Recently a class of quantum systems exhibiting weak ergodicity breaking has attracted much attention. These systems feature in the energy spectrum a special band of eigenstates called quantum many-body scar states. One prototype model that is known to host scar states is the so-called PXP model. In this work we study the fate of quantum many-body scar states in a 2D PXP model against random disorders. We show that in both the square lattice and the honeycomb lattice the scar states can persist up to a finite disorder strength, before eventually being erased by the disorder. We further study the localization properties of the system in the presence of even stronger disorders and show that whether a full localization transition occurs depends on the type of disorder we introduce. Our study thus reveals the fascinating interplay between disorder and quantum many-body scarring in a 2D system.
Recently a class of quantum systems exhibiting weak ergodicity breaking has attracted much attention. These systems feature in the energy spectrum a special band of eigenstates called quantum many-body scar states. One prototype model that is known to host scar states is the so-called PXP model. In this work we study the fate of quantum many-body scar states in a 2D PXP model against random disorders. We show that in both the square lattice and the honeycomb lattice the scar states can persist up to a finite disorder strength, before eventually being erased by the disorder. We further study the localization properties of the system in the presence of even stronger disorders and show that whether a full localization transition occurs depends on the type of disorder we introduce. Our study thus reveals the fascinating interplay between disorder and quantum many-body scarring in a 2D system.
Recently a class of quantum systems exhibiting weak ergodicity breaking has attracted much attention. These systems feature a special band of eigenstates called quantum many-body scar states in the energy spectrum. In this work we study the fate of quantum many-body scar states in a two-dimensional lattice against random disorders. We show that in both the square lattice and the honeycomb lattice the scar states can persist up to a finite disorder strength, before eventually being killed by the disorder. We further study the localization properties of the system in the presence of even stronger disorders and show that whether a full localization transition occurs depends on the type of disorder we introduce. Our study thus reveals the fascinating interplay between disorder and quantum many-body scarring in a two-dimensional system.
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 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.
The eigenstate thermalization hypothesis describes how most isolated many-body quantum systems reach thermal equilibrium. However, the hypothesis is violated by phenomena such as many-body localization and quantum many-body scars. In this work, we study a finite, two-dimensional, disordered model hosting a tower of scar states. This construction is a particular instance of a general framework and we demonstrate its generality by constructing two disordered models hosting a different tower of scar states. At weak disorder, we find numerically that the spectra are nonthermal, and the scar states appear as exact eigenstates with high entropy for certain bipartitions. At strong disorder, the spectra localize and the scar states are identified as inverted scars since the scar states are embedded in a localized background as opposed to a thermal background. We argue that, for the considered type of models, the localization is stronger than what would be naively expected, and we show this explicitly for one of the models. The argument also provides guidelines for obtaining similarly strong localization in other scarred models. We study the transition from the thermal phase to localization by observing the adjacent gap ratio shifting from the Wigner surmise to the Poisson distribution with increasing disorder strength. Moreover, the entanglement entropy transitions from volume-law scaling with system size at weak disorder to area-law scaling at strong disorder. Finally, we demonstrate that localization protects scar revivals for initial states with partial support in the scar subspace.
We investigate the emergence of quantum scars in a general ensemble of random Hamiltonians (of which the PXP is a particular realization), that we refer to as quantum local random networks. We find a class of scars, that we call “statistical”, and we identify specific signatures of the localized nature of these eigenstates by analyzing a combination of indicators of quantum ergodicity and properties related to the network structure of the model. Within this parallelism, we associate the emergence of statistical scars to the presence of “motifs” in the network, that reflects how these are associated to links with anomalously small connectivity. Most remarkably, statistical scars appear at well-defined values of energy, predicted solely on the base of network theory. We study the scaling of the number of statistical scars with system size: by continuously changing the connectivity of the system we find that there is a transition from a regime where the constraints are too weak for scars to exist for large systems to a regime where constraints are stronger and the number of statistical scars increases with system size. This allows to define the concept of “statistical robustness” of quantum scars.
Quantum dynamics in certain kinetically-constrained systems can display a strong sensitivity to the initial condition, wherein some initial states give rise to persistent quantum revivals---a type of weak ergodicity breaking known as ``quantum many-body scarring'' (QMBS). Recent work [Yao, Pan, Liu, and Zhai, Phys. Rev. B 105, 125123 (2022)] pointed out that QMBS gets destroyed by tuning the system to a quantum critical point, echoing the disappearance of long-range order in the system's ground state at equilibrium. Here we show that this picture can be much richer in systems that display QMBS dynamics from a continuous family of initial conditions: As the system is tuned across the critical point while at the same time deforming the initial state, the dynamical signatures of QMBS at intermediate times can undergo an apparently smooth evolution across the equilibrium phase transition point. We demonstrate this using the PXP model---a paradigmatic model of QMBS that has recently been realized in Rydberg atom arrays as well as ultracold bosonic atoms in a tilted optical lattice. Using exact diagonalization and matrix product state methods, we map out the dynamical phase diagram of the PXP model with the quenched chemical potential. We demonstrate the existence of a continuous family of initial states that give rise to QMBS and formulate a ramping protocol that can be used to prepare such states in experiment. Our results show the ubiquity of scarring in the PXP model and highlight its intriguing interplay with quantum criticality.