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arXiv:2610.22223

Constrained dissipation and the lifetime of quantum many-body scars

Weyner Ccuiro, Rosario Fazio, Alessandro Silva

quant-phcond-mat.stat-mechSubmitted Oct 15, 2026• Announced Oct 16, 2026• 0 citations• Revised Oct 16, 2026 (v2)
v1 · Oct 15, 2026v2 · Oct 16, 2026
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Abstract

We investigate the fate of quantum many-body scars in the PXP model subject to Markovian dissipation. We show that when local jump operators respect the same symmetries of the Hamiltonian the full Liouvillian spectrum displays a tower of states with properties analogous to standard quantum scars: large overlaps with Néel states and equally spaced gaps in the imaginary part of the eigenvalues, set by a single frequency. Whether the long-time dynamics is dominated by scars is determined by the real parts of the eigenvalues, which are set by the ratio between the two relaxation rates $γ_{\pm}$ describing spin flips down-to-up or up-to-down respectively. For asymmetric dissipation ($γ_+ > γ_-$) the scarred eigenvalues have the smallest real parts: the resulting enhanced fidelity oscillations are further stabilized by staggered jump operators. In contrast, replacing the full projection operator in the dissipators with a partial one breaks the symmetries of the problem and is seen to destroy dissipative scars altogether.

Comments
6 pages, 4 figures; plus 6 pages of Supplemental Material (3 figures)

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We investigate the fate of quantum many-body scars in the PXP model subject to Markovian dissipation. We show that when local jump operators respect the same symmetries of the Hamiltonian the full Liouvillian spectrum displays a tower of states with properties analogous to standard quantum scars: large overlaps with Néel states and equally spaced gaps in the imaginary part of the eigenvalues, set by a single frequency. Whether the long-time dynamics is dominated by scars is determined by the real parts of the eigenvalues, which are set by the ratio between the two relaxation rates γ±γ_{\pm}γ±​ describing spin flips down-to-up or up-to-down respectively. For asymmetric dissipation (γ+>γ−γ_+ > γ_-γ+​>γ−​) the scarred eigenvalues have the smallest real parts: the resulting enhanced fidelity oscillations are further stabilized by staggered jump operators. In contrast, replacing the full projection operator in the dissipators with a partial one breaks the symmetries of the problem and is seen to destroy dissipative scars altogether.
Abstract We investigated the stability of quantum many-body scars under perturbations using a PXP model. Using numerical simulations, we analyzed the fidelity and correlation functions of the system to track its evolution and assess the persistence of revivals. We explored two distinct types of perturbations: imperfections in the initial state, which naturally arise in experimental settings, and disorder in the Hamiltonian, which was introduced as a computational tool to probe the system’s response to external disturbances. We found that while certain initial state modifications can partially stabilize oscillations by restricting the system’s accessible dynamics, others accelerate thermalization by increasing overlap with the full eigenstate spectrum. Similarly, disorder in the Hamiltonian gradually suppresses revivals and enhances thermalization, but scars demonstrate robustness for small perturbations. Our results provide insights into the conditions under which quantum many-body scars persist, offering valuable implications for experimental realizations and controlled quantum dynamics.
Quantum many-body scars are nonthermal excited eigenstates of nonintegrable Hamiltonians, which could support coherent revival dynamics from special initial states when scars form an equally spaced tower in the energy spectrum. For open quantum systems, engineering many-body scarred dynamics by a controlled coupling to the environment remains largely unexplored. Here, we provide a general framework to exactly embed quantum many-body scars into the decoherence-free subspaces of Lindblad master equations. The dissipative scarred dynamics manifest persistent periodic oscillations for generic initial states, and can be practically utilized to prepare scar states with potential quantum metrology applications. We construct the Liouvillian dissipators with the local projectors that annihilate the whole scar towers, and utilize the Hamiltonian part to rotate the undesired states out of the null space of dissipators. We demonstrate our protocol through several typical models hosting many-body scar towers and propose an experimental scheme to observe the dissipative scarred dynamics based on digital quantum simulations and resetting ancilla qubits.
We study the nature of the ergodicity-breaking ``quantum many-body scar'' states that appear in the PXP model describing constrained Rabi oscillations. For a wide class of bipartite lattices of Rydberg atoms, we reveal that the nearly energy-equidistant tower of these states arises from the Hamiltonian's close proximity to a generalized projector-embedding form in Phys. Rev. Lett. 119, 030601 (2017), a structure common to many models hosting quantum many-body scars. We construct a non-Hermitian but strictly local extension of the PXP model hosting exact quantum scars and show how various Hermitian scar-stabilizing extensions from the literature can be naturally understood within this framework. The exact scar states are obtained analytically as large spin states of explicitly constructed pseudospins. The quasiperiodic motion ensuing from the N\'eel state is finally shown to be the projection onto the Rydberg-constrained subspace of the precession of the large pseudospin.
Quantum many-body scars have received much recent attention for being both intriguing nonergodic states in otherwise quantum chaotic systems and promising candidates to encode quantum information efficiently. So far, these studies have mostly been restricted to Hermitian systems. Here, we study many-body scars in many-body quantum chaotic systems coupled to a Markovian bath, which we term Lindblad many-body scars. They are defined as simultaneous eigenvectors of the Hamiltonian and dissipative parts of the vectorized Liouvillian. Importantly, because their eigenvalues are purely real, they are not related to revivals. The number and nature of the scars depend on both the symmetry of the Hamiltonian and the choice of jump operators. For a dissipative four-body Sachdev-Ye-Kitaev (SYK) model with N fermions, either Majorana or complex, we construct analytically some of these Lindblad scars while others could only be obtained numerically. As an example of the former, we identify N/2+1 scars for complex fermions due to the U(1) symmetry of the model and two scars for Majorana fermions as a consequence of the parity symmetry. Similar results are obtained for a dissipative XXZ spin chain. We also characterize the physical properties of Lindblad scars. First, the operator size is independent of the disorder realization and has a vanishing variance. By contrast, the operator size for nonscarred states, believed to be quantum chaotic, is well described by a distribution centered around a specific size and a finite variance, which could be relevant for a precise definition of the eigenstate thermalization hypothesis in dissipative quantum chaos. Moreover, the entanglement entropy of these scars has distinct features such as a strong dependence on the partition choice and, in certain cases, a large entanglement.
Quantum many-body scars are atypical, non-thermal eigenstates that constitute a mechanism of weak ergodicity breaking, yet their stability in realistic, open quantum systems remains an outstanding question. We investigate the interplay between stability and quantum information dynamics within the PXP model subjected to local dissipation. Employing a non-Hermitian formalism, we analytically demonstrate and numerically corroborate that scar eigenstates possess intrinsic decay rates parametrically smaller than those of the surrounding chaotic bulk, revealing a pronounced stability hierarchy. This spectral robustness is a direct manifestation of the approximate algebraic structure underpinning the scars. This resilience has direct dynamical consequences. We find a suppression of information scrambling, quantified by the out-of-time-order correlator (OTOC), for dynamics initiated from scar-like states. Analysis of entanglement dynamics reveals that quantum correlations in scar states persist for longer timescales under weak dissipation. These results demonstrate that algebraic confinement reduces the susceptibility of scar states to both dissipation and chaotic scrambling; the signature of this resilience is a persistent suppression of the scrambling rate and the presence of coherent oscillations, not a uniformly longer signal lifetime.
To provide a physical example of quantum scars, we study the many-body scars in the spin-1 Kitaev chain where the so-called PXP Hamiltonian is exactly embedded in the spectra. Regarding the conserved quantities, the Hilbert space is fragmented into disconnected subspaces and we explore the associated constrained dynamics. The continuous revivals of the fidelity and the entanglement entropy when the initial state is prepared in $|{\mathbb{Z}}_{k}\ensuremath{\rangle}$ (k=2,3k=2,3k=2,3) state illustrate the essential physics of the PXP model. We study the quantum phase transitions in the one-dimensional spin-1 Kitaev-Heisenberg model using the density-matrix renormalization group and Lanczos exact diagonalization methods, and determine the phase diagram. We parametrize the two terms in the Hamiltonian by the angle $\ensuremath{\phi}$, where the Kitaev term is $K\ensuremath{\equiv}sin(\ensuremath{\phi})$ and competes with the Heisenberg $J\ensuremath{\equiv}cos(\ensuremath{\phi})$ term. One finds a rich ground-state phase diagram as a function of the angle $\ensuremath{\phi}$. Depending on the ratio $K/J\ensuremath{\equiv}tan(\ensuremath{\phi})$, the system either breaks the symmetry to one of distinct symmetry broken phases, or preserves the symmetry in a quantum spin-liquid phase with frustrated interactions. We find that the scarred state is stable for perturbations which obey Z2{\mathbb{Z}}_{2}Z2​-symmetry, while it becomes unstable against Heisenberg-type perturbations.