We study the quantum thermalization and information scrambling dynamics of an experimentally realizable quantum spin model with homogeneous XX-type all-to-all interactions and random local potentials. We identify the thermalization-localization transition by changing the disorder strength, under a proper relative all-to-all interaction strength. The operator scrambling has no light-cone behavior and grows almost equally fast in both phases. In the thermal phase, we find that the scrambling dynamics exhibits fast scrambling without appealing to the semi-classical limit. The fast scrambling dynamics always exists at a fixed bare interaction strength regardless of the relative strength in the Hamiltonian. The model also shows faster or slower scrambling dynamics related to the bare interaction strength. We show that the seeming violation of the fast scrambling conjecture arises from the absence of a natural timescale in the infinite temperature ensemble. We suggest that one needs a proper timescale and the corresponding dimensionless time for fast scrambling dynamics. After introducing such a timescale, we give a general phase diagram of the fast scrambling dynamics in the thermal phase. We also briefly discuss the experimental realization of the model using superconducting qubit quantum simulators.
We study the quantum thermalization and information scrambling dynamics of an experimentally realizable quantum spin model with homogeneous XX-type all-to-all interactions and random local potentials. We identify the thermalization-localization transition by changing the disorder strength, under a proper relative all-to-all interaction strength. The operator scrambling has no light-cone behavior and grows almost equally fast in both phases. In the thermal phase, we find that the scrambling dynamics exhibits fast scrambling without appealing to the semi-classical limit. The fast scrambling dynamics always exists at a fixed bare interaction strength regardless of the relative strength in the Hamiltonian. The model also shows faster or slower scrambling dynamics related to the bare interaction strength. We show that the seeming violation of the fast scrambling conjecture arises from the absence of a natural timescale in the infinite temperature ensemble. We suggest that one needs a proper timescale and the corresponding dimensionless time for fast scrambling dynamics. After introducing such a timescale, we give a general phase diagram of the fast scrambling dynamics in the thermal phase. We also briefly discuss the experimental realization of the model using superconducting qubit quantum simulators.
We study the quantum thermalization and information scrambling dynamics of an experimentally realizable quantum spin model with homogeneous XX-type all-to-all interactions and random local potentials. We identify the thermalization-localization transition by changing the disorder strength, under a proper all-to-all interaction strength. The scrambling dynamics in the localization phase shows behaviors that are distinct from that of local models. The operator scrambling grows almost equally fast in the two phases. In the thermal phase, we show that fast scrambling is exhibited without appealing to the semiclassical limit. We also briefly discuss the experimental realization of the model using superconducting qubit quantum simulators.
We study quantum information scrambling, specifically the growth of Heisenberg operators, in large disordered spin chains using matrix product operator dynamics to scan across the thermalization-localization quantum phase transition. We observe ballistic operator growth for weak disorder, and a sharp transition to a phase with subballistic operator spreading. The critical disorder strength for the ballistic to subballistic transition is well below the many body localization phase transition, as determined from finite size scaling of energy eigenstate entanglement entropy in small chains. In contrast, we find that the transition from subballistic to logarithmic behavior at the actual eigenstate localization transition is not resolved in our finite numerics. These data are discussed in the context of a universal form for the growing operator shape and substantiated with a simple phenomenological model of rare regions.
We study quantum information scrambling in spin models with both long-range all-to-all and short-range interactions. We argue that a simple global, spatially homogeneous interaction together with local chaotic dynamics is sufficient to give rise to fast scrambling, which describes the spread of quantum information over the entire system in a time that is logarithmic in the system size. This is illustrated in two tractable models: (1) a random circuit with Haar random local unitaries and a global interaction and (2) a classical model of globally coupled nonlinear oscillators. We use exact numerics to provide further evidence by studying the time evolution of an out-of-time-order correlator and entanglement entropy in spin chains of intermediate sizes. Our results pave the way towards experimental investigations of fast scrambling and aspects of quantum gravity with quantum simulators.
Understanding how quantum matter behaves when driven out of equilibrium is one of the key focuses in quantum physics. Thanks to impressive progress in the control and precision achieved in quantum synthetic matter over the past decades, the nonequilibrium quantum many-body physics has become one of the most active research areas today, especially after the experimental realization of Bose-Einstein condensates and optical lattices, which allows us to directly observe and study nonequilibrium quantum matter with great accuracy and controllability. In this dissertation, I explore the rich landscape of nonequilibrium quantum many-body physics and how quantum phase transitions, both symmetry-breaking and topological, can be extended to the nonequilibrium setting. In the first part of the dissertation, I focus on spinor Bose-Einstein condensates as an isolated quantum many-body system, and reveal their various dynamical behaviors, including quantum collapse and revivals, thermalization and nonthermal equilibration with no revival even though the system has finite degrees of freedom. In contrast to typical integrable systems, which usually do not thermalize, we find that spinor condensates have a parameter range in which the system thermalizes via the Eigenstate Thermalization Hypothesis (ETH). We show that this observation is linked to the presence of rare nonthermal states whose fraction vanishes with system size, and contributes to the notion of thermalization via weak ETH. Next, I explore a dynamical process that is complementary to thermalization in isolated quantum systems: information scrambling, which could be probed via out-of-time-order correlators (OTOC). I propose a nonintegrable, disordered and quasi-1D spin model, the ladder-XX model, for a feasible detection of information scrambling in a cold atom simulator. This chapter poses a fundamental question: "What are the signatures of quantum phases and phase transitions in isolated interacting systems driven out-of-equilibrium?" I study the ladder-XX model in both clean and disordered potentials, and characterize different nonequilibrium phases, i.e., ergodic and many-body localized, of the model based on the decay properties of OTOCs. Emergent light cone shows sublinear behavior, while the butterfly cones drastically differ from the light cone by demonstrating superlinear spread of information with a velocity that is bounded by the light cone velocity. In the second part of the dissertation, I continue to search for answers to the question posed above, however this time with a particular focus on symmetry-breaking and topological quantum phase transitions. I pin down a universal mechanism underlying the relation between information scrambling at any temperature and quantum phases at low temperatures. Our method points to key ingredients to dynamically detect long-range order in gapped phases through OTOCs for symmetry-breaking quantum phase transitions and Z2 topological order associated with Majorana zero modes localized at the edges. Our results pave the way to an intriguing observation that phases of quantum matter could protect the information from scrambling and thermalization, even when the system is interacting and nonintegrable. Finally, I explore and propose utilizing short-time transient temporal regimes and single-site probes to detect the phases and phase transitions in quantum matter. These studies reveal a dynamical crossover and a dynamical phase transition, respectively for periodic and open-boundary chains. In both cases, a nonequilibrium scaling law appears in the vicinity of the crossover/transition with associated exponents that differ from the analytical predictions for long times. Feasibility of detecting such dynamical criticality in experimental systems are discussed.
Many proposed quantum mechanical models of black holes include highly nonlocal interactions.The time required for thermalization to occur in such models should reflect the relaxation times associated with classical black holes in general relativity.Moreover, the time required for a particularly strong form of thermalization to occur, sometimes known as scrambling, determines the time scale on which black holes should start to release information.It has been conjectured that black holes scramble in a time logarithmic in their entropy, and that no system in nature can scramble faster.In this article, we address the conjecture from two directions.First, we exhibit two examples of systems that do indeed scramble in logarithmic time: Brownian quantum circuits and the antiferromagnetic Ising model on a sparse random graph.Unfortunately, both fail to be truly ideal fast scramblers for reasons we discuss.Second, we use Lieb-Robinson techniques to prove a logarithmic lower bound on the scrambling time of systems with finite norm terms in their Hamiltonian.The bound holds in spite of any nonlocal structure in the Hamiltonian, which might permit every degree of freedom to interact directly with every other one.
How fast quantum information scrambles such that it becomes inaccessible by local probes turns out to be central to various fields. Motivated by recent works on spin systems with nonlocal interactions, we study information scrambling in different variants of the Ising model. Our work reveals that nonlocal interactions can induce operator dynamics not precisely captured by out-of-time-order correlators (OTOCs). In particular, the operator size exhibits a slowdown in systems with generic power-law interactions despite a highly nonlinear light cone. A recently proposed microscopic model for fast scrambling does not show this slowdown, which uncovers a distinct analogy between a local operator under unitary evolution and the entanglement entropy following a quantum quench. Our work gives new insights on scrambling properties of systems in reach of current quantum simulation platforms and complements results on possibly observing features of quantum gravity in the laboratory.