Showing papers by "Xie Chen published in 2014"

Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator

Abstract: The surfaces of three-dimensional topological insulators (3D TIs) are generally described as Dirac metals, with a single Dirac cone. It was previously believed that a gapped surface implied breaking of either time-reversal $\mathcal{T}$ or $\text{U}(1)$ charge conservation symmetry. Here, we discuss a possibility in the presence of interactions, a surface phase that preserves all symmetries but is nevertheless gapped and insulating. Then, the surface must develop topological order of a kind that can not be realized in a two-dimensional (2D) system with the same symmetries. We discuss candidate surface states, non-Abelian quantum Hall states which, when realized in 2D, have ${\ensuremath{\sigma}}_{xy}=\frac{1}{2}$ and hence break $\mathcal{T}$ symmetry. However, by constructing an exactly soluble 3D lattice model, we show they can be realized as $\mathcal{T}$-symmetric surface states. The corresponding 3D phases are confined, and have $\ensuremath{\theta}=\ensuremath{\pi}$ magnetoelectric response. Two candidate states have the same 12-particle topological order, the (Read-Moore) Pfaffian state with the neutral sector reversed, which we term T-Pfaffian topological order, but differ in their $\mathcal{T}$ transformation. Although we are unable to connect either of these states directly to the superconducting TI surface, we argue that one of them describes the 3D TI surface, while the other differs from it by a bosonic topological phase. We also discuss the 24-particle Pfaffian-antisemion topological order (which can be connected to the superconducting TI surface) and demonstrate that it can be realized as a $\mathcal{T}$-symmetric surface state.

Symmetry-protected topological phases from decorated domain walls

Abstract: Symmetry-protected topological phases generalize the notion of topological insulators to strongly interacting systems of bosons or fermions. A sophisticated group cohomology approach has been used to classify bosonic symmetry-protected topological phases, which however does not transparently predict their properties. Here we provide a physical picture that leads to an intuitive understanding of a large class of symmetry-protected topological phases in d=1,2,3 dimensions. Such a picture allows us to construct explicit models for the symmetry-protected topological phases, write down ground state wave function and discover topological properties of symmetry defects both in the bulk and on the edge of the system. We consider symmetries that include a Z2 subgroup, which allows us to define domain walls. While the usual disordered phase is obtained by proliferating domain walls, we show that symmetry-protected topological phases are realized when these domain walls are decorated, that is, are themselves symmetry-protected topological phases in one lower dimension. This construction works both for unitary Z2 and anti-unitary time reversal symmetry.

Exactly soluble model of a three-dimensional symmetry-protected topological phase of bosons with surface topological order

Abstract: We construct an exactly soluble Hamiltonian on the D=3 cubic lattice, whose ground state is a topological phase of bosons protected by time-reversal symmetry, i.e., a symmetry-protected topological (SPT) phase. In this model, excitations with anyonic statistics are shown to exist at the surface but not in the bulk. The statistics of these surface anyons is explicitly computed and shown to be identical to the three-fermion Z2 model, a variant of Z2 topological order which cannot be realized in a purely D=2 system with time-reversal symmetry. Thus the model realizes a novel surface termination for three-dimensional (3D) SPT phases, that of a fully symmetric gapped surface with topological order. The 3D phase found here was previously proposed from a field theoretic analysis but is outside the group cohomology classification that appears to capture all SPT phases in lower dimensions. Such phases may potentially be realized in spin-orbit-coupled magnetic insulators, which evade magnetic ordering. Our construction utilizes the Walker-Wang prescription to create a 3D confined phase with surface anyons, which can be extended to other topological phases.

Efficient lattice rescoring using recurrent neural network language models

Abstract: Recurrent neural network language models (RNNLM) have become an increasingly popular choice for state-of-the-art speech recognition systems due to their inherently strong generalization performance. As these models use a vector representation of complete history contexts, RNNLMs are normally used to rescore N-best lists. Motivated by their intrinsic characteristics, two novel lattice rescoring methods for RNNLMs are investigated in this paper. The first uses an n-gram style clustering of history contexts. The second approach directly exploits the distance measure between hidden history vectors. Both methods produced 1-best performance comparable with a 10k-best rescoring baseline RNNLM system on a large vocabulary conversational telephone speech recognition task. Significant lattice size compression of over 70% and consistent improvements after confusion network (CN) decoding were also obtained over the N-best rescoring approach.

Interaction effects on 3D topological superconductors: surface topological order from vortex condensation, the 16 fold way and fermionic Kramers doublets

Abstract: Three dimensional topological superconductors with time reversal symmetry (class DIII) are indexed by an integer $ u$, the number of surface Majorana cones, according to the free fermion classification The superfluid B phase of He$^3$ realizes the $ u=1$ phase Recently, it has been argued that this classification is reduced in the presence of interactions to Z$_{16}$ This was argued from the symmetry respecting surface topological orders of these states, which provide a non-perturbative definition of the bulk topological phase Here, we verify this conclusion by focusing on the even index case, $ u=2m$, where a vortex condensation approach can be used to explicitly derive the surface topological orders We show a direct relation to the well known result on one dimensional topological superconductors (class BDI), where interactions reduce the free fermion classification from Z down to Z$_8$ Finally, we discuss in detail the fermionic analog of Kramers time reversal symmetry, which allows semions of some surface topological orders to transform as $T^2=\pm i$

Efficient GPU-based Training of Recurrent Neural Network Language Models Using Spliced Sentence Bunch

Abstract: Copyright © 2014 ISCA. Recurrent neural network language models (RNNLMs) are becoming increasingly popular for a range of applications including speech recognition. However, an important issue that limits the quantity of data, and hence their possible application areas, is the computational cost in training. A standard approach to handle this problem is to use class-based outputs, allowing systems to be trained on CPUs. This paper describes an alternative approach that allows RNNLMs to be efficiently trained on GPUs. This enables larger quantities of data to be used, and networks with an unclustered, full output layer to be trained. To improve efficiency on GPUs, multiple sentences are "spliced" together for each mini-batch or "bunch" in training. On a large vocabulary conversational telephone speech recognition task, the training time was reduced by a factor of 27 over the standard CPU-based RNNLM toolkit. The use of an unclustered, full output layer also improves perplexity and recognition performance over class-based RNNLMs.

The NINJA-2 project: Detecting and characterizing gravitational waveforms modelled using numerical binary black hole simulations

Abstract: The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational-wave astrophysics communities. The purpose of NINJA is to study the ability to detect gravitational waves emitted from merging binary black holes and recover their parameters with next-generation gravitational-wave observatories. We report here on the results of the second NINJA project, NINJA-2, which employs 60 complete binary black hole hybrid waveforms consisting of a numerical portion modelling the late inspiral, merger, and ringdown stitched to a post-Newtonian portion modelling the early inspiral. In a "blind injection challenge" similar to that conducted in recent LIGO and Virgo science runs, we added 7 hybrid waveforms to two months of data recolored to predictions of Advanced LIGO and Advanced Virgo sensitivity curves during their first observing runs. The resulting data was analyzed by gravitational-wave detection algorithms and 6 of the waveforms were recovered with false alarm rates smaller than 1 in a thousand years. Parameter estimation algorithms were run on each of these waveforms to explore the ability to constrain the masses, component angular momenta and sky position of these waveforms. We also perform a large-scale monte-carlo study to assess the ability to recover each of the 60 hybrid waveforms with early Advanced LIGO and Advanced Virgo sensitivity curves. Our results predict that early Advanced LIGO and Advanced Virgo will have a volume-weighted average sensitive distance of 300Mpc (1Gpc) for $10M_{\odot}+10M_{\odot}$ ($50M_{\odot}+50M_{\odot}$) binary black hole coalescences. We demonstrate that neglecting the component angular momenta in the waveform models used in matched-filtering will result in a reduction in sensitivity for systems with large component angular momenta. [Abstract abridged for ArXiv, full version in PDF]

Impact of single-microphone dereverberation on DNN-based meeting transcription systems

Abstract: Over the past few decades, a range of front-end techniques have been proposed to improve the robustness of automatic speech recognition systems against environmental distortion. While these techniques are effective for small tasks consisting of carefully designed data sets, especially when used with a classical acoustic model, there has been limited evidence that they are useful for a state-of-the-art system with large scale realistic data. This paper focuses on reverberation as a type of distortion and investigates the degree to which dereverberation processing can improve the performance of various forms of acoustic models based on deep neural networks (DNNs) in a challenging meeting transcription task using a single distant microphone. Experimental results show that dereverberation improves the recognition performance regardless of the acoustic model structure and the type of the feature vectors input into the neural networks, providing additional relative improvements of 4.7% and 4.1% to our best configured speaker-independent and speaker-adaptive DNN-based systems, respectively. © 2014 IEEE.

Detection of symmetry-enriched topological phases

Abstract: Topologically ordered systems in the presence of symmetries can exhibit new structures which are referred to as symmetry-enriched topological (SET) phases. We introduce simple methods to detect certain SET orders directly from a complete set of topologically degenerate ground-state wave functions. In particular, we first show how to directly determine the characteristic symmetry fractionalization of the quasiparticles from the reduced density matrix of the minimally entangled states. Second, we show how a simple generalization of a nonlocal order parameter can be measured to detect SET phases. The usefulness of the proposed approach is demonstrated by examining two concrete model states which exhibit SET phases: (i) a spin-1 model on the honeycomb lattice and (ii) the resonating valence bond (RVB) state on a kagome lattice. We conclude that the spin-1 model and the RVB state are in the same SET phases.

Implementation of an F-statistic all-sky search for continuous gravitational waves in Virgo VSR1 data

Abstract: We present an implementation of the $\mathcal{F}$-statistic to carry out the first search in data from the Virgo laser interferometric gravitational wave detector for periodic gravitational waves from a priori unknown, isolated rotating neutron stars. We searched a frequency $f_0$ range from 100 Hz to 1 kHz and the frequency dependent spindown $f_1$ range from $-1.6\,(f_0/100\,{\rm Hz}) \times 10^{-9}\,$ Hz/s to zero. A large part of this frequency - spindown space was unexplored by any of the all-sky searches published so far. Our method consisted of a coherent search over two-day periods using the $\mathcal{F}$-statistic, followed by a search for coincidences among the candidates from the two-day segments. We have introduced a number of novel techniques and algorithms that allow the use of the Fast Fourier Transform (FFT) algorithm in the coherent part of the search resulting in a fifty-fold speed-up in computation of the $\mathcal{F}$-statistic with respect to the algorithm used in the other pipelines. No significant gravitational wave signal was found. The sensitivity of the search was estimated by injecting signals into the data. In the most sensitive parts of the detector band more than 90% of signals would have been detected with dimensionless gravitational-wave amplitude greater than $5 \times 10^{-24}$.

Detection of Symmetry Enriched Topological Phases

Abstract: Topologically ordered systems in the presence of symmetries can exhibit new structures which are referred to as symmetry enriched topological (SET) phases. We introduce simple methods to detect the SET order directly from a complete set of topologically degenerate ground state wave functions. In particular, we first show how to directly determine the characteristic symmetry fractionalization of the quasiparticles from the reduced density matrix of the minimally entangled states. Second, we show how a simple generalization of a non-local order parameter can be measured to detect SETs. The usefulness of the proposed approached is demonstrated by examining two concrete model states which exhibit SET: (i) a spin-1 model on the honeycomb lattice and (ii) the resonating valence bond state on a kagome lattice. We conclude that the spin-1 model and the RVB state are in the same SET phases.

`Gauging' time reversal symmetry in tensor network states

Abstract: It is well known that unitary symmetries can be `gauged', i.e. defined to act in a local way, which leads to a corresponding gauge field. Gauging, for example, the charge conservation symmetry leads to electromagnetic gauge fields. It is an open question whether an analogous process is possible for time reversal which is an anti-unitary symmetry. Here we discuss a route to gauging time reversal symmetry which applies to gapped quantum ground states that admit a tensor network representation. The tensor network representation of quantum states provides a notion of locality for the wave function coefficient and hence a notion of locality for the action of complex conjugation in anti-unitary symmetries. Based on that, we show how time reversal can be applied locally and also describe time reversal symmetry twists which act as gauge fluxes through nontrivial loops in the system. As with unitary symmetries, gauging time reversal provides useful access to the physical properties of the system. We show how topological invariants of certain time reversal symmetric topological phases in $D=1,2$ are readily extracted using these ideas.

An initial investigation of long-term adaptation for meeting transcription

Abstract: Xie Chen would like to thank Toshiba Research Europe Ltd, Cambridge Research Lab, for funding his work. The authors would like to thank the Toshiba Cambridge Speech Group for allowing the data to be collected, also would like to thank Chao Zhang and Eric Wang for providing DNN and CMLLR transform tools.

Anomalous Symmetry Fractionalization and Surface Topological Order

Abstract: In addition to possessing fractional statistics, anyon excitations of a 2D topologically ordered state can realize symmetry in distinct ways , leading to a variety of symmetry enriched topological (SET) phases. While the symmetry fractionalization must be consistent with the fusion and braiding rules of the anyons, not all ostensibly consistent symmetry fractionalizations can be realized in 2D systems. Instead, certain `anomalous' SETs can only occur on the surface of a 3D symmetry protected topological (SPT) phase. In this paper we describe a procedure for determining whether an SET of a discrete, onsite, unitary symmetry group $G$ is anomalous or not. The basic idea is to gauge the symmetry and expose the anomaly as an obstruction to a consistent topological theory combining both the original anyons and the gauge fluxes. Utilizing a result of Etingof, Nikshych, and Ostrik, we point out that a class of obstructions are captured by the fourth cohomology group $H^4( G, \,U(1))$, which also precisely labels the set of 3D SPT phases, with symmetry group $G$. We thus establish a general bulk-boundary correspondence between the anomalous SET and the 3d bulk SPT whose surface termination realizes it. We illustrate this idea using the chiral spin liquid ($U(1)_2$) topological order with a reduced symmetry $\mathbb{Z}_2 \times \mathbb{Z}_2 \subset SO(3)$, which can act on the semion quasiparticle in an anomalous way. We construct exactly solved 3d SPT models realizing the anomalous surface terminations, and demonstrate that they are non-trivial by computing three loop braiding statistics. Possible extensions to anti-unitary symmetries are also discussed.