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arXiv:2505.15711 · Physical Review Letters

Dissipative Phase Transition of Interacting Nonreciprocal Fermions

Rafael D. Soares, Matteo Brunelli, Marco Schirò

Published Apr 30, 2026• 3 citations
arXivHTMLPDF

Abstract

While nonreciprocal couplings are ubiquitous in classical systems, their impact on quantum many-body criticality and entanglement remains largely unexplored. Using exact numerical simulations, we study an interacting fermionic chain subject to nonreciprocal gain and loss. We show that the interplay between dissipation and interactions drives a dissipative phase transition, marked by the opening of a many-body gap and a crossover from power law to exponential relaxation. The weakly interacting regime displays nonreciprocal signatures, including nonzero currents and directional charge accumulation reminiscent of the skin effect. Notably, despite this localization, quantum trajectories exhibit volume-law entanglement. Finally, reciprocity is dynamically restored above a critical interaction strength.

DOI
10.1103/n8xv-kygx

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While nonreciprocal couplings are ubiquitous in classical systems, their impact on quantum many-body criticality and entanglement remains largely unexplored. Using exact numerical simulations, we study an interacting fermionic chain subject to nonreciprocal gain and loss. We show that the interplay between dissipation and interactions drives a dissipative phase transition, marked by the opening of a many-body gap and a crossover from power law to exponential relaxation. The weakly interacting regime displays nonreciprocal signatures, including nonzero currents and directional charge accumulation reminiscent of the skin effect. Notably, despite this localization, quantum trajectories exhibit volume-law entanglement. Finally, reciprocity is dynamically restored above a critical interaction strength.
We investigate the impact of nonreciprocity on universality and critical phenomena in open quantum interacting many-body systems. Nonreciprocal open quantum systems often have an exotic spectral sensitivity to boundary conditions, known as the Liouvillian skin effect (LSE). By considering an open quantum XXZ spin chain that exhibits LSE, we demonstrate the existence of a universal scaling regime that is not affected by the presence of the LSE. We resolve the critical exponents, which differ from those of free fermions, via tensor network methods and demonstrate that observables exhibit a universal scaling collapse, irrespective of the reciprocity. We find that the LSE only becomes relevant when a healing length scale ξ_{heal} at the system's edge (which is different from the localization length of the eigenstate of the Liouvillian) exceeds the system size, allowing edge properties to dominate the physics. We expect this result to be a generic feature of nonreciprocal models in the vicinity of a critical point. The driven-dissipative quantum criticality we observe has no classical analog and stems from the existence of multiple dark states.
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The non-Hermitian systems exhibit extreme sensitivity to the boundary conditions. The change in the eigenspectrum with tuning boundary parameter is intimately connected to the non-Hermitian skin effect. The single-particle systems are affected by the boundary perturbations; however, the interplay of a random disorder potential and nonreciprocal hopping under boundary perturbations of an interacting many-body system is not yet clear. In this work, we examine the boundary sensitivity of a non-Hermitian interacting fermionic system in the presence of a random disorder potential. A nonzero boundary parameter results in real-complex spectral transitions with nonreciprocal (or unidirectional) hopping at weak disorder, while the many-body localization at strong disorder washes away real-complex transitions leading to dynamical stability and real eigenvalue spectrum. We show that the boundary-driven real-complex spectral transitions of the non-Hermitian chain are accompanied by the corresponding changes in the level statistics and nearest level-spacing distributions. The intriguing features of nonreciprocity and boundary sensitivity are further revealed using the averaged inverse participation ratios. Finally, we find distinct behavior in the quench dynamics of local particle density, population imbalance, and entanglement entropy of charge-density-wave ordered state that corroborate the real-complex and localization transitions. Our results provide a route to understanding disordered many-body systems under a generalized boundary.
Recent years have seen remarkable development in open quantum systems effectively described by non-Hermitian Hamiltonians. A unique feature of non-Hermitian topological systems is the skin effect, anomalous localization of an extensive number of eigenstates driven by nonreciprocal dissipation. Despite its significance for non-Hermitian topological phases, the relevance of the skin effect to quantum entanglement and critical phenomena has remained unclear. Here, we find that the skin effect induces a nonequilibrium quantum phase transition in the entanglement dynamics. We show that the skin effect gives rise to a macroscopic flow of particles and suppresses the entanglement propagation and thermalization, leading to the area law of the entanglement entropy in the nonequilibrium steady state. Moreover, we reveal an entanglement phase transition induced by the competition between the unitary dynamics and the skin effect even without disorder or interactions. This entanglement phase transition accompanies nonequilibrium quantum criticality characterized by a nonunitary conformal field theory whose effective central charge is extremely sensitive to the boundary conditions. We also demonstrate that it originates from an exceptional point of the non-Hermitian Hamiltonian and the concomitant scale invariance of the skin modes localized according to the power law. Furthermore, we show that the skin effect leads to the purification and the reduction of von Neumann entropy even in Markovian open quantum systems described by the Lindblad master equation. Our work opens a way to control the entanglement growth and establishes a fundamental understanding of phase transitions and critical phenomena in open quantum systems far from thermal equilibrium.
We demonstrate that a boundary-localized periodic (Floquet) drive can induce nontrivial long-range correlations in a non-interacting fermionic chain which is additionally subject to boundary dissipation. Surprisingly, we find that this phenomenon occurs even when the corresponding isolated bulk is in a trivial gapped phase with exponentially decaying correlations. We argue that this boundary-drive induced non-equilibrium transition (as witnessed through the correlation matrix) is driven by a resonance mechanism whereby the drive frequency bridges bulk energy gaps, allowing boundary-injected particles and holes to propagate and mediate long-range correlations into the bulk. We also numerically establish that when the drive bridges a particle-hole gap, the induced long-range order scales as a power law with the bulk pairing potential (χ∼γ2χ\sim γ^2χ∼γ2). Our results highlight the potential of localized coherent driving for generating macroscopic order in open quantum systems.
The interplay between drives and dissipation in quantum many-body systems can lead to a plethora of nonequilibrium phenomena, yet such setups remain particularly challenging to study. Here, the authors explore analytically the dynamics of periodically driven Tomonaga-Luttinger liquids ---paradigmatic interacting quantum matter--- coupled to thermal baths. While in the detailed-balance regime, dissipation suppresses parametric resonances partially, the researchers find that chiral dissipation leads to a novel nonreciprocal phase, reminiscent of the non-Hermitian skin effect.