Quantum Scars Research Articles

Observing quantum many-body scars in random quantum circuits

Observing quantum many-body scars in random quantum circuits

Controllable quantum scars induced by spin–orbit couplings in quantum dots

Spin–orbit couplings (SOCs), originating from the relativistic corrections in the Dirac equation, offer nonlinearity in the classical limit and are capable of driving chaotic dynamics. In a nanoscale quantum dot confined by a two-dimensional parabolic potential with SOCs, various quantum scar states emerge quasi-periodically in the eigenstates of the system, when the ratio of confinement energies in the two directions is nearly commensurable. The scars, displaying both quantum interference and classical trajectory features on the electron density, due to relativistic effects, serve as a bridge between the classical and quantum behaviors of the system. When the strengths of Rashba and Dresselhaus SOCs are identical, the chaos in the classical limit is eliminated as the classical Hamilton’s equations become linear, leading to the disappearance of all quantum scar states. Importantly, the quantum scars induced by SOCs are robust against small perturbations of system parameters. With precise control achievable through external gating, the quantum scar induced by Rashba SOC is fully controllable and detectable.

Embedding Quantum Many-Body Scars into Decoherence-Free Subspaces.

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.

Broken unitary picture of dynamics in quantum many-body scars

Broken unitary picture of dynamics in quantum many-body scars

Prethermal Stability of Eigenstates under High Frequency Floquet Driving.

Systems subject to high-frequency driving exhibit Floquet prethermalization, that is, they heat exponentially slowly on a timescale that is large in the drive frequency, τ_{h}∼exp(ω). Nonetheless, local observables can decay much faster via energy conserving processes, which are expected to cause a rapid decay in the fidelity of an initial state. Here we show instead that the fidelities of eigenstates of the time-averaged Hamiltonian, H_{0}, display an exponentially long lifetime over a wide range of frequencies-even as generic initial states decay rapidly. When H_{0} has quantum scars, or highly excited eigenstates of low entanglement, this leads to long-lived nonthermal behavior of local observables in certain initial states. We present a two-channel theory describing the fidelity decay time τ_{f}: the interzone channel causes fidelity decay through energy absorption, i.e., coupling across Floquet zones, and ties τ_{f} to the slow heating timescale, while the intrazone channel causes hybridization between states in the same Floquet zone. Our work informs the robustness of experimental approaches for using Floquet engineering to generate interesting many-body Hamiltonians, with and without scars.

Inverting multiple quantum many-body scars via disorder

Inverting multiple quantum many-body scars via disorder

Classical route to ergodicity and scarring in collective quantum systems.

Ergodicity, a fundamental concept in statistical mechanics, is not yet a fully understood phenomena for closed quantum systems, particularly its connection with the underlying chaos. In this review, we consider a few examples of collective quantum systems to unveil the intricate relationship of ergodicity as well as its deviation due to quantum scarring phenomena with their classical counterpart. A comprehensive overview of classical and quantum chaos is provided, along with the tools essential for their detection. Furthermore, we survey recent theoretical and experimental advancements in the domain of ergodicity and its violations. This review aims to illuminate the classical perspective of quantum scarring phenomena in interacting quantum systems.

Quantum many-body scars in the Bose-Hubbard model with a three-body constraint

Quantum many-body scars in the Bose-Hubbard model with a three-body constraint

Quantum Many-Body Scars in Dual-Unitary Circuits.

Dual-unitary circuits are a class of quantum systems for which exact calculations of various quantities are possible, even for circuits that are nonintegrable. The array of known exact results paints a compelling picture of dual-unitary circuits as rapidly thermalizing systems. However, in this Letter, we present a method to construct dual-unitary circuits for which some simple initial states fail to thermalize, despite the circuits being "maximally chaotic," ergodic, and mixing. This is achieved by embedding quantum many-body scars in a circuit of arbitrary size and local Hilbert space dimension. We support our analytic results with numerical simulations showing the stark contrast in the rate of entanglement growth from an initial scar state compared to nonscar initial states. Our results are well suited to an experimental test, due to the compatibility of the circuit layout with the native structure of current digital quantum simulators.

Weak universality, quantum many-body scars, and anomalous infinite-temperature autocorrelations in a one-dimensional spin model with duality

Weak universality, quantum many-body scars, and anomalous infinite-temperature autocorrelations in a one-dimensional spin model with duality

Persistent revivals in a system of trapped bosonic atoms

Dynamical signatures of quantum chaos are observed in the survival probability of different initial states, in a system of cold atoms trapped in a linear chain with site noise and open boundary conditions. It is shown that chaos is present in the region of small disorder, at intermediate energies. The study is performed with different number of sites and atoms: 7, 8 and 9, but focusing on the case where the particle density is one. States of the occupation basis with energies in the chaotic region are evolved at long times. Remarkable differences in the behavior of the survival probability are found for states with different energy-eigenbasis participation ratio (PR). Whereas those with large PR clearly exhibit the characteristic random-matrix correlation hole before equilibration, those with small PR present a marginal or even no correlation hole which is replaced by revivals lasting up to the stage of equilibration, suggesting a connection with the quantum scarring phenomenon.

Exact quantum many-body scars in higher-spin kinetically constrained models

Exact quantum many-body scars in higher-spin kinetically constrained models

Using models with static quantum many-body scars to generate time-crystalline behavior under periodic driving

Using models with static quantum many-body scars to generate time-crystalline behavior under periodic driving

Quantum many-body scars in spin models with multibody interactions

Quantum many-body scars in spin models with multibody interactions

String-net formulation of Hamiltonian lattice Yang-Mills theories and quantum many-body scars in a nonabelian gauge theory

We study the Hamiltonian lattice Yang-Mills theory based on spin networks that provide a useful basis to represent the physical states satisfying the Gauss law constraints. We focus on SU(2) Yang-Mills theory in (2 + 1) dimensions. Following the string-net model, we introduce a regularization of the Kogut-Susskind Hamiltonian of lattice Yang-Mills theory based on the q deformation, which respects the (discretized) SU(2) gauge symmetry as quantum group, i.e., SU(2)k, and enables implementation of the lattice Yang-Mills theory both in classical and quantum algorithms by referring to those of the string-net model. Using the regularized Hamiltonian, we study quantum scars in a nonabelian gauge theory. Quantum scars are nonthermal energy eigenstates arising in the constrained quantum many-body systems. We find that quantum scars from zero modes, which have been found in abelian gauge theories arise even in a nonabelian gauge theory. We also show the spectrum of a single-plaquette model for SU(2)k and SU(3)k with naive cutoff and that based on the q-deformation to discuss cutoff dependence of the formulation.

Holographic quantum scars

We discuss a construction of quantum many-body scars in the context of holography. We consider two-dimensional conformal field theories and use their dynamical symmetries, naturally realized through the Virasoro algebra, to construct scarred states. By studying their Loschmidt amplitude, we evaluate the states’ periodic properties. A geometrical interpretation allows us to compute the expectation value of the stress tensor and entanglement entropy of these scarred states. We show that their holographic dual is related by a diffeomorphism to empty AdS, even for energies above the black hole threshold. We also demonstrate that expectation values in the scarred states are generally non-thermal and that their entanglement entropy grows with the energy as \log(E)log(E) in contrast to \sqrt{E}E for the typical (bulk) states. Furthermore, we identify fixed points on the CFT plane associated with divergent or vanishing entanglement entropy in the limit where the scarred states have infinite energy.

Embedding Semiclassical Periodic Orbits into Chaotic Many-Body Hamiltonians.

Protecting coherent quantum dynamics from chaotic environment is key to realizations of fragile many-body phenomena and their applications in quantum technology. We present a general construction that embeds a desired periodic orbit into a family of nonintegrable many-body Hamiltonians, whose dynamics is otherwise chaotic. Our construction is based on time-dependent variational principle that projects quantum dynamics onto a manifold of low-entangled states, and it complements earlier approaches for embedding nonthermal eigenstates, known as quantum many-body scars, into thermalizing spectra. By designing terms that suppress "leakage" of the dynamics outside the variational manifold, we engineer families of Floquet models that host exact scarred dynamics, as we illustrate using a driven Affleck-Kennedy-Lieb-Tasaki model and a recent experimental realization of scars in a dimerized superconducting qubit chain.

Quantum many-body scars in spin-1 Kitaev chain with uniaxial single-ion anisotropy

Quantum many-body scars in spin-1 Kitaev chain with uniaxial single-ion anisotropy

Anatomy of the fragmented Hilbert space: Eigenvalue tunneling, quantum scars, and localization in the perturbed random regular graph

Anatomy of the fragmented Hilbert space: Eigenvalue tunneling, quantum scars, and localization in the perturbed random regular graph

Quantum scar states in coupled random graph models

Quantum scar states in coupled random graph models