Dynamical Transitions from Slow to Fast Relaxation in Random Open Quantum Systems.

We explore the effects of spatial locality on the dynamics of random quantum systems subject to a Markovian noise. To this end, we study a model in which the system Hamiltonian and its couplings to the noise are random matrices whose entries decay as power laws of distance, with distinct exponents α_{H}, α_{L}. The steady state is always featureless, but the rate at which it is approached exhibits three phases depending on α_{H} and α_{L}: a phase where the approach is asymptotically exponential as a result of a gap in the spectrum of the Lindblad superoperator that generates the dynamics, and two gapless phases with subexponential relaxation, distinguished by the manner in which the gap decreases with system size. Within perturbation theory, the phase boundaries in the (α_{H},α_{L}) plane differ for weak and strong decoherence, suggesting phase transitions as a function of noise strength. We identify nonperturbative effects that prevent such phase transitions in the thermodynamic limit.

Spectral Gaps and Midgap States in Random Quantum Master Equations.

We discuss the decay rates of chaotic quantum systems coupled to noise. We model both the Hamiltonian and the system-noise coupling by random N×N Hermitian matrices, and study the spectral properties of the resulting Liouvillian superoperator. We consider various random-matrix ensembles, and find that for all of them the asymptotic decay rate remains nonzero in the thermodynamic limit; i.e., the spectrum of the superoperator is gapped as N→∞. For finite N, the probability of finding a very small gap vanishes as P(Δ)∼Δ^{cN}, where c is insensitive to the dissipation strength. A sharp spectral transition takes place as the dissipation strength is increased: for dissipation beyond a critical strength, the slowest-decaying eigenvalues of the Liouvillian correspond to isolated "midgap" states. We give evidence that midgap states exist also for nonrandom system-noise coupling and discuss some experimental implications of the above results.

Fixed Points of Wegner-Wilson Flows and Many-Body Localization.

Many-body localization (MBL) is a phase of matter that is characterized by the absence of thermalization. Dynamical generation of a large number of local quantum numbers has been identified as one key characteristic of this phase, quite possibly the microscopic mechanism of breakdown of thermalization and the phase transition itself. We formulate a robust algorithm, based on Wegner-Wilson flow (WWF) renormalization, for computing these conserved quantities and their interactions. We present evidence for the existence of distinct fixed point distributions of the latter: a Gaussian white-noise-like distribution in the ergodic phase, a 1/f law inside the MBL phase, and scale-free distributions in the transition regime.

Emergent surface superconductivity in the topological insulator Sb2Te3.

Surfaces of three-dimensional topological insulators have emerged as one of the most remarkable states of condensed quantum matter where exotic electronic phases of Dirac particles should arise. Here we report on superconductivity in the topological insulator Sb2Te3 with transition to zero resistance induced through a minor tuning of growth chemistry that depletes bulk conduction channels. The depletion shifts Fermi energy towards the Dirac point as witnessed by a factor of 300 reduction of bulk carrier density and by the largest carrier mobility (≳25,000 cm(2) V(-1) s(-1)) found in any topological material. Direct evidence from transport, the unprecedentedly large diamagnetic screening, and the presence of ∼25 meV gaps detected by scanning tunnelling spectroscopy reveal the superconducting condensate to emerge first in surface puddles, with the onset of global phase coherence at ∼9 K. The rich structure of this state lends itself to manipulation via growth conditions and the material parameters such as Fermi velocity and mean free path.

Singular robust room-temperature spin response from topological Dirac fermions.

Topological insulators are a class of solids in which the non-trivial inverted bulk band structure gives rise to metallic surface states that are robust against impurity scattering. In three-dimensional (3D) topological insulators, however, the surface Dirac fermions intermix with the conducting bulk, thereby complicating access to the low-energy (Dirac point) charge transport or magnetic response. Here we use differential magnetometry to probe spin rotation in the 3D topological material family (Bi2Se3, Bi2Te3 and Sb2Te3). We report a paramagnetic singularity in the magnetic susceptibility at low magnetic fields that persists up to room temperature, and which we demonstrate to arise from the surfaces of the samples. The singularity is universal to the entire family, largely independent of the bulk carrier density, and consistent with the existence of electronic states near the spin-degenerate Dirac point of the 2D helical metal. The exceptional thermal stability of the signal points to an intrinsic surface cooling process, probably of thermoelectric origin, and establishes a sustainable platform for the singular field-tunable Dirac spin response.

Multispin correlations and pseudo-thermalization of the transient density matrix in solid-state NMR: free induction decay and magic echo.

Quantum unitary evolution typically leads to thermalization of generic interacting many-body systems. There are very few known general methods for reversing this process, and we focus on the magic echo, a radio-frequency pulse sequence known to approximately "rewind" the time evolution of dipolar coupled homonuclear spin systems in a large magnetic field. By combining analytic, numerical, and experimental results we systematically investigate factors leading to the degradation of magic echoes, as observed in reduced revival of mean transverse magnetization. Going beyond the conventional analysis based on mean magnetization we use a phase encoding technique to measure the growth of spin correlations in the density matrix at different points in time following magic echoes of varied durations and compare the results to those obtained during a free induction decay (FID). While considerable differences are documented at short times, the long-time behavior of the density matrix appears to be remarkably universal among the types of initial states considered - simple low order multispin correlations are observed to decay exponentially at the same rate, seeding the onset of increasingly complex high order correlations. This manifestly athermal process is constrained by conservation of the second moment of the spectrum of the density matrix and proceeds indefinitely, assuming unitary dynamics.

Theory of dissipationless Nernst effects.

We develop a theory of transverse thermoelectric (Peltier) conductivity alpha(xy), in a strong magnetic field--this particular conductivity is often the most important contribution to the Nernst thermopower. We demonstrate that alpha(xy) of a free electron gas can be expressed purely and exactly as the entropy per carrier irrespective of temperature (which agrees with the seminal Hall bar result of Girvin and Jonson). In two dimensions we prove the universality of this result in the presence of disorder which allows explicit demonstration of a number of features of interest to experiments on graphene and other two-dimensional materials. We also exploit this relationship in the low-field regime and analyze the rich singularity structure in alpha(xy)(B,T) in three dimensions; we discuss its possible experimental implications.