Logarithmic entanglement scaling in dissipative free-fermion systems

Abstract

We study the quantum information spreading in one-dimensional free-fermion systems in the presence of localized thermal baths. We employ a nonlocal Lindblad master equation to describe the system-bath interaction, in the sense that the Lindblad operators are written in terms of the Bogoliubov operators of the closed system, and hence are nonlocal in space. The statistical ensemble describing the steady state is written in terms of a convex combination of the Fermi-Dirac distributions of the baths. Due to the singularity of the free-fermion dispersion, the steady-state mutual information exhibits singularities as a function of the system parameters. While the mutual information generically satisfies an area law, at the singular points it exhibits logarithmic scaling as a function of subsystem size. By employing the Fisher-Hartwig theorem, we derive the prefactor of the logarithmic scaling, which depends on the parameters of the baths and plays the role of an effective "central charge". This is upper bounded by the central charge governing ground-state entanglement scaling. We provide numerical checks of our results in the paradigmatic tight-binding chain and the Kitaev chain.

17 pages, 11 figures. Added two figures. Close to published version

References in corpus (16)

• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Strong dissipation inhibits losses and induces correlations in cold molecular gases
• The entanglement entropy of one-dimensional gases
• Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
• Universal corrections to scaling for block entanglement in spin-1/2 XX chains
• Coherent and dissipative dynamics at quantum phase transitions
• Solution of the fermionic entanglement problem with interface defects
• The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas
• Strong correlations in lossy one-dimensional quantum gases: from the quantum Zeno effect to the generalized Gibbs ensemble
• Enhanced entanglement negativity in boundary driven monitored fermionic chains
• Correlation engineering via non-local dissipation
• Dissipative quasi-particle picture for quadratic Markovian open quantum systems
• Unbounded entanglement production via a dissipative impurity
• Hydrodynamics of quantum entropies in Ising chains with linear dissipation
• Self-consistent microscopic derivation of Markovian master equations for open quadratic quantum systems
• Noninteracting fermionic systems with localized losses: Exact results in the hydrodynamic limit

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• Asymptotic freedom, lost: Complex conformal field theory in the two-dimensional $O(N>2)$ nonlinear sigma model and its realization in Heisenberg spin chains
• Rényi negativities in non-equilibrium open free-boson chains
• Macroscopic theory of multipartite correlations in permutation-invariant open quantum systems