The thermalization of one-dimensional quantum systems may be severely slowed by weak links, e.g., by the Griffiths regions that dominate the long-time dynamics of a system close to the many-body-localization transition. Here, the authors construct universal coarse-grained descriptions for entanglement production and for the dynamics of quantum operators in systems with weak links. They reveal unexpected differences between these processes (for example, entanglement growth can be slower than linear in time even when operators spread ballistically). The universal physics is explained using simple classical effective models. The authors' analysis of the spreading of quantum information and of conserved quantities shows that thermalization in the presence of weak links has a rich structure, featuring multiple dynamic length scales that diverge with different powers of time.
The thermalization of one-dimensional quantum systems may be severely slowed by weak links, e.g., by the Griffiths regions that dominate the long-time dynamics of a system close to the many-body-localization transition. Here, the authors construct universal coarse-grained descriptions for entanglement production and for the dynamics of quantum operators in systems with weak links. They reveal unexpected differences between these processes (for example, entanglement growth can be slower than linear in time even when operators spread ballistically). The universal physics is explained using simple classical effective models. The authors' analysis of the spreading of quantum information and of conserved quantities shows that thermalization in the presence of weak links has a rich structure, featuring multiple dynamic length scales that diverge with different powers of time.
We study three aspects of quantum nonequilibrium dynamics; (1) transport of conserved quantities, (2) entanglement spreading, and (3) construction of local operators which slowly relax to thermal equilibrium. Motivated by recent progresses in ultracold atom experiments, we first analyze transport phenomena of a population imbalanced two-component fermi gas with arbitrary strength of inter-species interaction in three dimension. Using the Boltzmann kinetic equation at dilute regime, we obtain the transport coefficients of linear responses to gradients of temperature and chemical potential imbalance. We identify the magneto-caloric effects, and determine how these effects depend on interaction strength and population imbalance. Then, we propose an experimental protocol to observe these effects in an experiment with ultracold atoms. Next, we study entanglement spreading in a one-dimensional quantum Ising chain with longitudinal and transverse fields, which is diffusive and nonintegrable. Fully diagonalizing the Hamiltonian matrix, we explicitly show that the entanglement spreading is ballistic, thus faster than diffusive transport of conserved quantities. We provide a local spreading picture of entanglement entropy in terms of logarithmic negativity. Then, we discuss a role of energy conservation in entanglement spreading through analyzing a Floquet system. Lastly, we construct local operators that relax slowly to equilibrium with the same one-dimensional Hamiltonian. By showing that the Hamiltonian satisfies the eigenstate thermalization hypothesis, we first conclude that this model relaxes local operators to thermal equilibrium. Then, we systematically construct local operators that relax slower than conventional diffusive modes.
The low-frequency response of systems near a many-body localization transition can be dominated by rare regions that are locally critical or ``in the other phase.'' It is known that in one dimension, these rare regions can cause the dc conductivity and diffusion constant to vanish even inside the delocalized thermal phase. Here, we present a general analysis of such Griffiths effects in the thermal phase near the many-body localization transition: we consider both one-dimensional and higher-dimensional systems, subject to quenched randomness, and discuss both linear response (including the frequency- and wave-vector-dependent conductivity) and more general dynamics. In all the regimes we consider, we identify observables that are dominated by rare-region effects. In some cases (one-dimensional systems and Floquet systems with no extensive conserved quantities), essentially all long-time local observables are dominated by rare-region effects; in others, generic observables are instead dominated by hydrodynamic long-time tails throughout the thermal phase, and one must look at specific probes, such as spin echo, to see Griffiths behavior.
The physics of information scrambling in quantum many-body systems is intimately related to thermalisation and emergence of chaos. However, its standard characterisation through bipartite entanglement or operator growth remains inherently coarse-grained, obscuring the spatiotemporal anatomy of how quantum information flows between different regions of the system and across various length scales. In this work, we develop a theory for the dynamics of local information in local random unitary circuits which resolves the fine-grained microscopic structures of local information flow in such systems. Using the framework of information lattice which systematises the information content at each length scale within each subsystem, we identify a distribution of length scales at which information resides and obtain the dynamics of the distribution. For Haar-random circuits with infinite local Hilbert-space dimensions, we map this dynamics onto an exact classical stochastic process which reveals that this distribution is described by a Tracy-Widom form which moves ballistically in time ($ \propto t$) toward larger scales, accompanied by a ∼t1/3 broadening. We also find the same qualitative behaviour for random Clifford circuits acting on qubits. The similar scaling behaviour in two rather different settings hints strongly towards the universality of our results. In the case of Clifford circuits, we develop a phenomenological Markov process for the dynamics of the stabiliser generators in a specific gauge which confirms the Tracy-Widom distribution and the t1/3 scaling of the fluctuations. Ultimately, our results establish the universal properties of the dynamics of local quantum information in a length scale-resolved fashion and provide a possible route towards bridging exact microscopic theories for information dynamics with emergent hydrodynamic descriptions of information flow.
Understanding the spread of quantum entanglement and scrambling of information across a quantum many-body system is a fundamental problem in quantum dynamics. A necessary part of the spread of the entanglement is the growth in time of Heisenberg operators of initially localized operators. This operator growth can be diagnosed by studying the space-time structure of commutators of well-separated operators. Previous studies in this area focused on translation invariant models, but the effects of disorder, which can radically alter the motion of heat and charge, had not been studied. Here, the authors study the growth of operators in interacting systems with quenched disorder. In the localized phase, they find that operator sizes grow logarithmically in time similar to other measures of entanglement spreading. In the disordered metal, they find that operator sizes grow linearly with time, i.e., ballistically, in contrast to the diffusive motion of charge and heat. The ballistic growth of operators is quantified by the butterfly velocity which the authors relate to the charge diffusion constant and the interaction-induced inelastic scattering rate. When the diffusion of charge is slow, the resulting butterfly velocity is much smaller than the maximum speed allowed by microscopic causality constraints.
Quantum quench is a non-equilibrium process where the Hamiltonian is suddenly changed during the quantum evolution. The change can be made by spatially local perturbations (local quench) or globally switching to a completely different Hamiltonian (global quench). This thesis investigates the post-quench non-equilibrium dynamics with an emphasis on the time dependence of the quantum entanglement. We inspect the scaling of entanglement entropy (EE) to learn how correlation and entanglement built up in a quench. We begin with two local quench examples. In Chap. 2, we apply a local operator to the groundstate of the quantum Lifshitz model and monitor the change of the EE. We find that the entanglement grows according to the dynamical exponent z = 2 and then saturates to the scaling dimension of the perturbing operator -- a value representing its strength. In Chap. 3, we study the evolution after connecting two different one-dimensional critical chains at their ends. The Loschmidt echo which measures the similarity between the evolved state and the initial one decays with a power law, whose exponent is the scaling dimension of the defect (junction). Among other conclusions, we see that the local quench dynamics contain universal information of the (critical) theory. In the global quench scenario, the change of the Hamiltonian affects all parts of the system. In this thesis, we focus on the global chaotic quench driven by generic non-integrable Hamiltonians. In Chap. 4, we propose to use the operator entanglement entropy of the unitary operator as a probe. Its fast linear entanglement production is sharply contrasted to the slow logarithmic spreading of the many-body localized system. The entanglement saturation suggests that the evolution operator in the long time can be modeled by a random unitary matrix. In Chap. 5, we construct a random tensor network which consists of random unitary matrices connected locally to model chaotic evolution with local interactions. We find that the entanglement dynamics is mapped to the statistical mechanics of interacting random walks. This appealing emergent picture allows us to understand the universal linear growth as well as the fluctuations of entanglement in a chaotic quench.
In two-dimensional Floquet systems, many-body localized dynamics in the bulk may give rise to a chaotic evolution at the one-dimensional edges that is characterized by a nonzero chiral topological index. Such anomalous dynamics is qualitatively different from local-Hamiltonian evolution. Here we show how the presence of a nonzero index affects entanglement generation and the spreading of local operators, focusing on the coarse-grained description of generic systems. We tackle this problem by analyzing exactly solvable models of random quantum cellular automata (QCA) that generalize random circuits. We find that a nonzero index leads to asymmetric butterfly velocities with different diffusive broadening of the light cones and to a modification of the order relations between the butterfly and entanglement velocities. We propose that these results can be understood via a generalization of the recently introduced entanglement membrane theory, by allowing for a spacetime entropy current, which in the case of a generic QCA is fixed by the index. We work out the implications of this current on the entanglement "membrane tension" and show that the results for random QCA are recovered by identifying the topological index with a background velocity for the coarse-grained entanglement dynamics.