Many body localization with long range interactions

Many body localization (MBL) has emerged as a powerful paradigm for understanding non-equilibrium quantum dynamics. Folklore based on perturbative arguments holds that MBL only arises in systems with short range interactions. Here we advance non-perturbative arguments indicating that MBL can arise in systems with long range (Coulomb) interactions. In particular, we show using bosonization that MBL can arise in one dimensional systems with ~ r interactions, a problem that exhibits charge confinement. We also argue that (through the Anderson-Higgs mechanism) MBL can arise in two dimensional systems with log r interactions, and speculate that our arguments may even extend to three dimensional systems with 1/r interactions. Our arguments are `asymptotic' (i.e. valid up to rare region corrections), yet they open the door to investigation of MBL physics in a wide array of long range interacting systems where such physics was previously believed not to arise.Comment: Expanded discussion of higher dimensions, updated reference

On the magnetization of two-dimensional superconductors

We calculate the magnetization of a two-dimensional superconductor in a perpendicular magnetic field near its Kosterlitz-Thouless transition and at lower temperatures. We find that the critical behavior is more complex than assumed in the literature and that, in particular, the critical magnetization is {\it not} field independent as naive scaling predicts. In the low temperature phase we find a substantial fluctuation renormalization of the mean-field result. We compare our analysis with the data on the cuprates.Comment: 8 pages, 3 figure

On product, generic and random generic quantum satisfiability

We report a cluster of results on k-QSAT, the problem of quantum satisfiability for k-qubit projectors which generalizes classical satisfiability with k-bit clauses to the quantum setting. First we define the NP-complete problem of product satisfiability and give a geometrical criterion for deciding when a QSAT interaction graph is product satisfiable with positive probability. We show that the same criterion suffices to establish quantum satisfiability for all projectors. Second, we apply these results to the random graph ensemble with generic projectors and obtain improved lower bounds on the location of the SAT--unSAT transition. Third, we present numerical results on random, generic satisfiability which provide estimates for the location of the transition for k=3 and k=4 and mild evidence for the existence of a phase which is satisfiable by entangled states alone.Comment: 9 pages, 5 figures, 1 table. Updated to more closely match published version. New proof in appendi

AKLT Models with Quantum Spin Glass Ground States

We study AKLT models on locally tree-like lattices of fixed connectivity and find that they exhibit a variety of ground states depending upon the spin, coordination and global (graph) topology. We find a) quantum paramagnetic or valence bond solid ground states, b) critical and ordered N\'eel states on bipartite infinite Cayley trees and c) critical and ordered quantum vector spin glass states on random graphs of fixed connectivity. We argue, in consonance with a previous analysis, that all phases are characterized by gaps to local excitations. The spin glass states we report arise from random long ranged loops which frustrate N\'eel ordering despite the lack of randomness in the coupling strengths.Comment: 10 pages, 1 figur

A New Transport Regime in the Quantum Hall Effect

This paper describes an experimental identification and characterization of a new low temperature transport regime near the quantum Hall-to-insulator transition. In this regime, a wide range of transport data are compactly described by a simple phenomenological form which, on the one hand, is inconsistent with either quantum Hall or insulating behavior and, on the other hand, is also clearly at odds with a quantum-critical, or scaling, description. We are unable to determine whether this new regime represents a clearly defined state or is a consequence of finite temperature and sample-size measurements.Comment: Revtex, 3 pages, 2 figure

Current fluctuations near to the 2D superconductor-insulator quantum critical point

Systems near to quantum critical points show universal scaling in their response functions. We consider whether this scaling is reflected in their fluctuations; namely in current-noise. Naive scaling predicts low-temperature Johnson noise crossing over to noise power $\propto E^{z/(z+1)}$ at strong electric fields. We study this crossover in the metallic state at the 2d z=1 superconductor/insulator quantum critical point. Using a Boltzmann-Langevin approach within a 1/N-expansion, we show that the current noise obeys a scaling form $S_j=T \Phi[T/T_{eff}(E)]$ with $T_{eff} \propto \sqrt{E}$. We recover Johnson noise in thermal equilibrium and $S_j \propto \sqrt{E}$ at strong electric fields. The suppression from free carrier shot noise is due to strong correlations at the critical point. We discuss its interpretation in terms of a diverging carrier charge $\propto 1/\sqrt{E}$ or as out-of-equilibrium Johnson noise with effective temperature $\propto \sqrt{E}$.Comment: 5 page

Double-Talk Robust Fast Converging Algorithms for Network Echo Cancellation

Echo cancelers which cover longer impulse responses (greater than or equal to 64 ms) are desirable. Long responses create a need for more rapidly converging algorithms in order to meet the specifications for network echo cancelers devised by the ITU (International Telecommunication Union). In general, faster convergence implies a higher sensitivity to near-end disturbances, especially double-talk . Recently, a fast converging algorithm called proportionate NLMS (normalized least mean squares) algorithm (PNLMS) has been proposed. This algorithm exploits the sparseness of the echo path. In this paper we propose a method for making the PNLMS algorithm more robust against double-talk. The slower divergence rate of these robust algorithms in combination with a standard Geigel double-talk detector improves the performance of a network echo canceler considerably during double-talk. This results in the robust PNLMS algorithm which diverges much slower than PNLMS and standard NLMS. A generalization of the robust PNLMS algorithm to a robust proportionate affine projection algorithm (APA) is also presented. It converges very fast, and unlike PNLMS, is not as dependent on the assumption of a sparse echo path response. Trade off between convergence and divergence rate is easily tuned with one parameter and the added complexity is about 7 instructions per sample

The Weakly Coupled Pfaffian as a Type I Quantum Hall Liquid

The Pfaffian phase of electrons in the proximity of a half-filled Landau level is understood to be a p+ip superconductor of composite fermions. We consider the properties of this paired quantum Hall phase when the pairing scale is small, i.e. in the weak-coupling, BCS, limit, where the coherence length is much larger than the charge screening length. We find that, as in a Type I superconductor, the vortices attract so that, upon varying the magnetic field from its magic value at \nu=5/2, the system exhibits Coulomb frustrated phase separation. We propose that the weakly and strongly coupled Pfaffian states exemplify a general dichotomy between Type I and Type II quantum Hall fluids.Comment: 4 pages, 1 figur