We explore the high-temperature dynamics of the disordered, one-dimensional XXZ model near the many-body localization (MBL) transition, focusing on the delocalized (i.e., "metallic") phase. In the vicinity of the transition, we find that this phase has the following properties: (i) local magnetization fluctuations relax subdiffusively; (ii) the ac conductivity vanishes near zero frequency as a power law; and (iii) the distribution of resistivities becomes increasingly broad at low frequencies, approaching a power law in the zero-frequency limit. We argue that these effects can be understood in a unified way if the metallic phase near the MBL transition is a quantum Griffiths phase. We establish scaling relations between the associated exponents, assuming a scaling form of the spin-diffusion propagator. A phenomenological classical resistor-capacitor model captures all the essential features.

We address the hydrodynamics of operator spreading in interacting integrable lattice models. In these models, operators spread through the ballistic propagation of quasiparticles, with an operator front whose velocity is locally set by the fastest quasiparticle velocity. In interacting integrable systems, this velocity depends on the density of the other quasiparticles, so equilibrium density fluctuations cause the front to follow a biased random walk, and therefore to broaden diffusively. Ballistic front propagation and diffusive front broadening are also generically present in non-integrable systems in one dimension; thus, although the mechanisms for operator spreading are distinct in the two cases, these coarse grained measures of the operator front do not distinguish between the two cases. We present an expression for the front-broadening rate; we explicitly derive this for a particular integrable model (the "Floquet-Fredrickson-Andersen" model), and argue on kinetic grounds that it should apply generally. Our results elucidate the microscopic mechanism for diffusive corrections to ballistic transport in interacting integrable models. arXiv:1809.02126v3 [cond-mat.stat-mech]

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We argue that the a.c. conductivity σ(ω) in the many-body localized phase is a power law of frequency ω at low frequency: specifically, σ(ω) ∼ ω α with the exponent α approaching 1 at the phase transition to the thermal phase, and asymptoting to 2 deep in the localized phase. We identify two separate mechanisms giving rise to this power law: deep in the localized phase, the conductivity is dominated by rare resonant pairs of configurations; close to the transition, the dominant contributions are rare regions that are locally critical or in the thermal phase. We present numerical evidence supporting these claims, and discuss how these power laws can also be seen through polarization-decay measurements in ultracold atomic systems.

In a many-body localized (MBL) quantum system, the ergodic hypothesis breaks down completely, giving rise to a fundamentally new many-body phase. Whether and under which conditions MBL can occur in higher dimensions remains an outstanding challenge both for experiments and theory. Here, we experimentally explore the relaxation dynamics of an interacting gas of fermionic potassium atoms loaded in a two-dimensional optical lattice with different quasi-periodic potentials along the two directions. We observe a dramatic slowing down of the relaxation for intermediate disorder strengths and attribute this partially to configurational rare-region effects. Beyond a critical disorder strength, we see negligible relaxation on experimentally accessible timescales, indicating a possible transition into a two-dimensional MBL phase. Our experiments reveal a distinct interplay of interactions, disorder, and dimensionality and provide insights into regimes where controlled theoretical approaches are scarce.

Systems of strongly interacting dipoles offer an attractive platform to study many-body localized phases, owing to their long coherence times and strong interactions. We explore conditions under which such localized phases persist in the presence of power-law interactions and supplement our analytic treatment with numerical evidence of localized states in one dimension. We propose and analyze several experimental systems that can be used to observe and probe such states, including ultracold polar molecules and solidstate magnetic spin impurities.

We consider strongly interacting systems of effective spins, subject to dissipative spin-flip processes associated with optical pumping. We predict the existence of novel magnetic phases in the steadystate of this system, which emerge due to the competition between coherent and dissipative processes. Specifically, for strongly anisotropic spin-spin interactions, we find ferromagnetic, antiferromagnetic, spin-density-wave, and staggered-XY steady states, which are separated by nonequilibrium phase transitions meeting at a Lifshitz point. These transitions are accompanied by quantum correlations, resulting in spin squeezing. Experimental implementations in ultracold atoms and trapped ions are discussed. PACS numbers:Exotic magnetic states play a central role in the physics of quantum many-body systems, and have been explored in a wide variety of strongly correlated materials [1]. Realizing and exploring magnetic states has recently emerged as a central goal in ultracold atomic physics [2,3]. Due to highly controllable and tunable interactions, ensembles of ultracold neutral atoms and ions may provide a unique laboratory to study exotic quantum magnetism [2-9] Among the main obstacles are relatively small energy scales associated with magnetic ordering (e.g., the superexchange scale in the Hubbard model), requiring cooling atomic systems down to very low temperatures [2] and the slow timescales involved in spin thermalization [10][11][12]. Furthermore, ultracold atoms are fundamentally open, driven quantum systems far away from their absolute thermal equilibrium. This motivates the exploration of spin dynamics in the presence of driving and dissipation [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30].Recently a number of schemes involving dissipation to create magnetic phases have been proposed. These typically use engineered reservoirs involving coupling multiple lattice sites [13][14][15]. At the same time, one expects single-site dissipation such as spontaneous decay to be detrimental to realizing interesting magnetic states, resulting e.g. in unwanted decoherence. In this Letter, we demonstrate that optical pumping and spontaneous decay can instead enrich the phase diagram, resulting in new phases and phase transitions that do not exist in conventional equilibrium systems. Significantly, these novel states can be observed under conditions when realization of conventional, equilibrium states is difficult.The key idea of this work can be understood by considering the anisotropic spin-1/2 Heisenberg model (i.e., the XYZ model), which is governed by the Hamiltonian H = 1 2d mn

Isolated quantum many-body systems with integrable dynamics generically do not thermalize when taken far from equilibrium. As one perturbs such systems away from the integrable point, thermalization sets in, but the nature of the crossover from integrable to thermalizing behavior is an unresolved and actively discussed question. We explore this question by studying the dynamics of the momentum distribution function in a dipolar quantum Newton's cradle consisting of highly magnetic dysprosium atoms. This is accomplished by creating the first one-dimensional Bose gas with strong magnetic dipole-dipole interactions. These interactions provide tunability of both the strength of the integrability-breaking perturbation and the nature of the near-integrable dynamics. We provide the first experimental evidence that thermalization close to a strongly interacting integrable point occurs in two steps: prethermalization followed by near-exponential thermalization. Exact numerical calculations on a two-rung lattice model yield a similar two-timescale process, suggesting that this is generic in strongly interacting near-integrable models. Moreover, the measured thermalization rate is consistent with a parameter-free theoretical estimate, based on identifying the types of collisions that dominate thermalization. By providing tunability between regimes of integrable and nonintegrable dynamics, our work sheds light on the mechanisms by which isolated quantum many-body systems thermalize and on the temporal structure of the onset of thermalization.