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arXiv:2603.13165

Towers of quantum many-body scars under stochastic resetting

Lorenzo Gotta, Manas Kulkarni, Gabriele Perfetto

Published Mar 13, 2026• 0 citations
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Abstract

Towers of quantum many-body scars are sets of highly-excited eigenstates of nonintegrable Hamiltonians whose dynamics shows athermal behavior and persistent oscillations in time. The preparation of such states is, however, challenging due to their entanglement content. In this work, we show that local properties of such states can be prepared by interspersing the scarred dynamics with stochastic resets to much simpler unentangled product states. Stochastic resetting amounts to reinitializing the many-body wavefunction of the system at random times to a predefined state, which we choose to be in the scarred subspace. We derive several analytical results for the ensuing dynamics, e.g., for the time evolution of the fidelity and of local observables. Resetting damps the scarred oscillations and generates spatial off-diagonal long-range order in the ensuing stationary state. The latter shows mixedness that scales logarithmically as a function of the system size, which follows from the structure of the scarred eigenstates. We prove that such stationary states are locally equivalent, in the sparse-resetting limit, to a single pure scarred eigenstate, which is determined by the reset state. This protocol thereby might represent a route to the experimental preparation of the local properties of correlated and entangled states through resetting.

DOI
10.48550/arxiv.2603.13165

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Towers of quantum many-body scars are sets of highly-excited eigenstates of nonintegrable Hamiltonians whose dynamics shows athermal behavior and persistent oscillations in time. The preparation of such states is, however, challenging due to their entanglement content. In this work, we show that local properties of such states can be prepared by interspersing the scarred dynamics with stochastic resets to much simpler unentangled product states. Stochastic resetting amounts to reinitializing the many-body wavefunction of the system at random times to a predefined state, which we choose to be in the scarred subspace. We derive several analytical results for the ensuing dynamics, e.g., for the time evolution of the fidelity and of local observables. Resetting damps the scarred oscillations and generates spatial off-diagonal long-range order in the ensuing stationary state. The latter shows mixedness that scales logarithmically as a function of the system size, which follows from the structure of the scarred eigenstates. We prove that such stationary states are locally equivalent, in the sparse-resetting limit, to a single pure scarred eigenstate, which is determined by the reset state. This protocol thereby might represent a route to the experimental preparation of the local properties of correlated and entangled states through resetting.
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.
Quantum many-body scars are non-thermal eigenstates embedded in the spectra of otherwise non-integrable Hamiltonians. Paradigmatic examples often appear as quasiparticle towers of states, such as the maximally ferromagnetic spin-1/2 states, also known as Dicke states. A distinguishing feature of quantum many-body scars is that they admit multiple local "parent" Hamiltonians for which they are exact eigenstates. In this work, we show that the locality of such parent Hamiltonians strongly constrains the relative placement of these states within the energy spectrum. In particular, we prove that if the full set of Dicke states are exact eigenstates of an extensive local Hamiltonian, then their energies must necessarily be equally spaced. Our proof builds on recent results concerning parent Hamiltonians of the WWW state, together with general algebraic structures underlying such quasiparticle towers. We further demonstrate that this equal spacing property extends to local Hamiltonians defined on arbitrary bounded-degree graphs, including regular lattices in any spatial dimension and expander graphs. Hamiltonians with kkk-local interactions and a bounded number of interaction terms per site are also encompassed by our proof. On the same classes of graphs, we additionally establish equal spacing for towers constructed from multi-site quasiparticles on top of product states. For the towers considered here, an immediate corollary of the equal spacing property is that any state initialized entirely within the quantum many-body scar manifold exhibits completely frozen entanglement dynamics under any local Hamiltonian for which those scars are exact eigenstates. Overall, our results reveal a stringent interplay between locality and the structure of quantum many-body scars.
Isolated quantum many-body systems are often well described by the eigenstate thermalization hypothesis. There are, however, mechanisms that cause different behavior: many-body localization and quantum many-body scars. Here, we show how one can find disordered Hamiltonians hosting a tower of scars by adapting a known method for finding parent Hamiltonians. Using this method, we construct a spin-12\frac{1}{2}21​ model which is both partially localized and contains scars. We demonstrate that the model is partially localized by studying numerically the level spacing statistics and bipartite entanglement entropy. As disorder is introduced, the adjacent gap ratio transitions from the Gaussian orthogonal ensemble to the Poisson distribution and the entropy shifts from volume-law to area-law scaling. We investigate the properties of scars in a partially localized background and compare with a thermal background. At strong disorder, states initialized inside or outside the scar subspace display different dynamical behavior but have similar entanglement entropy and Schmidt gap. We demonstrate that localization stabilizes scar revivals of initial states with support both inside and outside the scar subspace. Finally, we show how strong disorder introduces additional approximate towers of eigenstates.
Quantum many-body scar states are highly excited eigenstates of many-body systems that exhibit atypical entanglement and correlation properties relative to typical eigenstates at the same energy density. Scar states also give rise to infinitely long-lived coherent dynamics when the system is prepared in a special initial state having finite overlap with them. Many models with exact scar states have been constructed, but the fate of scarred eigenstates and dynamics when these models are perturbed is difficult to study with classical computational techniques. In this work, we propose state preparation protocols that enable the use of quantum computers to study this question. We present protocols both for individual scar states in a particular model, as well as superpositions of them that give rise to coherent dynamics. For superpositions of scar states, we present both a system-size-linear depth unitary and a finite-depth nonunitary state preparation protocol, the latter of which uses measurement and postselection to reduce the circuit depth. For individual scarred eigenstates, we formulate an exact state preparation approach based on matrix product states that yields quasipolynomial-depth circuits, as well as a variational approach with a polynomial-depth ansatz circuit. We also provide proof of principle state-preparation demonstrations on superconducting quantum hardware.
Quantum many-body scars have been put forward as counterexamples to the eigenstate thermalization hypothesis. These atypical states are observed in a range of correlated models as long-lived oscillations of local observables in quench experiments starting from selected initial states. The long-time memory is a manifestation of quantum nonergodicity generally linked to a subextensive generation of entanglement entropy, the latter of which is widely used as a diagnostic for identifying quantum many-body scars numerically as low entanglement outliers. Here we show that by adding kinetic constraints to a fractionalized orthogonal metal, we can construct a minimal model with orthogonal quantum many-body scars leading to persistent oscillations with infinite lifetime coexisting with rapid volume-law entanglement generation. Our example provides new insights into the link between quantum ergodicity and many-body entanglement while opening new avenues for exotic nonequilibrium dynamics in strongly correlated multicomponent quantum systems.
We construct a 1D model Hamiltonian of spinless fermions for which the spinless analog of $\ensuremath{\eta}$-pairing states are quantum many-body scars of the model. These states are excited states and display subvolume entanglement entropy scaling; they form a tower of states that are equally spaced in energy (resulting in periodic oscillations in the Loschmidt echo and in the time evolution of observables for initial states prepared in a superposition of them) and are atypical in the sense that they weakly break the eigenstate thermalization hypothesis, while the other excited states are thermal. We extend the approach by presenting models with a tower of scar states generated by multimers located at the edge of the Brillouin zone.