Quantum many-body scars (QMBSs) are a novel paradigm for the violation of the eigenstate thermalization hypothesis -- Hamiltonians of these systems exhibit mid-spectrum eigenstates that are equidistant in energy and which possess low entanglement and evade thermalization for long times. We present a novel approach for understanding the anomalous dynamical behavior in these systems. Specifically, we postulate that QMBS Hamiltonians $H$ can generically be partitioned into a set of terms $O_a$ which do not commute over the entire Hilbert space, but commute to all orders within the subspace of scar states. All states in the scar subspace thus evolve according to a `broken unitary' $U_s(t) = \prod_a e^{-iO_at}$, where $H = \sum_a O_a$; alternatively, the scar subspace may be viewed as being spawned by common eigenstates of all $O_a$. While the scar Hamiltonian $H$ may be non-integrable, operators $O_a$ usually exhibit a trivial spectrum with equidistant eigenergies which gives rise to revivals at an appropriate period. Two classes of scar models emerge in this picture -- those with a finite set of $O_a$, as pertaining to, for instance, scars in the AKLT model, and those with an extensive set of such operators, such as eta pairing scar states in the Hubbard model. Besides discussing how well known scar models fit into the above picture, we use this dynamical decoupling to generalize conditions under which scar subspaces can be engendered in the two settings, generalizing constraints satisfied by quasiparticles in the Matrix Product State (MPS) construction of scar eigenstates, and the Shiraishi-Mori approach. We also discuss connections between this approach and others in the literature.
Quantum many-body scars in random unitary circuits
Université Paris-Saclay（巴黎萨克雷大学）；CNRS（法国国家科学研究中心）；Laboratoire de Physique de l’École normale supérieure（巴黎高等师范学院物理实验室）；ENS（巴黎高等师范学院）；Université PSL（巴黎文理研究大学）；Sorbonne Université（索邦大学）；Université Paris Cité（巴黎西岱大学）
We present an interpretation of scar states and quantum revivals as weakly "broken" representations of Lie algebras spanned by a subset of eigenstates of a many-body quantum system. We show that the PXP model, describing strongly-interacting Rydberg atoms, supports a "loose" embedding of multiple $\mathrm{su(2)}$ Lie algebras corresponding to distinct families of scarred eigenstates. Moreover, we demonstrate that these embeddings can be made progressively more accurate via an iterative process which results in optimal perturbations that stabilize revivals from arbitrary charge density wave pro…
Topological edge states arise in parity-time ($\mathcal{PT}$)-symmetric non-unitary quantum dynamics but have so far only been discussed in the $\mathcal{PT}$-symmetry-unbroken regime. Here we report the experimental detection of robust topological edge states in one-dimensional photonic quantum walks with spontaneously broken $\mathcal{PT}$ symmetry, thus establishing the existence of topological phenomena therein. We theoretically prove and experimentally confirm that the global Berry phase in non-unitary quantum-walk dynamics unambiguously defines topological invariants of the system in bot…
We introduce a family of non-integrable 1D lattice models that feature robust periodic revivals under a global quench from certain initial product states, thus generalizing the phenomenon of many-body scarring recently observed in Rydberg atom quantum simulators. Our construction is based on a systematic embedding of the single-site unitary dynamics into a kinetically-constrained many-body system. We numerically demonstrate that this construction yields new families of models with robust wave-function revivals, and it includes kinetically-constrained quantum clock models as a special case. We …
Highly excited eigenstates of quantum many-body systems are typically featureless thermal states. Some systems, however, possess a small number of special, low-entanglement eigenstates known as quantum scars. We introduce a quantum-inspired machine learning platform based on a Quantum Variational Autoencoder (QVAE) that detects families of scar states in spectra of many-body systems. Unlike a classical autoencoder, QVAE performs a parametrized unitary operation, allowing us to compress a single eigenstate into a smaller number of qubits. We demonstrate that the autoencoder trained on a scar st…
We present a general symmetry-based framework for obtaining many-body Hamiltonians with scarred eigenstates that do not obey the eigenstate thermalization hypothesis. Our models are derived from parent Hamiltonians with a non-Abelian (or q-deformed) symmetry, whose eigenspectra are organized as degenerate multiplets that transform as irreducible representations of the symmetry (`tunnels'). We show that large classes of perturbations break the symmetry, but in a manner that preserves a particular low-entanglement multiplet of states -- thereby giving generic, thermal spectra with a `shadow' of …
The control of many-body quantum dynamics in complex systems is a key challenge in the quest to reliably produce and manipulate large-scale quantum entangled states. Recently, quench experiments in Rydberg atom arrays (Bluvstein et. al., arXiv:2012.12276) demonstrated that coherent revivals associated with quantum many-body scars can be stabilized by periodic driving, generating stable subharmonic responses over a wide parameter regime. We analyze a simple, related model where these phenomena originate from spatiotemporal ordering in an effective Floquet unitary, corresponding to discrete time…
Ongoing development of quantum simulators allows for a progressively finer degree of control of quantum many-body systems. This motivates the development of efficient approaches to facilitate the control of such systems and enable the preparation of non-trivial quantum states. Here we formulate an approach to control quantum systems based on matrix product states~(MPS). We compare counter-diabatic and leakage minimization approaches to the so-called local steering problem, that consists in finding the best value of the control parameters for generating a unitary evolution of the specific MPS s…
Novel categories of electronic devices and quantum materials are obtained by pipelining the unitary evolution of electron quantum states as described by Schroedinger's equation with non-unitary processes that interrupt the coherent propagation of electrons. These devices and materials reside in the fascinating transition regime between quantum mechanics and classical physics. The devices are designed such that a nonreciprocal unitary state evolution is achieved by means of a broken inversion symmetry, for example as induced at material interfaces. This coherent state evolution is interrupted b…
We experimentally simulate non-unitary quantum dynamics using a single-photon interferometric network and study the information flow between a parity-time (PT)-symmetric non-Hermitian system and its environment. We observe oscillations of quantum-state distinguishability and complete information retrieval in the PT-symmetry-unbroken regime. We then characterize in detail critical phenomena of the information flow near the exceptional point separating the PT-unbroken and -broken regimes, and demonstrate power-law behavior in key quantities such as the distinguishability and the recurrence time.…
