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arXiv:2112.13550

Fate of entanglement in one-dimensional fermion liquid with coherent particle loss

Wei-Zhu Yi, Lin, Hao-Jie, Ze-Xun Lin, Wei-Qiang Chen

Published Dec 27, 2021• 1 citation
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Abstract

Quantum many-body systems and quantum devices experience the detrimental effects of noise and particle losses, necessitating their treatment as open quantum systems or, in approximation, as non-Hermitian systems. These systems exhibit nontrivial characteristics in their time evolution that differ significantly from closed systems. In this Letter, we study the dynamic properties of a one-dimensional fermionic system with adjacent-lattice particle loss. By utilizing time-dependent correlation matrix methods and bosonization techniques, we demonstrate that, as the system evolves over time, its (bipartite) von Neumann entropy exhibits a universal behavior of rapid increase due to thermalization effects at short times, independent of the effective Hamiltonian and Liouvillian spectra, even in the presence of interactions. Additionally, we show that the asymmetric non-Hermitian terms in the effective Hamiltonian caused by adjacent-lattice quantum jumps lead to left-right asymmetry of quasiparticles in momentum space, which is ubiquitous in non-Hermitian skin effects and introduces momentum-space entanglement independent of the interaction strength at early times. Our study illuminates the universal fate of non-Hermitian fermionic liquids in the open quantum context, enriching our understanding of non-Hermitian many-body systems over the entire time range. Furthermore, our findings provide valuable insights for near-term quantum devices and the quantum simulation of open systems.

DOI
10.48550/arxiv.2112.13550

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The universal dynamical phenomenon of von Neumann entropy plays an important role in understanding the nature of open many-body systems, as it uncovers general collective properties driven by correlation and quantum dynamics. Here, we reveal a universal time evolution behavior of bipartite von Neumann entropy in open quantum systems with dissipation into the surrounding environments. The coupling with the environment leads to a rapid growth of the entropy, resulting in an exotic short-time evolution law, S ( t ) ∼ − t ln t . Such a fast growth behavior is proved to be a general phenomenon for generic many-body systems in dissipative environments, as long as the systems exhibit well-defined fermionic quasiparticles. Interestingly, even for strongly interacting Luttinger liquids, which display vanishing fermionic but emergent bosonic quasiparticles, the same dynamical phenomenon is still found to persist. These results demonstrate a universal Liouvillian dynamical feature that has no counterpart in isolated Hamiltonian systems.
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The Wannier-Stark localization dynamically alters the entanglement behavior of non-Hermitian free fermions. Utilizing the single-particle correlation matrix technique, we analyze the effective Hamiltonian of these fermions with a Wannier-Stark ladder. Under open boundary conditions, we observe steady-state half-chain entanglement entropy (EE) and identify two distinct area-law regions and an algebraic scaling region. Finite-sized scaling analysis reveals critical scaling behavior of the half-chain EE. Notably, the system demonstrates unique entanglement characteristics under periodic boundary conditions, which diverge from the (1+1)d(1+1)d(1+1)d conformal field theory predictions for Anderson localization. Our findings highlight entanglement phases emerging from the interplay between the non-Hermitian skin effect and disorder-free localization.
We study an interacting one-dimensional gas of spin-1/2 fermions with two-body losses. The dynamical phase diagram that characterizes the approach to the stationary state displays a wide quantum Zeno region, identified by a peculiar behavior of the lowest eigenvalues of the associated non-Hermitian Hamiltonian. We characterize the universal dynamics of this Zeno regime using an approximation scheme based on an effective decoupling of charge and spin degrees of freedom, where the latter effectively evolve according to a non-Hermitian Heisenberg Hamiltonian. We present detailed results for the time evolution from initial states with one particle per site with either incoherent or antiferromagnetic spin order, showing how peculiar charge properties witnessed by the momentum distribution function build up in time.
The competition between unitary time evolution and quantum measurements could induce phase transitions in the entanglement characteristics of quantum many-body dynamics. In this work, we reveal such entanglement transitions in the context of non-Hermitian Floquet systems. Focusing on noninteracting fermions in a representative bipartite lattice with balanced gain/loss and under time-periodic quenches, we uncover rich patterns of entanglement transitions due to the interplay between driving and non-Hermitian effects. Specially, we find that the monotonic increase of quenched hopping amplitude could flip the system between volume-law and area-law entangled Floquet phases, yielding alternated entanglement transitions. Meanwhile, the increase of gain/loss strength could trigger area-law to volume-law reentrant transitions in the scaling behavior of steady-state entanglement entropy, which are abnormal and highly unexpected in nondriven systems. Connections between entanglement transitions and parity-time-reversal (PT) transitions in Floquet spectra are further established. Our findings not only build a foundation for exploring entanglement phase transitions in Floquet non-Hermitian setups, but also provide efficient means to engineer and control such transitions by driving fields. Published by the American Physical Society 2024
Non-Hermitian dynamics is ubiquitous in various physical systems. While recent study shows that such a dynamics leads to an area-law scaling of the entanglement entropy due to the non-Hermitian skin effects, it remains unclear how disorder changes the behavior of the entanglement entropy in a non-Hermitian system with skin effects. Here we study the dynamics of a many-body state of free fermions in the paradigmatic Hatano-Nelson model with open boundaries, and find that the area-law behavior of the entanglement entropy in the pristine Hatano-Nelson model develops into a logarithmic scaling for small disorder strength. As we further increase the disorder strength, the system reenters an area-law regime through an entanglement phase transition. At the critical point, the entanglement entropy exhibits a universal algebraic scaling. We further demonstrate the absence of a conformal invariance in the log-law regime by examining the subsystem entanglement entropy, the connected correlation function and the mutual information. Finally, we show the existence of disorder induced entanglement phase transitions in the Hatano-Nelson model with periodic boundaries.