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Machine learning quantum states in the NISQ eraMay 10 2019We review the development of generative modeling techniques in machine learning for the purpose of reconstructing real, noisy, many-qubit quantum states. Motivated by its interpretability and utility, we discuss in detail the theory of the restricted ... More

Machine learning phases of matterMay 05 2016Neural networks can be used to identify phases and phase transitions in condensed matter systems via supervised machine learning. Readily programmable through modern software libraries, we show that a standard feed-forward neural network can be trained ... More

Latent Space Purification via Neural Density OperatorsJan 29 2018Jun 16 2018Machine learning is actively being explored for its potential to design, validate, and even hybridize with near-term quantum devices. A central question is whether neural networks can provide a tractable representation of a given quantum state of interest. ... More

Deep Learning the Ising Model Near CriticalityAug 15 2017It is well established that neural networks with deep architectures perform better than shallow networks for many tasks in machine learning. In statistical physics, while there has been recent interest in representing physical data with generative modelling, ... More

Kernel methods for interpretable machine learning of order parametersApr 19 2017Machine learning is capable of discriminating phases of matter, and finding associated phase transitions, directly from large data sets of raw state configurations. In the context of condensed matter physics, most progress in the field of supervised learning ... More

Quantum Kagome IceJun 30 2014Actively shought since the turn of the century, two-dimensional quantum spin liquids (QSLs) are exotic phases of matter where magnetic moments remain disordered even at extremely low temperatures. Despite ongoing searches, QSLs remain elusive, due to ... More

Entanglement Entropy and Topological Order in Resonating Valence-Bond Quantum Spin LiquidsOct 26 2015Apr 20 2016On the triangular and kagome lattices, short-ranged resonating valence bond (RVB) wave functions can be sampled without the sign problem using a recently-developed Pfaffian Monte Carlo scheme. In this paper, we study the Renyi entanglement entropy in ... More

Tripartite entangled plaquette state in a cluster magnetApr 11 2017Using large-scale quantum Monte Carlo simulations we show that a spin-$1/2$ XXZ model on a two-dimensional anisotropic Kagome lattice exhibits a tripartite entangled plaquette state that preserves all of the Hamiltonian symmetries. It is connected via ... More

Machine Learning Phases of Strongly Correlated FermionsSep 08 2016Sep 11 2017Machine learning offers an unprecedented perspective for the problem of classifying phases in condensed matter physics. We employ neural-network machine learning techniques to distinguish finite-temperature phases of the strongly correlated fermions on ... More

Reconstructing quantum states with generative modelsOct 24 2018Jul 29 2019A major bottleneck in the quest for scalable many-body quantum technologies is the difficulty in benchmarking their preparations, which suffer from an exponential `curse of dimensionality' inherent to their quantum states. We present an experimentally ... More

Machine Learning $\mathbb{Z}_{2}$ Quantum Spin Liquids with Quasi-particle StatisticsMay 04 2017Nov 30 2017After decades of progress and effort, obtaining a phase diagram for a strongly-correlated topological system still remains a challenge. Although in principle one could turn to Wilson loops and long-range entanglement, evaluating these non-local observables ... More

Universal divergence of the Renyi entropy of a thinly sliced torus at the Ising fixed pointApr 18 2019The entanglement entropy of a quantum critical system can provide new universal numbers that depend on the geometry of the entangling bipartition. We calculate a universal number called $\kappa$, which arises when a quantum critical system is embedded ... More

Cornering gapless quantum states via their torus entanglementMar 08 2016Nov 02 2016The entanglement entropy (EE) has emerged as an important window into the structure of complex quantum states of matter. We analyze the universal part of the EE for gapless systems put on tori in 2d/3d, denoted by $\chi$. Focusing on scale invariant systems, ... More

Machine learning vortices at the Kosterlitz-Thouless transitionOct 26 2017Efficient and automated classification of phases from minimally processed data is one goal of machine learning in condensed matter and statistical physics. Supervised algorithms trained on raw samples of microstates can successfully detect conventional ... More

Cubic trihedral corner entanglement for a free scalarMar 09 2017We calculate the universal contribution to the $\alpha$-Renyi entropy from a cubic trihedral corner in the boundary of the entangling region in 3+1 dimensions for a massless free scalar. The universal number, $v_{\alpha}$, is manifest as the coefficient ... More

The learnability scaling of quantum states: restricted Boltzmann machinesAug 20 2019Aug 26 2019Generative modeling with machine learning has provided a new perspective on the data-driven task of reconstructing quantum states from a set of qubit measurements. As increasingly large experimental quantum devices are built in laboratories, the question ... More

Wavefunction positivization via automatic differentiationJun 11 2019We introduce a procedure to systematically search for a local unitary transformation that maps a wavefunction with a non-trivial sign structure into a positive-real form. The transformation is parametrized as a quantum circuit compiled into a set of one ... More

Dynamic scaling of topological ordering in classical systemsNov 09 2017Jan 25 2018We analyze scaling behaviors of simulated annealing carried out on various classical systems with topological order, obtained as appropriate limits of the toric code in two and three dimensions. We first consider the three-dimensional $\mathbb{Z}_2$ (Ising) ... More

Unusual Corrections to Scaling and Convergence of Universal Renyi Properties at Quantum Critical PointsSep 01 2015At a quantum critical point, bipartite entanglement entropies have universal quantities which are subleading to the ubiquitous area law. For Renyi entropies, these terms are known to be similar to the von Neumann entropy, while being much more amenable ... More

Simulations of Quantum XXZ Models on Two-Dimensional Frustrated LatticesAug 01 2006We report recent progress in the study of a particular class of spin 1/2 XXZ model on two-dimensional lattices with frustrated diagonal and unfrustrated off-diagonal interactions. Quantum Monte Carlo simulations can be constructed without a sign problem, ... More

Quantum Boltzmann MachineJan 08 2016Inspired by the success of Boltzmann Machines based on classical Boltzmann distribution, we propose a new machine learning approach based on quantum Boltzmann distribution of a transverse-field Ising Hamiltonian. Due to the non-commutative nature of quantum ... More

Many-body quantum state tomography with neural networksMar 15 2017Oct 23 2017The experimental realization of increasingly complex synthetic quantum systems calls for the development of general theoretical methods, to validate and fully exploit quantum resources. Quantum-state tomography (QST) aims at reconstructing the full quantum ... More

Mott Insulators in a Fully-Frustrated Bose Hubbard Model on the Honeycomb LatticeDec 20 2010We examine the effects of quantum fluctuations on a classical spin liquid state in the fully-frustrated honeycomb lattice Bose Hubbard model using quantum Monte Carlo simulations. Frustration is induced explicitly in the model by modulating the sign of ... More

Entanglement at a Two-Dimensional Quantum Critical Point: a T=0 Projector Quantum Monte Carlo StudyMay 06 2013Although the leading-order scaling of entanglement entropy is non-universal at a quantum critical point (QCP), sub-leading scaling can contain universal behaviour. Such universal quantities are commonly studied in non-interacting field theories, however ... More

A Neural Decoder for Topological CodesOct 13 2016We present an algorithm for error correction in topological codes that exploits modern machine learning techniques. Our decoder is constructed from a stochastic neural network called a Boltzmann machine, of the type extensively used in deep learning. ... More

A Wang-Landau method for calculating Renyi entropies in finite-temperature quantum Monte Carlo simulationsJul 20 2012Jul 30 2012We implement a Wang-Landau sampling technique in quantum Monte Carlo (QMC) for the purpose of calculating the Renyi entanglement entropies and associated mutual information. The algorithm converges an estimate for an analogue to the density of states ... More

Learning Thermodynamics with Boltzmann MachinesJun 08 2016A Boltzmann machine is a stochastic neural network that has been extensively used in the layers of deep architectures for modern machine learning applications. In this paper, we develop a Boltzmann machine that is capable of modelling thermodynamic observables ... More

Quantum spin liquid in a kagome lattice spin-1/2 XY model with four-site exchangeJun 03 2011We study the ground state phase diagram of a two-dimensional kagome lattice spin-1/2 XY model (J) with a four-site ring exchange interaction (K) using quantum Monte Carlo simulations. We find that the superfluid phase, existing in the regime of small ... More

A short-loop algorithm for quantum Monte Carlo simulationsSep 11 2007Dec 12 2007We present an algorithmic framework for a variant of the quantum Monte Carlo operator-loop algorithm, where non-local cluster updates are constructed in a way that makes each individual loop smaller. The algorithm is designed to increase simulation efficiency ... More

Stochastic series expansion algorithm for the S=1/2 XY model with four-site ring exchangeSep 05 2004We describe a stochastic series expansion (SSE) quantum Monte Carlo method for a two-dimensional S=1/2 XY-model (or, equivalently, hard-core bosons at half-filling) which in addition to the standard pair interaction J includes a four-particle term K that ... More

Scaling in the Fan of an Unconventional Quantum Critical PointJul 19 2007Jan 09 2008We present results of extensive finite-temperature Quantum Monte Carlo simulations on a SU(2) symmetric S=1/2 quantum antiferromagnet with a four-spin interaction [Sandvik, Phys. Rev. Lett. 98, 227202 (2007)]. Our simulations, which are free of the sign-problem ... More

Geometrical mutual information at the tricritical point of the two-dimensional Blume-Capel modelApr 08 2016Jul 15 2016The spin-1 classical Blume-Capel model on a square lattice is known to exhibit a finite-temperature phase transition described by the tricritical Ising CFT in 1+1 space-time dimensions. This phase transition can be accessed with classical Monte Carlo ... More

Spinon walk in quantum spin iceOct 04 2015Apr 22 2016We study a minimal model for the dynamics of spinons in quantum spin ice. The model captures the essential strong coupling between the spinon and the disordered background spins. We demonstrate that the spinon motion can be mapped to a random walk with ... More

A path integral Monte Carlo method for Rényi entanglement entropiesApr 28 2014Aug 04 2014We introduce a quantum Monte Carlo algorithm to measure the R\'enyi entanglement entropies in systems of interacting bosons in the continuum. This approach is based on a path integral ground state method that can be applied to interacting itinerant bosons ... More

Supersolid Order from Disorder: Hard-Core Bosons on the Triangular LatticeMay 10 2005Jul 14 2005We study the interplay of Mott localization, geometric frustration, and superfluidity for hard-core bosons with nearest-neighbor repulsion on the triangular lattice. For this model at half-filling, we demonstrate that superfluidity survives for arbitrarily ... More

Entangling qubit registers via many-body states of ultracold atomsDec 21 2015Dec 30 2015Inspired by the experimental measurement of the Renyi entanglement entropy in a lattice of ultracold atoms by Islam et al., [Nature 528, 77 (2015)] we propose a method to entangle two spatially-separated qubits using the quantum many-body state as a resource. ... More

Entanglement area law in superfluid $^4$HeOct 26 2016Area laws were first discovered by Bekenstein and Hawking, who found that the entropy of a black hole grows proportional to its surface area, and not its volume. Entropy area laws have since become a fundamental part of modern physics, from the holographic ... More

Particle entanglement in continuum many-body systems via quantum Monte CarloOct 30 2013Apr 07 2014Entanglement of spatial bipartitions, used to explore lattice models in condensed matter physics, may be insufficient to fully describe itinerant quantum many-body systems in the continuum. We introduce a procedure to measure the R\'enyi entanglement ... More

Finite Size Scaling of Mutual Information: A Scalable SimulationJul 13 2010We develop a quantum Monte Carlo procedure to compute the Renyi mutual information of an interacting quantum many-body system at non-zero temperature. Performing simulations on a spin-1/2 XXZ model, we observe that for a subregion of fixed size embedded ... More

Classical Topological Order in Kagome IceNov 01 2010We examine the onset of classical topological order in a nearest-neighbor kagome ice model. Using Monte Carlo simulations, we characterize the topological sectors of the groundstate using a non-local cut measure which circumscribes the toroidal geometry ... More

Thermodynamic singularities in the entanglement entropy at a 2D quantum critical pointApr 05 2012We study the bipartite entanglement entropy of the two-dimensional (2D) transverse-field Ising model in the thermodynamic limit using series expansion methods. Expansions are developed for the Renyi entropy around both the small-field and large-field ... More

A generalized Monte Carlo loop algorithm for frustrated Ising modelsJul 21 2010We introduce a Generalized Loop Move (GLM) update for Monte Carlo simulations of frustrated Ising models on two-dimensional lattices with bond-sharing plaquettes. The GLM updates are designed to enhance Monte Carlo sampling efficiency when the system's ... More

Fate of CP(N-1) fixed points with q-monopolesJul 01 2013Oct 16 2013We present an extensive quantum Monte Carlo study of the N\'eel-valence bond solid (VBS) phase transition on rectangular and honeycomb lattice SU($N$) antiferromagnets in sign problem free models. We find that in contrast to the honeycomb lattice and ... More

A single layer of Mn in a GaAs quantum well: a ferromagnet with quantum fluctuationsApr 11 2006Jan 31 2007Some of the highest transition temperatures achieved for Mn-doped GaAs have been in delta-doped heterostructures with well-separated planes of Mn. But in the absence of magnetic anisotropy, the Mermin-Wagner theorem implies that a single plane of magnetic ... More

Superfluid and supersolid phases of lattice bosons with ring-exchange interactionNov 07 2008We examine the superfluid phase of a hard-core boson model with nearest-neighbor exchange J and four-particle ring-exchange K at half-filling on the square lattice. At zero temperature we find that the superfluid in the pure-J model is quickly destroyed ... More

Universal Signatures of Fractionalized Quantum Critical PointsAug 09 2011Groundstates of certain materials can support exotic excitations with a charge that's a fraction of the fundamental electron charge. The condensation of these fractionalized particles has been predicted to drive novel quantum phase transitions, which ... More

Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulationsApr 24 2012We discuss designer Hamiltonians---lattice models tailored to be free from sign problems ("de-signed") when simulated with quantum Monte Carlo methods but which still host complex many-body states and quantum phase transitions of interest in condensed ... More

Detecting Classical Phase Transitions with Renyi Mutual InformationOct 08 2012Mar 14 2013By developing a method to represent the Renyi entropies via a replica-trick on classical statistical mechanical systems, we introduce a procedure to calculate the Renyi Mutual Information in any Monte Carlo simulation. Through simulations on several classical ... More

Geometric mutual information at classical critical pointsDec 13 2013Mar 27 2014A practical use of the entanglement entropy in a 1d quantum system is to identify the conformal field theory describing its critical behavior. It is exactly $(c/3)\ln \ell$ for an interval of length $\ell$ in an infinite system, where $c$ is the central ... More

Entanglement in gapless resonating valence bond statesJul 16 2012Jan 21 2013We study resonating-valence-bond (RVB) states on the square lattice of spins and of dimers, as well as SU(N)-invariant states that interpolate between the two. These states are ground states of gapless models, although the SU(2)-invariant spin RVB state ... More

Self-correction in Wegner's 3D Ising lattice gauge theoryDec 10 2018Motivated by the growing interest in self-correcting quantum memories, we study the feasibility of self-correction in classical lattice systems composed of bounded degrees of freedom with local interactions. We argue that self-correction, including a ... More

Super-resolving the Ising model with convolutional neural networksOct 04 2018Jan 30 2019Machine learning is becoming widely used in condensed matter physics. Inspired by the concept of image super-resolution, we propose a method to increase the size of lattice spin configurations using deep convolutional neural networks. Through supervised ... More

Analysis of parametric models - linear methods and approximationsJun 04 2018Jun 17 2018Parametric models in vector spaces are shown to possess an associated linear map. This linear operator leads directly to reproducing kernel Hilbert spaces and affine- / linear- representations in terms of tensor products. From the associated linear map ... More

Analysis of parametric models for coupled systemsJun 17 2018Nov 22 2018In many instances one has to deal with parametric models. Such models in vector spaces are connected to a linear map. The reproducing kernel Hilbert space and affine- / linear- representations in terms of tensor products are directly related to this linear ... More

Machine Learning Phases of Strongly Correlated FermionsSep 08 2016Machine learning offers an unprecedented perspective for the problem of classifying phases in condensed matter physics. We employ neural network machine learning techniques to distinguish finite-temperature phases of the strongly-correlated fermions on ... More

Topological Entanglement Entropy of a Bose-Hubbard Spin LiquidFeb 08 2011The Landau paradigm of classifying phases by broken symmetries was demonstrated to be incomplete when it was realized that different quantum Hall states could only be distinguished by more subtle, topological properties. Today, the role of topology as ... More

Self-Correcting Quantum Memories Beyond the Percolation ThresholdSep 10 2013We analyze several high dimensional generalizations of the toric code at nonzero temperature. We find that in large enough dimension, there can be a distinct separation between the critical temperature $T_c$, given by thermodynamic singularities, and ... More

Reconstructing quantum states with generative modelsOct 24 2018A major bottleneck in the quest for scalable many-body quantum technologies is the difficulty in benchmarking their preparations, which suffer from an exponential `curse of dimensionality' inherent to their quantum states. We present an experimentally ... More

Monte Carlo study of degenerate groundstates and residual entropy in a frustrated honeycomb lattice Ising modelDec 17 2008Mar 27 2009We study a classical fully-frustrated honeycomb lattice Ising model using Markov chain Monte Carlo methods and exact calculations . The Hamiltonian realizes a degenerate ground state manifold of equal-energy states, where each hexagonal plaquette of the ... More

A Large-$S$ Study of Quantum Kagome IceDec 12 2015Mar 18 2016We present a large-$S$ study of a quantum spin ice Hamiltonian, introduced by Huang, et al., [PRL 112, 167203 (2014)], on the kagome lattice. This model involves a competition between the frustrating Ising term of classical kagome ice, a Zeeman magnetic ... More

Machine learning quantum phases of matter beyond the fermion sign problemAug 28 2016State-of-the-art machine learning techniques promise to become a powerful tool in statistical mechanics via their capacity to distinguish different phases of matter in an automated way. Here we demonstrate that convolutional neural networks (CNN) can ... More

Detecting Goldstone Modes with Entanglement EntropyFeb 05 2015In the face of mounting numerical evidence, Metlitski and Grover [arXiv:1112.5166] have given compelling analytical arguments that systems with spontaneous broken continuous symmetry contain a sub-leading contribution to the entanglement entropy that ... More

Identifying polymer states by machine learningJan 16 2017The ability of a feed-forward neural network to learn and classify different states of polymer configurations is systematically explored. Performing numerical experiments, we find that a simple network model can, after adequate training, recognize multiple ... More

Sobolev Algebra CounterexamplesMay 13 2016In the Euclidean setting the Sobolev spaces $W^{\alpha,p}\cap L^\infty$ are algebras for the pointwise product when $\alpha>0$ and $p\in(1,\infty)$. This property has recently been extended to a variety of geometric settings. We produce a class of fractal ... More

Embedding convex geometries and a bound on convex dimensionFeb 06 2015Oct 13 2016The notion of an abstract convex geometry offers an abstraction of the standard notion of convexity in a linear space. Kashiwabara, Nakamura and Okamoto introduce the notion of a generalized convex shelling into $\mathbb{R}$ and prove that a convex geometry ... More

Large-N estimates of universal amplitudes of the CP^{N-1} theory and comparison with the JQ modelApr 14 2008We present computations of certain finite-size scaling functions and universal amplitude ratios in the large-N limit of the CP^{N-1} field theory. We pay particular attention to the uniform susceptibility, the spin stiffness and the specific heat. Field ... More

Efficient Bayesian experimentation using an expected information gain lower boundMay 30 2015Mar 10 2016Experimental design is crucial for inference where limitations in the data collection procedure are present due to cost or other restrictions. Optimal experimental designs determine parameters that in some appropriate sense make the data the most informative ... More

Derivations and Dirichlet forms on fractalsJun 07 2011Jul 16 2012We study derivations and Fredholm modules on metric spaces with a local regular conservative Dirichlet form. In particular, on finitely ramified fractals, we show that there is a non-trivial Fredholm module if and only if the fractal is not a tree (i.e. ... More

Estimating correlation from high, low, opening and closing pricesApr 01 2008In earlier studies, the estimation of the volatility of a stock using information on the daily opening, closing, high and low prices has been developed; the additional information in the high and low prices can be incorporated to produce unbiased (or ... More

Estimate nothingJan 22 2014In the econometrics of financial time series, it is customary to take some parametric model for the data, and then estimate the parameters from historical data. This approach suffers from several problems. Firstly, how is estimation error to be quantified, ... More

Entanglement at a Two-Dimensional Quantum Critical Point: a Numerical Linked Cluster Expansion StudyDec 20 2012May 09 2013We develop a method to calculate the bipartite entanglement entropy of quantum models, in the thermodynamic limit, using a Numerical Linked Cluster Expansion (NLCE) involving only rectangular clusters. It is based on exact diagonalization of all n x m ... More

A continuous Mott transition between a metal and a quantum spin liquidMar 17 2014Jun 29 2015More than half a century after first being proposed by Sir Nevill Mott, the deceptively simple question of whether the interaction-driven electronic metal-insulator transition may be continuous remains enigmatic. Recent experiments on two-dimensional ... More

Angular fluctuations of a multi-component order describe the pseudogap regime of the cuprate superconductorsSep 25 2013Dec 26 2013The hole-doped cuprate high temperature superconductors enter the pseudogap regime as their superconducting critical temperature, $T_c$, falls with decreasing hole density. Experiments have probed this regime for over two decades, but we argue that decisive ... More

Diamagnetism and density wave order in the pseudogap regime of YBa$_2$Cu$_3$O$_{6+x}$Jun 10 2014Clear experimental evidence of charge density wave correlations competing with superconducting order in YBCO have thrust their relationship with the pseudogap regime into the spotlight. To aid in characterizing the pseudogap regime, we propose a dimensionless ... More

Imaging bond order near non-magnetic impurities in square lattice antiferromagnetsAug 05 2008We study the textures of generalized "charge densities" (scalar objects invariant under time reversal), in the vicinity of non-magnetic impurities in square-lattice quantum anti-ferromagnets, by order parameter field theories. Our central finding is the ... More

Valence Bond and von Neumann Entanglement Entropy in Heisenberg LaddersMay 26 2009Jul 09 2009We present a direct comparison of the recently-proposed valence bond entanglement entropy and the von Neumann entanglement entropy on spin 1/2 Heisenberg systems using quantum Monte Carlo and density-matrix renormalization group simulations. For one-dimensional ... More

Thermodynamic Properties of the Dipolar Spin Ice ModelAug 14 2003We present a detailed theoretical overview of the thermodynamic properties of the dipolar spin ice model, which has been shown to be an excellent quantitative descriptor of the Ising pyrochlore materials Dy_2Ti_2O_7 and Ho_2Ti_2O_7. We show that the dipolar ... More

Corner contribution to the entanglement entropy of an O(3) quantum critical point in 2+1 dimensionsJan 15 2014Feb 19 2014The entanglement entropy for a quantum critical system across a boundary with a corner exhibits a sub-leading logarithmic scaling term with a scale-invariant coefficient. Using a Numerical Linked Cluster Expansion, we calculate this universal quantity ... More

Entanglement scaling in two-dimensional gapless systemsDec 19 2011Apr 24 2012We numerically determine subleading scaling terms in the ground-state entanglement entropy of several two-dimensional (2D) gapless systems, including a Heisenberg model with N\'eel order, a free Dirac fermion in the {\pi}-flux phase, and the nearest-neighbor ... More

Finite Temperature Transitions in Large Magnetic Field in Dipolar Spin IceOct 15 2004Sep 26 2005We use Monte Carlo simulations to identify the mechanism that allows for phase transitions in dipolar spin ice to occur and survive for applied magnetic field, H, much larger in strength than that of the spin-spin interactions. In the most generic and ... More

Fluctuating orders and quenched randomness in the cupratesMay 22 2015Nov 10 2015We study a quasi-2D classical Landau-Ginzburg-Wilson effective field theory in the presence of quenched disorder in which incommensurate charge-density wave and superconducting orders are intertwined. The disorder precludes long-range charge-density wave ... More

Long Range Order at Low Temperature in Dipolar Spin IceSep 14 2000Feb 26 2001Recently it has been suggested that long range magnetic dipolar interactions are responsible for spin ice behavior in the Ising pyrochlore magnets ${\rm Dy_{2}Ti_{2}O_{7}}$ and ${\rm Ho_{2}Ti_{2}O_{7}}$. We report here numerical results on the low temperature ... More

Supersolidity from defect-condensation in the extended boson Hubbard modelAug 14 2007Oct 26 2007We study the ground state phase diagram of the hard-core extended boson Hubbard model on the square lattice with both nearest- (nn) and next-nearest-neighbor (nnn) hopping and repulsion, using Gutzwiller mean field theory and quantum Monte Carlo simulations. ... More

Anomalies in the Entanglement Properties of the Square Lattice Heisenberg ModelJul 14 2011Apr 15 2013We compute the bipartite entanglement properties of the spin-half square-lattice Heisenberg model by a variety of numerical techniques that include valence bond quantum Monte Carlo (QMC), stochastic series expansion QMC, high temperature series expansions ... More

Measuring Renyi Entanglement Entropy with Quantum Monte CarloJan 13 2010Mar 03 2010We develop a quantum Monte Carlo procedure, in the valence bond basis, to measure the Renyi entanglement entropy of a many-body ground state as the expectation value of a unitary {\it Swap} operator acting on two copies of the system. An improved estimator ... More

The learnability scaling of quantum states: restricted Boltzmann machinesAug 20 2019Generative modeling with machine learning has provided a new perspective on the data-driven task of reconstructing quantum states from a set of qubit measurements. As increasingly large experimental quantum devices are built in laboratories, the question ... More

Corner contribution to the entanglement entropy of strongly-interacting O(2) quantum critical systems in 2+1 dimensionsSep 22 2014In a D=2+1 quantum critical system, the entanglement entropy across a boundary with a corner contains a subleading logarithmic scaling term with a universal coefficient. It has been conjectured that this coefficient is, to leading order, proportional ... More

Probing trihedral corner entanglement for Dirac fermionsOct 05 2018We investigate the universal information contained in the Renyi entanglement entropies for a free massless Dirac fermion in three spatial dimensions. Using numerical calculations on the lattice, we examine the case where the entangling boundary contains ... More

A Superglass Phase of Interacting BosonsSep 09 2009May 09 2010We introduce a Bose-Hubbard Hamiltonian with random disordered interactions as a model to study the interplay of superfluidity and glassiness in a system of three-dimensional hard-core bosons at half-filling. Solving the model using large-scale quantum ... More

Finite Temperature Critical Behavior of Mutual InformationJan 02 2011Mar 04 2011We study mutual information for Renyi entropy of arbitrary index n, in interacting quantum systems at finite-temperature critical points, using high-temperature expansion, quantum Monte Carlo simulations and scaling theory. We find that for n>1, the critical ... More

Making Trotters Sprint: A Variational Imaginary Time Ansatz for Quantum Many-body SystemsMar 29 2019We introduce a variational wavefunction for many-body ground states that involves imaginary time evolution with two different Hamiltonians in an alternating fashion with variable time intervals. Using our ansatz to target the quantum critical point of ... More

Universal corner entanglement of Dirac fermions and gapless bosons from the continuum to the latticeJun 09 2016A quantum critical (QC) fluid exhibits universal subleading corrections to the area law of its entanglement entropies. In two dimensions when the partition involves a corner of angle $\theta$, the subleading term is logarithmic with coefficient $a_\alpha(\theta)$ ... More

Making Trotters Sprint: A Variational Imaginary Time Ansatz for Quantum Many-body SystemsMar 29 2019Aug 19 2019We introduce a variational wavefunction for many-body ground states that involves imaginary time evolution with two different Hamiltonians in an alternating fashion with variable time intervals. We successfully apply the ansatz on the one- and two-dimensional ... More

An exotic symplectic $\mathbf{R}^6$Jul 31 2015An explicit example of an exotic symplectic $\mathbf{R}^6$ is given. Together with an earlier known example on $\mathbf{R}^4$, this yields an explicit exotic symplectic form on $\mathbf{R}^{2n}$ for all $n\geq2$.

Semi-Supervised Learning via New Deep Network InversionNov 12 2017We exploit a recently derived inversion scheme for arbitrary deep neural networks to develop a new semi-supervised learning framework that applies to a wide range of systems and problems. The approach outperforms current state-of-the-art methods on MNIST ... More

Destroying a topological quantum bit by condensing Ising vorticesMar 17 2014Dec 17 2014The imminent realization of topologically-protected qubits in fabricated systems will provide not only an elementary implementation of fault-tolerant quantum computing architecture, but also an experimental vehicle for the general study of topological ... More

Equation-Free Particle-Based Computations: Coarse Projective Integration and Coarse Dynamic Renormalization in 2DNov 21 2005Equation-free approaches have been proposed in recent years for the computational study of multiscale phenomena in engineering problems where evolution equations for the coarse-grained, system-level behavior are not explicitly available. In this paper ... More

Solvers and precondtioners based on Gauss-Seidel and Jacobi algorithms for non-symmetric stochastic Galerkin system of equationsApr 13 2019In this work, solvers and preconditioners based on Gauss-Seidel and Jacobi algorithms are explored for stochastic Galerkin discretization of partial differential equations (PDEs) with random input data. Gauss-Seidel and Jacobi algorithms are formulated ... More

The Vela Pulsar in the UltravioletMar 15 2005We describe time-tagged observations of the Vela pulsar (PSR B0833-45) with the HST STIS MAMA-UV detectors. Using an optimal extraction technique, we obtain a NUV light curve and crude FUV phase-resolved spectra. The pulse is dominated by complex non-thermal ... More

Renormalization Group Approach to Oscillator SynchronizationOct 17 2008Dec 09 2008We develop a renormalization group method to investigate synchronization clusters in a one-dimensional chain of nearest-neighbor coupled phase oscillators. The method is best suited for chains with strong disorder in the intrinsic frequencies and coupling ... More