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arXiv:2106.11997 · Physical review. B./Physical review. B

Dissipative quasiparticle picture for quadratic Markovian open quantum systems

Federico Carollo, Vincenzo Alba

Published Apr 22, 2022• 44 citations
arXivHTMLPDF

Abstract

Correlations between different regions of a quantum many-body system can be quantified through measures based on entropies of (reduced) subsystem states. For closed systems, several analytical and numerical tools, e.g., hydrodynamic theories or tensor networks, can accurately capture the time evolution of subsystem entropies, thus allowing for a profound understanding of the unitary dynamics of quantum correlations. However, these methods either cannot be applied to open quantum systems or do not permit an efficient computation of quantum entropies for mixed states. Here we make progress in solving this issue by developing a dissipative quasiparticle picture---describing quantum entropies and the mutual information in the limit of large space-time coordinates with their ratio being fixed---and showing its validity for quadratic open quantum systems. Our results demonstrate that the open quantum many-body dynamics of correlations can be understood in terms of propagating (dissipative) quasiparticles.

DOI
10.1103/physrevb.105.144305

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Correlations between different regions of a quantum many-body system can be quantified through measures based on entropies of (reduced) subsystem states. For closed systems, several analytical and numerical tools, e.g., hydrodynamic theories or tensor networks, can accurately capture the time evolution of subsystem entropies, thus allowing for a profound understanding of the unitary dynamics of quantum correlations. However, these methods either cannot be applied to open quantum systems or do not permit an efficient computation of quantum entropies for mixed states. Here we make progress in solving this issue by developing a dissipative quasiparticle picture---describing quantum entropies and the mutual information in the limit of large space-time coordinates with their ratio being fixed---and showing its validity for quadratic open quantum systems. Our results demonstrate that the open quantum many-body dynamics of correlations can be understood in terms of propagating (dissipative) quasiparticles.
Correlations between different regions of a quantum many-body system can be quantified through measures based on entropies of (reduced) subsystem states. For closed systems, several analytical and numerical tools, e.g., hydrodynamic theories or tensor networks, can accurately capture the time-evolution of subsystem entropies, thus allowing for a profound understanding of the unitary dynamics of quantum correlations. However, so far, these methods either cannot be applied to open quantum systems or do not permit an efficient computation of quantum entropies for mixed states. Here, we make progress in solving this issue by formulating a dissipative quasi-particle picture -- describing the dynamics of quantum entropies in the hydrodynamic limit -- for a general class of noninteracting open quantum systems. Our results show that also in dissipative many-body systems, correlations are generically established through the propagation of quasi-particles.
In a non-equilibrium many-body system, the quantum information dynamics between non-complementary regions is a crucial feature to understand the local relaxation towards statistical ensembles. Unfortunately, its characterization is a formidable task, as non-complementary parts are generally in a mixed state. We show that for integrable systems, this quantum information dynamics can be quantitatively understood within the quasiparticle picture for the entanglement spreading. Precisely, we provide an exact prediction for the time evolution of the logarithmic negativity after a quench. In the space-time scaling limit of long times and large subsystems, the negativity becomes proportional to the Rényi mutual information with Rényi index α = 1 / 2 . We provide robust numerical evidence for the validity of our results for free-fermion and free-boson models, but our framework applies to any interacting integrable system.
We develop a hydrodynamic description for the driven-dissipative dynamics of the entanglement negativity, which quantifies the genuine entanglement in mixed-state systems. We focus on quantum quenches in fermionic and bosonic systems subject to linear dissipation, as described by quadratic Lindblad master equations. In the spirit of hydrodynamics, we divide the system into mesoscopic cells. At early times, correlations are generated in each cell by the unitary component of the evolution. Correlations are then transported across different cells via ballistic quasiparticle propagation, while simultaneously evolving under the action of the environment. We show that in the hydrodynamic limit the negativity can be reconstructed from the correlations between the independently propagating quasiparticles. We benchmark our approach considering quenches from both homogeneous and inhomogeneous initial states in the Kitaev chain, the tight-binding chain, and the harmonic chain in the presence of gain or loss dissipation.
Abstract We study the dynamics of quantum information and of quantum correlations after a quantum quench, in transverse field Ising chains subject to generic linear dissipation. As we show, in the hydrodynamic limit of long times, large system sizes, and weak dissipation, entropy-related quantities—such as the von Neumann entropy, the Rényi entropies, and the associated mutual information—admit a simple description within the so-called quasiparticle picture. Specifically, we analytically derive a hydrodynamic formula, recently conjectured for generic noninteracting systems, which allows us to demonstrate a universal feature of the dynamics of correlations in such dissipative noninteracting system. For any possible dissipation, the mutual information grows up to a time scale that is proportional to the inverse dissipation rate, and then decreases, always vanishing in the long time limit. In passing, we provide analytic formulas describing the time-dependence of arbitrary functions of the fermionic covariance matrix, in the hydrodynamic limit.
The spreading of information forms the basis of several quantum nonequilibrium phenomena, such as seen in the emergence of thermodynamics and statistical physics. Recently, much progress has been made in understanding the dynamics of information in isolated integrable systems after a quantum quench, by using a quasiparticle picture predicting ballistic spreading of quantum correlations. This paper shows how to apply these ideas to describe the dissipative dynamics of correlations and of entanglement in open quantum many-body systems.
The time evolution of a quantum state with short-range correlations after a quench to a one-dimensional critical Hamiltonian can be understood using the quasiparticle picture, which states that local entanglement spreads as if it was carried by quasiparticles which separate at a fixed speed. We extend the quasiparticle picture using the recently introduced link representation of entanglement, allowing us to apply it to initial states presenting long-range correlations. The entanglement links are current correlators, and therefore follow a wave equation on the appropriate configurational space which allows us to predict the time evolution of the entanglement entropies. Our results are checked numerically for free fermionic chains with different initial entanglement patterns.