Phase transitions in random circuit sampling.

Undesired coupling to the surrounding environment destroys long-range correlations in quantum processors and hinders coherent evolution in the nominally available computational space. This noise is an outstanding challenge when leveraging the computation power of near-term quantum processors. It has been shown that benchmarking random circuit sampling with cross-entropy benchmarking can provide an estimate of the effective size of the Hilbert space coherently available.

Dynamics of magnetization at infinite temperature in a Heisenberg spin chain.

Understanding universal aspects of quantum dynamics is an unresolved problem in statistical mechanics. In particular, the spin dynamics of the one-dimensional Heisenberg model were conjectured as to belong to the Kardar-Parisi-Zhang (KPZ) universality class based on the scaling of the infinite-temperature spin-spin correlation function. In a chain of 46 superconducting qubits, we studied the probability distribution of the magnetization transferred across the chain's center, [Formula: see text].

Stable quantum-correlated many-body states through engineered dissipation.

Engineered dissipative reservoirs have the potential to steer many-body quantum systems toward correlated steady states useful for quantum simulation of high-temperature superconductivity or quantum magnetism. Using up to 49 superconducting qubits, we prepared low-energy states of the transverse-field Ising model through coupling to dissipative auxiliary qubits. In one dimension, we observed long-range quantum correlations and a ground-state fidelity of 0.

Formation of robust bound states of interacting microwave photons.

Systems of correlated particles appear in many fields of modern science and represent some of the most intractable computational problems in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles. The lack of general solutions for the three-body problem and acceptable theory for strongly correlated electrons shows that our understanding of correlated systems fades when the particle number or the interaction strength increases.

Noise-resilient edge modes on a chain of superconducting qubits.

Inherent symmetry of a quantum system may protect its otherwise fragile states. Leveraging such protection requires testing its robustness against uncontrolled environmental interactions. Using 47 superconducting qubits, we implement the one-dimensional kicked Ising model, which exhibits nonlocal Majorana edge modes (MEMs) with [Formula: see text] parity symmetry.

Temporal Entanglement, Quasiparticles, and the Role of Interactions.

In quantum many-body dynamics admitting a description in terms of noninteracting quasiparticles, the Feynman-Vernon influence matrix (IM), encoding the effect of the system on the evolution of its local subsystems, can be analyzed exactly. For discrete dynamics, the temporal entanglement (TE) of the corresponding IM satisfies an area law, suggesting the possibility of an efficient representation of the IM in terms of matrix-product states. A natural question is whether integrable interactions, preserving stable quasiparticles, affect the behavior of the TE.

Bilayer WSe as a natural platform for interlayer exciton condensates in the strong coupling limit.

Exciton condensates (ECs) are macroscopic coherent states arising from condensation of electron-hole pairs. Bilayer heterostructures, consisting of two-dimensional electron and hole layers separated by a tunnel barrier, provide a versatile platform to realize and study ECs. The tunnel barrier suppresses recombination, yielding long-lived excitons.

Nucleation of Ergodicity by a Single Mobile Impurity in Supercooled Insulators.

We consider a disordered Hubbard model and show that, at sufficiently weak disorder, a single spin-down mobile impurity can thermalize an extensive initially localized system of spin-up particles. Thermalization is enabled by resonant processes that involve correlated hops of the impurity and localized particles. This effect indicates that Anderson localized insulators behave as "supercooled" systems, with mobile impurities acting as ergodic seeds.

Slow Nonthermalizing Dynamics in a Quantum Spin Glass.

Spin glasses and many-body localization (MBL) are prime examples of ergodicity breaking, yet their physical origin is quite different: the former phase arises due to rugged classical energy landscape, while the latter is a quantum-interference effect. Here, we study quantum dynamics of an isolated 1D spin glass under application of a transverse field. At high energy densities, the system is ergodic, relaxing via a resonance avalanche mechanism, that is also responsible for the destruction of MBL in nonglassy systems with power-law interactions.

Emergent SU(2) Dynamics and Perfect Quantum Many-Body Scars.

Motivated by recent experimental observations of coherent many-body revivals in a constrained Rydberg atom chain, we construct a weak quasilocal deformation of the Rydberg-blockaded Hamiltonian, which makes the revivals virtually perfect. Our analysis suggests the existence of an underlying nonintegrable Hamiltonian which supports an emergent SU(2)-spin dynamics within a small subspace of the many-body Hilbert space. We show that such perfect dynamics necessitates the existence of atypical, nonergodic energy eigenstates-quantum many-body scars.

Locality and heating in periodically driven, power-law-interacting systems.

We study the heating time in periodically driven -dimensional systems with interactions that decay with the distance as a power law . Using linear-response theory, we show that the heating time is exponentially long as a function of the drive frequency for . For systems that may not obey linear-response theory, we use a more general Magnus-like expansion to show the existence of quasiconserved observables, which imply exponentially long heating time, for .

Bounds on Energy Absorption and Prethermalization in Quantum Systems with Long-Range Interactions.

Long-range interacting systems such as nitrogen vacancy centers in diamond and trapped ions serve as experimental setups to probe a range of nonequilibrium many-body phenomena. In particular, via driving, various effective Hamiltonians with physics potentially quite distinct from short-range systems can be realized. In this Letter, we derive general rigorous bounds on the linear response energy absorption rates of periodically driven systems of spins or fermions with long-range interactions that are sign changing and fall off as 1/r^{α} with α>d/2.

Critical Time Crystals in Dipolar Systems.

We analyze the quantum dynamics of periodically driven, disordered systems in the presence of long-range interactions. Focusing on the stability of discrete time crystalline (DTC) order in such systems, we use a perturbative procedure to evaluate its lifetime. For 3D systems with dipolar interactions, we show that the corresponding decay is parametrically slow, implying that robust, long-lived DTC order can be obtained.

Power-Law Entanglement Spectrum in Many-Body Localized Phases.

The entanglement spectrum of the reduced density matrix contains information beyond the von Neumann entropy and provides unique insights into exotic orders or critical behavior of quantum systems. Here, we show that strongly disordered systems in the many-body localized phase have power-law entanglement spectra, arising from the presence of extensively many local integrals of motion. The power-law entanglement spectrum distinguishes many-body localized systems from ergodic systems, as well as from ground states of gapped integrable models or free systems in the vicinity of scale-invariant critical points.

Landau Level Splittings, Phase Transitions, and Nonuniform Charge Distribution in Trilayer Graphene.

We report on magnetotransport studies of dual-gated, Bernal-stacked trilayer graphene (TLG) encapsulated in boron nitride crystals. We observe a quantum Hall effect staircase which indicates a complete lifting of the 12-fold degeneracy of the zeroth Landau level. As a function of perpendicular electric field, our data exhibit a sequence of phase transitions between all integer quantum Hall states in the filling factor interval -8<ν<0.

Interferometric measurements of many-body topological invariants using mobile impurities.

Topological quantum phases cannot be characterized by Ginzburg-Landau type order parameters, and are instead described by non-local topological invariants. Experimental platforms capable of realizing such exotic states now include synthetic many-body systems such as ultracold atoms or photons. Unique tools available in these systems enable a new characterization of strongly correlated many-body states.

Exponentially Slow Heating in Periodically Driven Many-Body Systems.

We derive general bounds on the linear response energy absorption rates of periodically driven many-body systems of spins or fermions on a lattice. We show that, for systems with local interactions, the energy absorption rate decays exponentially as a function of driving frequency in any number of spatial dimensions. These results imply that topological many-body states in periodically driven systems, although generally metastable, can have very long lifetimes.

Many-body localization in periodically driven systems.

We consider disordered many-body systems with periodic time-dependent Hamiltonians in one spatial dimension. By studying the properties of the Floquet eigenstates, we identify two distinct phases: (i) a many-body localized (MBL) phase, in which almost all eigenstates have area-law entanglement entropy, and the eigenstate thermalization hypothesis (ETH) is violated, and (ii) a delocalized phase, in which eigenstates have volume-law entanglement and obey the ETH. The MBL phase exhibits logarithmic in time growth of entanglement entropy when the system is initially prepared in a product state, which distinguishes it from the delocalized phase.

Interferometric probes of many-body localization.

We propose a method for detecting many-body localization (MBL) in disordered spin systems. The method involves pulsed coherent spin manipulations that probe the dephasing of a given spin due to its entanglement with a set of distant spins. It allows one to distinguish the MBL phase from a noninteracting localized phase and a delocalized phase.

Interacting Weyl semimetals: characterization via the topological Hamiltonian and its breakdown.

Weyl semimetals (WSMs) constitute a 3D phase with linearly dispersing Weyl excitations at low energy, which lead to unusual electrodynamic responses and open Fermi arcs on boundaries. We derive a simple criterion to identify and characterize WSMs in an interacting setting using the exact electronic Green's function at zero frequency, which defines a topological Bloch Hamiltonian. We apply this criterion by numerically analyzing, via cluster and other methods, interacting lattice models with and without time-reversal symmetry.

Bilayer graphene. Tunable fractional quantum Hall phases in bilayer graphene.

Symmetry-breaking in a quantum system often leads to complex emergent behavior. In bilayer graphene (BLG), an electric field applied perpendicular to the basal plane breaks the inversion symmetry of the lattice, opening a band gap at the charge neutrality point. In a quantizing magnetic field, electron interactions can cause spontaneous symmetry-breaking within the spin and valley degrees of freedom, resulting in quantum Hall effect (QHE) states with complex order.

Observation of even denominator fractional quantum Hall effect in suspended bilayer graphene.

We investigate low-temperature magneto-transport in recently developed, high-quality multiterminal suspended bilayer graphene devices, enabling the independent measurement of the longitudinal and transverse resistance. We observe clear signatures of the fractional quantum Hall effect with different states that are either fully developed, and exhibit a clear plateau in the transverse resistance with a concomitant dip in longitudinal resistance or incipient, and exhibit only a longitudinal resistance minimum. All observed states scale as a function of filling factor ν, as expected.

Topological phases in the zeroth Landau level of bilayer graphene.

We analyze the phase diagram of the zeroth Landau level of bilayer graphene, taking into account the realistic effects of screening of the Coulomb interaction and strong mixing between two degenerate sublevels. We identify robust quantum Hall states at filling factors ν=-1, -4/3, -5/3, -8/5, -1/2 and discuss the nature of their ground states, collective excitations, and relation to the more familiar states in GaAs using a tractable model. In particular, we present evidence that the ν=-1/2 state is non-Abelian and described by either the Moore-Read wave function or its particle-hole conjugate, while ruling out other candidates such as the 331 state.