arXiv subjects

Dong-Ling Deng

Publications and source records attributed to Dong-Ling Deng.

At least 91 records · Page 5Linked to original sources

arXiv2017

Machine Learning Bell Nonlocality in Quantum Many-body Systems

Machine learning, the core of artificial intelligence and big data science, is one of today's most rapidly growing interdisciplinary fields. Recently, its tools and techniques have been adopted to tackle intricate quantum many-body problems. In this work, we introduce machine learning techniques to the detection of quantum nonlocality in many-body systems, with a focus on the restricted-Boltzmann-machine (RBM) architecture. Using reinforcement learning, we demonstrate that RBM is capable of finding the maximum quantum violations of multipartite Bell inequalities with given measurement settings. Our results build a novel bridge between computer-science-based machine learning and quantum many-body nonlocality, which will benefit future studies in both areas.

quant-ph↗

arXiv2017

Transport properties across the many-body localization transition in quasiperiodic and random systems

We theoretically study transport properties in one-dimensional interacting quasiperiodic systems at infinite temperature. We compare and contrast the dynamical transport properties across the many-body localization (MBL) transition in quasiperiodic and random models. Using exact diagonalization we compute the optical conductivity $σ(ω)$ and the return probability $R(τ)$ and study their average low-frequency and long-time power-law behavior, respectively. We show that the low-energy transport dynamics is markedly distinct in both the thermal and MBL phases in quasiperiodic and random models and find that the diffusive and MBL regimes of the quasiperiodic model are more robust than those in the random system. Using the distribution of the DC conductivity, we quantify the contribution of sample-to-sample and state-to-state fluctuations of $σ(ω)$ across the MBL transition. We find that the activated dynamical scaling ansatz works poorly in the quasiperiodic model but holds in the random model with an estimated activation exponent $ψ\approx 0.9$. We argue that near the MBL transition in quasiperiodic systems, critical eigenstates give rise to a subdiffusive crossover regime on finite-size systems.

cond-mat.dis-nn↗

arXiv2017

Quantum Entanglement in Neural Network States

Machine learning, one of today's most rapidly growing interdisciplinary fields, promises an unprecedented perspective for solving intricate quantum many-body problems. Understanding the physical aspects of the representative artificial neural-network states is recently becoming highly desirable in the applications of machine learning techniques to quantum many-body physics. Here, we study the quantum entanglement properties of neural-network states, with a focus on the restricted-Boltzmann-machine (RBM) architecture. We prove that the entanglement of all short-range RBM states satisfies an area law for arbitrary dimensions and bipartition geometry. For long-range RBM states we show by using an exact construction that such states could exhibit volume-law entanglement, implying a notable capability of RBM in representing efficiently quantum states with massive entanglement. We further examine generic RBM states with random weight parameters. We find that their averaged entanglement entropy obeys volume-law scaling and meantime strongly deviates from the Page-entropy of the completely random pure states. We show that their entanglement spectrum has no universal part associated with random matrix theory and bears a Poisson-type level statistics. Using reinforcement learning, we demonstrate that RBM is capable of finding the ground state (with power-law entanglement) of a model Hamiltonian with long-range interaction. In addition, we show, through a concrete example of the one-dimensional symmetry-protected topological cluster states, that the RBM representation may also be used as a tool to analytically compute the entanglement spectrum. Our results uncover the unparalleled power of artificial neural networks in representing quantum many-body states, which paves a novel way to bridge computer science based machine learning techniques to outstanding quantum condensed matter physics problems.

cond-mat.dis-nn↗

arXiv2017

Logarithmic Entanglement Lightcone in Many-Body Localized Systems

We theoretically study the response of a many-body localized system to a local quench from a quantum information perspective. We find that the local quench triggers entanglement growth throughout the whole system, giving rise to a logarithmic lightcone. This saturates the modified Lieb-Robinson bound for quantum information propagation in many-body localized systems previously conjectured based on the existence of local integrals of motion. In addition, near the localization-delocalization transition, we find that the final states after the local quench exhibit volume-law entanglement. We also show that the local quench induces a deterministic orthogonality catastrophe for highly excited eigenstates, where the typical wave-function overlap between the pre- and post-quench eigenstates decays {\it exponentially} with the system size.

cond-mat.dis-nn↗

arXiv2017

Intrinsic decoherence in isolated quantum systems

We study the intrinsic, disorder-induced decoherence of an isolated quantum system under its own dynamics. Specifically, we investigate the characteristic time scale (i.e., the decoherence time) associated with an interacting many-body system losing the memory of its initial state. To characterize the erasure of the initial state memory, we define a time scale, the intrinsic decoherence time, by thresholding the gradual decay of the disorder-averaged return probability. We demonstrate the system-size independence of the intrinsic decoherence time in different models, and we study its dependence on the disorder strength. We find that the intrinsic decoherence time increases monotonically as the disorder strength increases in accordance with the relaxation of locally measurable quantities. We investigate several interacting spin (e.g., Ising and Heisenberg) and fermion (e.g., Anderson and Aubry-André) models to obtain the intrinsic decoherence time as a function of disorder and interaction strength.

cond-mat.dis-nn↗

arXiv2016

Probe knots and Hopf insulators with ultracold atoms

Knots and links are fascinating and intricate topological objects. Their influence spans from DNA and molecular chemistry to vortices in superfluid helium, defects in liquid crystals and cosmic strings in the early universe. Here, we find that knotted structures also exist in a peculiar class of three-dimensional topological insulators---the Hopf insulators. In particular, we demonstrate that the momentum-space spin textures of Hopf insulators are twisted in a nontrivial way, which implies the presence of various knot and link structures. We further illustrate that the knots and nontrivial spin textures can be probed via standard time-of-flight images in cold atoms as preimage contours of spin orientations in stereographic coordinates. The extracted Hopf invariants, knots, and links are validated to be robust to typical experimental imperfections. Our work establishes the existence of knotted structures in Hopf insulators, which may have potential applications in spintronics and quantum information processing.

cond-mat.mes-hall↗

arXiv2016

Many-body localization in incommensurate models with a mobility edge

We review the physics of many-body localization in models with incommensurate potentials. In particular, we consider one-dimensional quasiperiodic models with single-particle mobility edges. Although a conventional perspective suggests that delocalized states act as a thermalizing bath for the localized states in the presence of of interactions, there is evidence that such systems can display non-ergodicity. This is in part due to the fact that the delocalized states do not have any kind of protection due to symmetry or topology and are thus susceptible to localization. A study of non-interacting incommensurate models shows that they admit extended, partially extended, and fully localized many-body states. These models cannot thermalize dynamically and remain localized upon the introduction of interactions. In particular, for a certain range of energy, the system can host a non-ergodic extended (i.e. metallic) phase in which the energy eigenstates violate the eigenstate thermalization hypothesis (ETH) but the entanglement entropy obeys volume-law scaling. The level statistics and entanglement growth also indicate the lack of ergodicity in these models. The phenomenon of localization and non-ergodicity in a system with interactions despite the presence of single-particle delocalized states is closely related to the so-called "many-body proximity effect" and can also be observed in models with disorder coupled to systems with delocalized degrees of freedom. Many-body localization in systems with incommensurate potentials (without single-particle mobility edges) have been realized experimentally, and we show how this can be modified to study the the effects of such mobility edges. Demonstrating the failure of thermalization in the presence of a single-particle mobility edge in the thermodynamic limit would indicate a more robust violation of the ETH.

cond-mat.str-el↗

arXiv2016

Statistical Bubble Localization with Random Interactions

We study one-dimensional spinless fermions with random interactions, but without any on-site disorder. We find that random interactions generically stabilize a many-body localized phase, in spite of the completely extended single-particle degrees of freedom. In the large randomness limit, we construct "bubble-neck" eigenstates having a universal area-law entanglement entropy on average, with the number of volume-law states being exponentially suppressed. We argue that this statistical localization is beyond the phenomenological local-integrals-of-motion description of many-body localization. With exact diagonalization, we confirm the robustness of the many-body localized phase at finite randomness by investigating eigenstate properties such as level statistics, entanglement/participation entropies, and nonergodic quantum dynamics. At weak random interactions, the system develops a thermalization transition when the single-particle hopping becomes dominant.

cond-mat.stat-mech↗

arXiv2016

Majorana spintronics

We propose a systematic magnetic-flux-free approach to detect, manipulate and braid Majorana fermions in a semiconductor nanowire-based topological Josephson junction by utilizing the Majorana spin degree of freedom. We find an intrinsic $π$-phase difference between spin-triplet pairings enforced by the Majorana zeros modes (MZMs) at the two ends of a one-dimensional spinful topological superconductor. This $π$-phase is identified to be a spin-dependent superconducting phase, referred to as the spin-phase, which we show to be tunable by controlling spin-orbit coupling strength via electric gates. This electric controllable spin-phase not only affects the coupling energy between MZMs but also leads to a fractional Josephson effect in the absence of any applied magnetic flux, which enables the efficient topological qubit readout. We thus propose an all-electrically controlled superconductor-semiconductor hybrid circuit to manipulate MZMs and to detect their non-Abelian braiding statistics properties. Our work on spin properties of topological Josephson effects potentially opens up a new thrust for spintronic applications with Majorana-based semiconductor quantum circuits.

cond-mat.supr-con↗

arXiv2016

Quantum nonergodicity and fermion localization in a system with a single-particle mobility edge

We study the many-body localization aspects of single-particle mobility edges in fermionic systems. We investigate incommensurate lattices and random disorder Anderson models. Many-body localization and quantum nonergodic properties are studied by comparing entanglement and thermal entropy, and by calculating the scaling of subsystem particle number fluctuations, respectively. We establish a nonergodic extended phase as a generic intermediate phase (between purely ergodic extended and nonergodic localized phases) for the many-body localization transition of non-interacting fermions where the entanglement entropy manifests a volume law (`extended'), but there are large fluctuations in the subsystem particle numbers (`nonergodic'). We argue such an intermediate phase scenario may continue holding even for the many-body localization in the presence of interactions as well. We find for many-body states in non-interacting 1d Aubry-Andre and 3d Anderson models that the entanglement entropy density and the normalized particle-number fluctuation have discontinuous jumps at the localization transition where the entanglement entropy is sub-thermal but obeys the "volume law". In the vicinity of the localization transition we find that both the entanglement entropy and the particle number fluctuations obey a single parameter scaling. We argue using numerical and theoretical results that such a critical scaling behavior should persist for the interacting many-body localization problem with important consequences. Our work provides persuasive evidence in favor of there being two transitions in many-body systems with single-particle mobility edges, the first one indicating a transition from the purely localized nonergodic many-body localized phase to a nonergodic extended many-body metallic phase, and the second one being a transition eventually to the usual ergodic many-body extended phase.

cond-mat.stat-mech↗

arXiv2016

Noise-induced collective quantum state preservation in spin qubit arrays

The hyperfine interaction with nuclear spins (or, Overhauser noise) has long been viewed as a leading source of decoherence in individual quantum dot spin qubits. Here we show that in a coupled multi-qubit system consisting of as few as four spins, interactions with nuclear spins can have the opposite effect where they instead preserve the collective quantum state of the system. This noise-induced state preservation can be realized in a linear spin qubit array using current technological capabilities. Our proposal requires no control over the Overhauser fields in the array; only experimental control over the average interqubit coupling between nearest neighbors is needed, and this is readily achieved by tuning gate voltages. Our results illustrate how the role of the environment can transform from harmful to helpful in the progression from single-qubit to multi-qubit quantum systems.

cond-mat.mes-hall↗

arXiv2015

Exponential Orthogonality Catastrophe in Single-Particle and Many-Body Localized Systems

We investigate the statistical orthogonality catastrophe (StOC) in single-particle and many-body localized systems by studying the response of the many-body ground state to a local quench. Using scaling arguments and exact numerical calculations, we establish that the StOC gives rise to a wave function overlap between the pre- and post-quench ground states that has an \emph{exponential} decay with the system size, in sharp contrast to the well-known power law Anderson orthogonality catastrophe in metallic systems. This exponential decay arises from a statistical charge transfer process where a particle can be effectively "transported" to an arbitrary lattice site. In a many-body localized phase, this non-local transport and the associated exponential StOC phenomenon persist in the presence of interactions. We study experimental consequences of the exponential StOC on Loschmidt echo and spectral function, establishing that this phenomenon should be observable in cold atomic experiments through Ramsey interference and radio-frequency spectroscopy.

cond-mat.str-el↗

arXiv2015

Hamiltonian tomography for quantum many-body systems with arbitrary couplings

Characterization of qubit couplings in many-body quantum systems is essential for benchmarking quantum computation and simulation. We propose a tomographic measurement scheme to determine all the coupling terms in a general many-body Hamiltonian with arbitrary long-range interactions, provided the energy density of the Hamiltonian remains finite. Different from quantum process tomography, our scheme is fully scalable with the number of qubits as the required rounds of measurements increase only linearly with the number of coupling terms in the Hamiltonian. The scheme makes use of synchronized dynamical decoupling pulses to simplify the many-body dynamics so that the unknown parameters in the Hamiltonian can be retrieved one by one. We simulate the performance of the scheme under the influence of various pulse errors and show that it is robust to typical noise and experimental imperfections.

quant-ph↗

arXiv2015

Quantized electromagnetic response of three-dimensional chiral topological insulators

Protected by the chiral symmetry, three dimensional chiral topological insulators are characterized by an integer-valued topological invariant. How this invariant could emerge in physical observables is an important question. Here we show that the magneto-electric polarization can identify the integer-valued invariant if we gap the system without coating a quantum Hall layer on the surface. The quantized response is demonstrated to be robust against weak perturbations. We also study the topological properties by adiabatically coupling two nontrivial phases, and find that gapless states appear and are localized at the boundary region. Finally, an experimental scheme is proposed to realize the Hamiltonian and measure the quantized response with ultracold atoms in optical lattices.

cond-mat.mes-hall↗

arXiv2014

Direct Probe of Topological Order for Cold Atoms

Cold-atom experiments in optical lattices offer a versatile platform to realize various topological quantum phases. A key challenge in those experiments is to unambiguously probe the topological order. We propose a method to directly measure the characteristic topological invariants (order) based on the time-of-flight imaging of cold atoms. The method is generally applicable to detection of topological band insulators in one, two, or three dimensions characterized by integer topological invariants. Using detection of the Chern number for the 2D anomalous quantum Hall states and the Chern-Simons term for the 3D chiral topological insulators as examples, we show that the proposed detection method is practical, robust to typical experimental imperfections such as limited imaging resolution, inhomogeneous trapping potential, and disorder in the system.

cond-mat.quant-gas↗

arXiv2014

An experimental proposal to observe non-abelian statistics of Majorana-Shockley fermions in an optical lattice

We propose an experimental scheme to observe non-abelian statistics with cold atoms in a two dimensional optical lattice. We show that the Majorana-Schockley modes associated with line defects obey non-abelian statistics and can be created, braided, and fused, all through adiabatic shift of the local chemical potentials. The detection of the topological qubit is transformed to local measurement of the atom number on a single lattice site. We demonstrate the robustness of the braiding operation by incorporating noise and experiential imperfections in numerical simulations, and show that the requirement fits well with the current experimental technology.

quant-ph↗

arXiv2014

Probe of Three-Dimensional Chiral Topological Insulators in an Optical Lattice

We propose a feasible experimental scheme to realize a three-dimensional chiral topological insulator with cold fermionic atoms in an optical lattice, which is characterized by an integer topological invariant distinct from the conventional $Z_2$ topological insulators and has a remarkable macroscopic zero-energy flat band. To probe its property, we show that its characteristic surface states---the Dirac cones---can be probed through time-of-flight imaging or Bragg spectroscopy and the flat band can be detected via measurement of the atomic density profile in a weak global trap. The realization of this novel topological phase with a flat band in an optical lattice will provide a unique experimental platform to study the interplay between interaction and topology and open new avenues for application of topological states.

cond-mat.str-el↗

arXiv2014

Systematic Construction of tight-binding Hamiltonians for Topological Insulators and Superconductors

A remarkable discovery in recent years is that there exist various kinds of topological insulators and superconductors characterized by a periodic table according to the system symmetry and dimensionality. To physically realize these peculiar phases and study their properties, a critical step is to construct experimentally relevant Hamiltonians which support these topological phases. We propose a general and systematic method based on the quaternion algebra to construct the tight binding Hamiltonians for all the three-dimensional topological phases in the periodic table characterized by arbitrary integer topological invariants, which include the spin-singlet and the spin-triplet topological superconductors, the Hopf and the chiral topological insulators as particular examples. For each class, we calculate the corresponding topological invariants through both geometric analysis and numerical simulation.

cond-mat.mes-hall↗