We describe the non-equilibrium quench dynamics of the Sachdev-Ye-Kitaev models of fermions with random all-to-all interactions. These provide tractable models of the dynamics of quantum systems without quasiparticle excitations. The Kadanoff-Baym equations show that the final state is thermal, and their numerical analysis is consistent with a thermalization rate proportional to the absolute temperature of the final state. We also obtain an exact analytic solution of the quench dynamics in the large q limit of a model with q fermion interactions: in this limit, the thermalization of the fermion Green's function is instantaneous.

We report on a Dirac-like Fermi surface in three-dimensional bulk materials in a distorted spinel structure on the basis of density functional theory (DFT) as well as tight-binding theory. The four examples we provide in this paper are BiZnSiO4, BiCaSiO4, BiMgSiO4, and BiAlInO4. A necessary characteristic of these structures is that they contain a Bi lattice which forms a hierarchy of chain-like substructures, with consequences for both fundamental understanding and materials design.Following the discovery of topological insulators, there 6 has been considerable interest in studying semimetal- 66As shown in Fig. 1, the cubic unit cell distorts to an or- (Fig. 3). Both the crystal and electronic

Recently, it has been proposed that the butterfly velocity -a speed at which quantum information propagates -may provide a fundamental bound on diffusion constants in dirty incoherent metals. We analytically compute the charge diffusion constant and the butterfly velocity in charge-neutral holographic matter with long wavelength "hydrodynamic" disorder in a single spatial direction. In this limit, we find that the butterfly velocity does not set a sharp lower bound for the charge diffusion constant.

The Schwinger-boson theory of the frustrated square lattice antiferromagnet yields a stable, gapped Z 2 spin liquid ground state with time-reversal symmetry, incommensurate spin correlations and long-range Ising-nematic order. We obtain an equivalent description of this state using fermionic spinons (the fermionic spinons can be considered to be bound states of the bosonic spinons and the visons). Upon doping, the Z 2 spin liquid can lead to a fractionalized Fermi liquid (FL*) with small Fermi pockets of electron-like quasiparticles, while preserving the Z 2 topological and Ising-nematic orders. We describe a Higgs transition out of this deconfined metallic state into a confining superconducting state which is almost always of the Fulde-Ferrell-Larkin-Ovchinnikov type, with spatial modulation of the superconducting order. arXiv:1603.03041v2 [cond-mat.str-el] 9 Jul 2016 Acknowledgments 26 A. Derivation of the bosonic PSG 27 3 B. PSG corresponding to the nematic bosonic ansatz 28 C. Alternate derivation of the vison PSG 30 D. Derivation of the fermionic PSG 34 E. Trivial and non-trivial fusion rules 35 F. Solution for the fermionic ansatz 38 G. Alternative derivation of the specific fermionic PSG 40 H. PSG for the site bosons and constraints on H B 41 References 42

We study the real time dynamics of N F flavors of fermions coupled to a U (1) gauge field in 2 + 1 dimensions to leading order in a 1/N F expansion. For large enough N F , this is an interacting conformal field theory and describes the low energy properties of the Dirac spin liquid. We focus on thermalization and the onset of many-body quantum chaos which can be diagnosed from the growth of initally anti-commuting fermion field operators. We compute such anti-commutators in this gauge theory to leading order in 1/N F . We find that the anti-commutator grows exponentially in time and compute the quantum Lyapunov exponent. We briefly comment on chaos, locality, and gauge invariance. t ß t ß t ß (a) t ß t ß t ß (b)

We examine the low frequency spin susceptibility of the paramagnetic phase of the quantum Ising chain in transverse field at temperatures well below the energy gap. We find that the imaginary part is dominated by rare quantum processes in which the number of quasiparticles changes by an odd number.We obtain exact results for the NMR relaxation rate in the low temperature limit for the integrable model with nearest-neighbor Ising interactions, and derive exact universal scaling results applicable to generic Ising chains near the quantum critical point. These results resolve certain discrepancies between the energy scales measured with different experimental probes in the quantum disordered paramagnetic phase of the Ising chain system CoNb 2 O 6 .

A long standing challenge in biological and artificial intelligence is to understand how new knowledge can be constructed from known building blocks in a way that is amenable for computation by neuronal circuits. Here we focus on the task of storage and recall of structured knowledge in long-term memory. Specifically, we ask how recurrent neuronal networks can store and retrieve multiple knowledge structures. We model each structure as a set of binary relations between events and attributes (attributes may represent e.g., temporal order, spatial location, role in semantic structure), and map each structure to a distributed neuronal activity pattern using a vector symbolic architecture (VSA) scheme. We then use associative memory plasticity rules to store the binarized patterns as fixed points in a recurrent network. By a combination of signal-to-noise analysis and numerical simulations, we demonstrate that our model allows for efficient storage of these knowledge structures, such that the memorized structures as well as their individual building blocks (e.g., events and attributes) can be subsequently retrieved from partial retrieving cues. We show that long-term memory of structured knowledge relies on a new principle of computation beyond the memory basins. Finally, we show that our model can be extended to store sequences of memories as single attractors.

A long standing challenge in biological and artificial intelligence is to understand how new knowledge can be constructed from known building blocks in a way that is amenable for computation by neuronal circuits. Here we focus on the task of storage and recall of structured knowledge in long-term memory. Specifically, we ask how recurrent neuronal networks can store and retrieve multiple knowledge structures. We model each structure as a set of binary relations between events and attributes (attributes may represent e.g., temporal order, spatial location, role in semantic structure), and map each structure to a distributed neuronal activity pattern using a vector symbolic architecture scheme.We then use associative memory plasticity rules to store the binarized patterns as fixed points in a recurrent network. By a combination of signal-to-noise analysis and numerical simulations, we demonstrate that our model allows for efficient storage of these knowledge structures, such that the memorized structures as well as their individual building blocks (e.g., events and attributes) can be subsequently retrieved from partial retrieving cues. We show that long-term memory of structured knowledge relies on a new principle of computation beyond the memory basins. Finally, we show that our model can be extended to store sequences of memories as single attractors.