes of the impurity. We derive this hydrodynamic framework from the ab initio calculation of the microscopic dynamics. This allows us to analytically characterize the effect of losses for several theoretically relevant initial states, such as a uniform Fermi sea, homogeneous product states, or the inhomogeneous state obtained by joining two Fermi seas. In this latter setting, when both gain and loss processes are present, we observe the emergence of exotic nonequilibrium steady states with stepwise uniform density profiles. In all instances, for strong loss and gain rates the coherent dynamics of the system is arrested, which is a manifestation of the celebrated quantum Zeno effect
Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics
No full textWe consider a molecular dynamics method, the so-called flea gas for computing the evolution of entanglement after inhomogeneous quantum quenches in an integrable quantum system. In such systems the evolution of local observables is described at large space-time scales by the Generalized Hydrodynamics approach, which is based on the presence of stable, ballistically propagating quasiparticles. Recently it was shown that the GHD approach can be joined with the quasiparticle picture of entanglement evolution, providing results for entanglement growth after inhomogeneous quenches. Here we apply the flea gas simulation of GHD to obtain numerical results for entanglement growth. We implement the flea gas dynamics for the gapped anisotropic Heisenberg XXZ spin chain, considering quenches from globally homogeneous and piecewise homogeneous initial states. While the flea gas method applied to the XXZ chain is not exact even in the scaling limit (in contrast to the Lieb–Liniger model), it yields a very good approximation of analytical results for entanglement growth in the cases considered. Furthermore, we obtain the full-time dynamics of the mutual information after quenches from inhomogeneous settings, for which no analytical results are available
Spreading of correlations in Markovian open quantum systems
Full text linkUnderstanding the spreading of quantum correlations in out-of-equilibrium many-body systems is one of the major challenges in physics. For isolated systems, a hydrodynamic theory explains the origin and spreading of entanglement via the propagation of quasiparticle pairs. However, when systems interact with their surrounding much less has been established. Here we show that the quasiparticle picture remains valid for open quantum systems: While information is still spread by quasiparticles, the environment modifies their correlation and introduces incoherent and mixing effects. For free fermions with gain/loss dissipation we provide formulas fully describing incoherent and quasiparticle contributions in the spreading of entropy and mutual information. Importantly, the latter is not affected by entanglement of the system with the external environment. The mutual information is exponentially damped at short times and eventually vanishes signaling the onset of a classical limit. The behavior of the logarithmic negativity is similar and this scenario is common to other dissipations. For weak dissipation, the presence of quasiparticles underlies remarkable scaling behaviors
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