arXiv subjects

Zhao Liu

Publications and source records attributed to Zhao Liu.

At least 109 records · Page 6Linked to original sources

arXiv2020

Engineering Quantum Hall Phases in Synthetic Bilayer Graphene System

Synthetic quantum Hall bilayer (SQHB), realized by optically driven monolayer graphene in the quantum Hall regime, provides a flexible platform for engineering quantum Hall phases as discussed in [Phys. Rev. Lett. 119, 247403]. The coherent driving which couples two Landau levels mimicks an effective tunneling between synthetic layers. The tunneling strength, the effective Zeeman coupling, and two-body interaction matrix elements are tunable by varying the driving frequency and the driving strength. Using infinite density matrix renormalization group (iDMRG) techniques combined with exact diagonalization (ED), we show that the system exhibits a non-abelian bilayer Fibonacci phase at filling fraction $ν= 2/3$. Moreover, at integer filling $ν= 1$, the SQHB exhibits quantum Hall ferromagnetism. Using Hartree-Fock theory and exact diagonalization, we show that excitations of the quantum Hall ferromagnet are topological textures known as skyrmions.

cond-mat.str-el↗

arXiv2020

Particle-Hole Duality, Emergent Fermi Liquids and Fractional Chern Insulators in Moiré Flatbands

Moiré flatbands, occurring, e.g., in twisted bilayer graphene at magic angles, have attracted ample interest due to their high degree of experimental tunability and the intriguing possibility of generating novel strongly interacting phases. Here we consider the core problem of Coulomb interactions within fractionally filled spin and valley polarized Moiré flatbands and demonstrate that the dual description in terms of holes, which acquire a nontrivial hole dispersion, provides key physical intuition and enables the use of standard perturbative techniques for this strongly correlated problem. In experimentally relevant examples such as ABC stacked trilayer and twisted bilayer graphene aligned with boron nitride, it leads to emergent interaction-driven Fermi liquid states at electronic filling fractions down to around $1/3$ and $2/3$ respectively. At even lower filling fractions, the electron density still faithfully tracks the single-hole dispersion while exhibiting distinct non-Fermi liquid behavior. Most saliently, we provide microscopic evidence that high temperature fractional Chern insulators can form in twisted bilayer graphene aligned with hexagonal boron nitride.

cond-mat.mes-hall↗

arXiv2020

Microscopic Diagnosis of Universal Geometric Responses in Fractional Quantum Hall Liquids

Topological quantum liquids contain internal degrees of freedom that are coupled to geometric response. Yet, an explicit and microscopic identification of geometric response remains difficult. Here, taking notable fractional quantum Hall (FQH) states as typical examples, we systematically investigate a promising protocol -- the Dehn twist deformation on the torus geometry, to probe the geometric response of correlated topological states and establish the relation between such response and the universal properties of pertinent states. Based on analytical derivations and numerical simulations, we find that the geometry-induced Berry phase encodes novel features for a broad class of FQH states at the Laughlin, hierarchy, Halperin and non-Abelian Moore-Read fillings. Our findings conclusively demonstrate that the adiabatic Dehn twist deformation can faithfully capture the geometry of elementary FQH droplets and intrinsic modular information including topological spin and chiral central charge. Our approach provides a powerful way to reveal topological orders of generic FQH states and allows us to address previously open questions.

cond-mat.str-el↗

arXiv2019

Electronic and Magnetic Structure of Infinite-layer $\textrm{NdNiO}_2$: Trace of Antiferromagnetic Metal

The recent discovery of Sr-doped infinite-layer nickelate $\textrm{NdNiO}_2$ [D. Li et al. Nature 572, 624 (2019)] offers an exciting platform for investigating unconventional superconductivity in nickelatebased compounds. In this work, we present a first-principles calculations for the electronic and magnetic properties of undoped parent $\textrm{NdNiO}_2$. Intriguingly, we found that: 1) the paramagnetic phase has complex Fermi pockets with 3D characters near the Fermi level; 2) by including electronelectron interactions, 3d-electrons of Ni tend to form $(π, π, π)$ antiferromagnetic ordering at low temperatures; 3) with moderate interaction strength, 5d-electrons of Nd contribute small Fermi pockets that could weaken the magnetic order akin to the self-doping effect. Our results provide a plausible interpretation for the experimentally observed resistivity minimum and Hall coefficient drop. Moreover, we elucidate that antiferromagnetic ordering in $\textrm{NdNiO}_2$ is relatively weak, arising from the small exchange coupling between 3d-electrons of Niand also hybridization with 5d-electrons of Nd.

cond-mat.str-el↗

arXiv2019

Classification of nonnegative solutions to static Schrödinger-Hartree-Maxwell type equations

In this paper, we are mainly concerned with the physically interesting static Schrödinger-Hartree-Maxwell type equations \begin{equation*} (-Δ)^{s}u(x)=\left(\frac{1}{|x|^σ}\ast |u|^{p}\right)u^{q}(x) \,\,\,\,\,\,\,\,\,\,\,\, \text{in} \,\,\, \mathbb{R}^{n} \end{equation*} involving higher-order or higher-order fractional Laplacians, where $n\geq1$, $0<s:=m+\fracα{2}<\frac{n}{2}$, $m\geq0$ is an integer, $0<α\leq2$, $0<σ<n$, $0<p\leq\frac{2n-σ}{n-2s}$ and $0<q\leq\frac{n+2s-σ}{n-2s}$. We first prove the super poly-harmonic properties of nonnegative classical solutions to the above PDEs, then show the equivalence between the PDEs and the following integral equations \begin{equation*} u(x)=\int_{\mathbb{R}^n}\frac{R_{2s,n}}{|x-y|^{n-2s}}\left(\int_{\mathbb{R}^{n}}\frac{1}{|y-z|^σ}u^p(z)dz\right)u^{q}(y)dy. \end{equation*} Finally, we classify all nonnegative solutions to the integral equations via the method of moving spheres in integral form. As a consequence, we obtain the classification results of nonnegative classical solutions for the PDEs. Our results completely improved the classification results in \cite{CD,DFQ,DL,DQ,Liu}. In critical and super-critical order cases (i.e., $\frac{n}{2}\leq s:=m+\fracα{2}<+\infty$), we also derive Liouville type theorem.

math.AP↗

arXiv2019

Strain engineering of oxide thin films for photocatalytic applications

Photocatalytic materials are pivotal for the implementation of disruptive clean energy applications such as conversion of H$_{2}$O and CO$_{2}$ into fuels and chemicals driven by solar energy. However, efficient and cost-effective materials able to catalyze the chemical reactions of interest when exposed to visible light are scarce due to the stringent electronic conditions that they must satisfy. Chemical and nanostructuring approaches are capable of improving the catalytic performance of known photoactive compounds however the complexity of the synthesized nanomaterials and sophistication of the employed methods make systematic design of photocatalysts difficult. Here, we show by means of first-principles simulation methods that application of biaxial stress, $η$, on semiconductor oxide thin films can modify their optoelectronic and catalytic properties in a significant and predictable manner. In particular, we show that upon moderate tensile strains CeO$_{2}$ and TiO$_{2}$ thin films become suitable materials for photocatalytic conversion of H$_{2}$O into H$_{2}$ and CO$_{2}$ into CH$_{4}$ under sunlight. The band gap shifts induced by $η$ are reproduced qualitatively by a simple analytical model that depends only on structural and dielectric susceptibility changes. Thus, epitaxial strain represents a promising route for methodical screening and rational design of photocatalytic materials.

cond-mat.mtrl-sci↗

arXiv2019

Implementation and Performance of Barnes-Hut N-body algorithm on Extreme-scale Heterogeneous Many-core Architectures

In this paper, we report the implementation and measured performance of our extreme-scale global simulation code on Sunway TaihuLight and two PEZY-SC2 systems: Shoubu System B and Gyoukou. The numerical algorithm is the parallel Barnes-Hut tree algorithm, which has been used in many large-scale astrophysical particle-based simulations. Our implementation is based on our FDPS framework. However, the extremely large numbers of cores of the systems used (10M on TaihuLight and 16M on Gyoukou) and their relatively poor memory and network bandwidth pose new challenges. We describe the new algorithms introduced to achieve high efficiency on machines with low memory bandwidth. The measured performance is 47.9, 10.6 PF, and 1.01PF on TaihuLight, Gyoukou and Shoubu System B (efficiency 40\%, 23.5\% and 35.5\%). The current code is developed for the simulation of planetary rings, but most of the new algorithms are useful for other simulations, and are now available in the FDPS framework.

astro-ph.IM↗

arXiv2019

Maximum principles and monotonicity of solutions for fractional p-equations in unbounded domains

In this paper, we consider the following non-linear equations in unbounded domains $Ω$ with exterior Dirichlet condition: \begin{equation*}\begin{cases} (-Δ)_p^s u(x)=f(u(x)), & x\inΩ,\\ u(x)>0, &x\inΩ,\\ u(x)\leq0, &x\in \mathbb{R}^n\setminus Ω, \end{cases}\end{equation*} where $(-Δ)_p^s$ is the fractional p-Laplacian defined as \begin{equation} (-Δ)_p^s u(x)=C_{n,s,p}P.V.\int_{\mathbb{R}^n}\frac{|u(x)-u(y)|^{p-2}[u(x)-u(y)]}{|x-y|^{n+s p}}dy \label{0} \end{equation} with $0<s<1$ and $p\geq 2$. We first establish a maximum principle in unbounded domains involving the fractional p-Laplacian by estimating the singular integral in (\ref{0}) along a sequence of approximate maximum points. Then, we obtain the asymptotic behavior of solutions far away from the boundary. Finally, we develop a sliding method for the fractional p-Laplacians and apply it to derive the monotonicity and uniqueness of solutions. There have been similar results for the regular Laplacian \cite{BCN1} and for the fractional Laplacian \cite{DSV}, which are linear operators. Unfortunately, many approaches there no longer work for the fully non-linear fractional p-Laplacian here. To circumvent these difficulties, we introduce several new ideas, which enable us not only to deal with non-linear non-local equations, but also to remarkably weaken the conditions on $f(\cdot)$ and on the domain $Ω$. We believe that the new methods developed in our paper can be widely applied to many problems in unbounded domains involving non-linear non-local operators.

math.AP↗

arXiv2019

Similarity Grouping-Guided Neural Network Modeling for Maritime Time Series Prediction

Reliable and accurate prediction of time series plays a crucial role in maritime industry, such as economic investment, transportation planning, port planning and design, etc. The dynamic growth of maritime time series has the predominantly complex, nonlinear and non-stationary properties. To guarantee high-quality prediction performance, we propose to first adopt the empirical mode decomposition (EMD) and ensemble EMD (EEMD) methods to decompose the original time series into high- and low-frequency components. The low-frequency components can be easily predicted directly through traditional neural network (NN) methods. It is more difficult to predict high-frequency components due to their properties of weak mathematical regularity. To take advantage of the inherent self-similarities within high-frequency components, these components will be divided into several continuous small (overlapping) segments. The grouped segments with high similarities are then selected to form more proper training datasets for traditional NN methods. This regrouping strategy can assist in enhancing the prediction accuracy of high-frequency components. The final prediction result is obtained by integrating the predicted high- and low-frequency components. Our proposed three-step prediction frameworks benefit from the time series decomposition and similar segments grouping. Experiments on both port cargo throughput and vessel traffic flow have illustrated its superior performance in terms of prediction accuracy and robustness.

cs.CE↗

arXiv2019

Fractional quantum Hall states with gapped boundaries in an extreme lattice limit

We present a detailed microscopic investigation of fractional quantum Hall states with gapped boundaries in a coupled bilayer lattice model featuring holes whose counterpropagating chiral edge states are hybridized and gapped out. We focus on a lattice limit for cold-atom experiments, in which each hole just consists of a single removed site. Although the holes distort the original band structure and lead to ingap remnants of the continuum edge modes, we find that the lowest nearly flat band representing a higher-genus system may naturally form by controlling the local hopping terms that gap out the boundaries. Remarkably, local interactions in this new flat band lead to various Abelian and non-Abelian fractional quantum Hall states with gapped boundaries residing on emergent higher-genus surfaces, which we identify by extracting the nontrivial topological ground-state degeneracies and the fractional statistics of quasiparticles. These results demonstrate the feasibility of realizing novel fractional quantum Hall states with gapped boundaries even in the extreme lattice limit, thus enabling a possible new route towards universal topological quantum computation.

cond-mat.str-el↗

arXiv2019

Characterization of quasiholes in two-component fractional quantum Hall states and fractional Chern insulators in $|C|=2$ flat bands

We perform an exact-diagonalization study of quasihole excitations for the two-component Halperin $(221)$ state in the lowest Landau level and for several $ν=1/3$ bosonic fractional Chern insulators in topological flat bands with Chern number $|C|=2$. Properties including the quasihole size, charge, and braiding statistics are evaluated. For the Halperin $(221)$ model state, we observe isotropic quasiholes with a clear internal structure, and obtain the quasihole charge and statistics matching the theoretical values. Interestingly, we also extract the same quasihole size, charge, and braiding statistics for the continuum model states of $|C|=2$ fractional Chern insulators, although the latter possess a "color-entangled" nature that does not exist in ordinary two-component Halperin states. We also consider two real lattice models with a band having $|C|=2$. There, we find that a quasihole can exhibit much stronger oscillations of the density profile, while having the same charge and statistics as those in the continuum models.

cond-mat.str-el↗

arXiv2019

Stein-Weiss inequalities with the fractional Poisson kernel

In this paper, we establish the following Stein-Weiss inequality with the fractional Poisson kernel (see Theorem 1.1): \begin{equation}\label{int1} \int_{\mathbb{R}^n_{+}}\int_{\partial\mathbb{R}^n_{+}}|ξ|^{-α}f(ξ)P(x,ξ,γ)g(x)|x|^{-β}dξdx\leq C_{n,α,β,p,q'}\|g\|_{L^{q'}(\mathbb{R}^n_{+})}\|f\|_{L^p(\partial \mathbb{R}^{n}_{+})}, \end{equation} where $P(x,ξ,γ)=\frac{x_n}{(|x'-ξ|^2+x_n^2)^{\frac{n+2-γ}{2}}}$, $2\le γ<n$, $f\in L^{p}(\partial\mathbb{R}^n_{+})$, $g\in L^{q'}(\mathbb{R}^n_{+})$ and $p,\ q'\in (1,\infty)$ and satisfy $\frac{n-1}{n}\frac{1}{p}+\frac{1}{q'}+\frac{α+β+2-γ}{n}=1$. Then we prove that there exist extremals for the Stein-Weiss inequality (0.1) and the extremals must be radially decreasing about the origin (see Theorem 1.5). We also provide the regularity and asymptotic estimates of positive solutions to the integral systems which are the Euler-Lagrange equations of the extremals to the Stein-Weiss inequality (0.1) with the fractional Poisson kernel (see Theorems 1.7 and 1.8). Our result is inspired by the work of Hang, Wang and Yan [29] where the Hardy-Littlewood-Sobolev type inequality was first establishedmwhen $γ=2$ and $α=β=0$ (see (1.5)). The proof of the Stein-Weiss inequality (0.1) with the fractional Poisson kernel in this paper uses our recent work on the Hardy-Littlewood-Sobolev inequality with the fractional Poisson kernel [18] and the present paper is a further study in this direction.

math.AP↗

arXiv2018

On buffered double autoregressive time series models

A buffered double autoregressive (BDAR) time series model is proposed in this paper to depict the buffering phenomenon of conditional mean and conditional variance in time series. To build this model, a novel flexible regime switching mechanism is introduced to modify the classical threshold time series model by capturing the stickiness of signal. Besides, considering the inadequacy of traditional models under the lack of information, a signal retrospection is run in this model to provide a more accurate judgment. Moreover, formal proofs suggest strict stationarity and geometric ergodicity of BDAR model under several sufficient conditions. A Gaussian quasi-maximum likelihood estimation (QMLE) is employed and the asymptotic distributions of its estimators are derived. It has been demonstrated that the estimated thresholds of the BDAR model are $n$-consistent, each of which converges weakly to a functional of a two-sided compound Poisson process. The remaining parameters are $\sqrt{n}$-consistent and asymptotically normal. Furthermore, a model selection criteria and its asymptotic property have been established. Simulation studies are constructed to evaluate the finite sample performance of QMLE and model selection criteria. Finally, an empirical analysis of Hang Seng Index (HSI) using BDAR model reveals the asymmetry of investors' preference over losses and gains as well as the asymmetry of volatility structure.

stat.ME↗

arXiv2018

Geometric quench and nonequilibrium dynamics of fractional quantum Hall states

We introduce a quench of the geometry of Landau level orbitals as a probe of nonequilibrium dynamics of fractional quantum Hall (FQH) states. We show that such geometric quenches induce coherent many-body dynamics of neutral degrees of freedom of FQH fluids. The simplest case of mass anisotropy quench can be experimentally implemented as a sudden tilt of the magnetic field, and the resulting dynamics reduces to the harmonic motion of the spin-$2$ "graviton" mode, i.e., the long wavelength limit of the Girvin-MacDonald-Platzman magnetoroton. We derive an analytical description of the graviton dynamics using the bimetric theory of FQH states, and find agreement with exact numerical simulations at short times. We show that certain types of geometric quenches excite higher-spin collective modes, thus establishing their existence in a microscopic model and motivating an extension of geometric theories of FQH states.

cond-mat.str-el↗

arXiv2018

Learning-based Regularization for Cardiac Strain Analysis with Ability for Domain Adaptation

Reliable motion estimation and strain analysis using 3D+time echocardiography (4DE) for localization and characterization of myocardial injury is valuable for early detection and targeted interventions. However, motion estimation is difficult due to the low-SNR that stems from the inherent image properties of 4DE, and intelligent regularization is critical for producing reliable motion estimates. In this work, we incorporated the notion of domain adaptation into a supervised neural network regularization framework. We first propose an unsupervised autoencoder network with biomechanical constraints for learning a latent representation that is shown to have more physiologically plausible displacements. We extended this framework to include a supervised loss term on synthetic data and showed the effects of biomechanical constraints on the network's ability for domain adaptation. We validated both the autoencoder and semi-supervised regularization method on in vivo data with implanted sonomicrometers. Finally, we showed the ability of our semi-supervised learning regularization approach to identify infarcted regions using estimated regional strain maps with good agreement to manually traced infarct regions from postmortem excised hearts.

cs.CV↗

arXiv2018

Two-dimensional Penta-Pt2N4: an ideal material for nanoelectronics

Since the discovery of graphene, two-dimensional (2D) materials have paved a new routine for designing high-performance nanoelectronic devices. To facilitate the device applications, there are three key requirements for a material: sizeable band gap, high carrier mobility and robust environmental stability. However, for the hottest 2D materials studied in recent years, graphene is gapless, transition metal dichalcogenides have low carrier mobility, and black phosphorene is environmentally sensitive. So far, these three characteristics can seldom be satisfied in one single material. Therefore, it becomes a great challenge for finding an ideal 2D material to overcome such a limitation. In this work, we theoretically predict a novel planar 2D material: Penta-Pt2N4, which are designed by the fantastic Cario pentagonal tiling as well as the rare nitrogen double bond. Most significantly, the 2D Penta-Pt2N4 exhibits excellent intrinsic properties, including large direct band gap up to 1.51 eV, high carrier mobility up to 105 cm2V-1s-1, giant Young's module up to 0.70 TPa, and robust dynamic, thermal and chemical stability. Moreover, Penta-Pt2N4 is a global minimal with PtN2 stoichiometry in 2D, so we also propose a CVD/MBE scheme to enable its experimental synthesis. We envision that the 2D Penta-Pt2N4 may find a wide application for future nanoelectronics.

cond-mat.mtrl-sci↗

arXiv2018

MVP2P: Layer-Dependency-Aware Live MVC Video Streaming over Peer-to-Peer Networks

Multiview video supports observing a scene from different viewpoints. The Joint Video Team (JVT) developed H.264/MVC to enhance the compression efficiency for multiview video, however, MVC encoded multiview video (MVC video) still requires high bitrates for transmission. This paper investigates live MVC video streaming over Peer-to-Peer (P2P) networks. The goal is to minimize the server bandwidth costs whist ensuring high streaming quality to peers. MVC employs intra-view and inter-view prediction structures, which leads to a complicated layer dependency relationship. As the peers' outbound bandwidth is shared while supplying all the MVC video layers, the bandwidth allocation to one MVC layer affects the available outbound bandwidth of the other layers. To optimise the utilisation of the peers' outbound bandwidth for providing video layers, a maximum flow based model is proposed which considers the MVC video layer dependency and the layer supplying relationship between peers. Based on the model, a layer dependency aware live MVC video streaming method over a BitTorrent-like P2P network is proposed, named MVP2P. The key components of MVP2P include a chunk scheduling strategy and a peer selection strategy for receiving peers, and a bandwidth scheduling algorithm for supplying peers. To evaluate the efficiency of the proposed solution, MVP2P is compared with existing methods considering the constraints of peer bandwidth, peer numbers, view switching rates, and peer churns. The test results show that MVP2P significantly outperforms the existing methods.

cs.MM↗

arXiv2017

Evolution of quantum entanglement with disorder in fractional quantum Hall liquids

We present a detailed study of the ground-state entanglement in disordered fractional quantum Hall liquids. We consider electrons at various filling fractions $f$ in the lowest Landau level, with Coulomb interactions. At $f=1/3,1/5$ and $2/5$ where an incompressible ground-state manifold exists at zero disorder, we observe a pronounced minimum in the derivative of entanglement entropy with respect to disorder. At each filling, the position of this minimum is stable against increasing system size, but its magnitude grows monotonically and appears to diverge in the thermodynamic limit. We consider this behaviour of the entropy derivative as a compelling signal of the expected disorder-driven phase transition from a topological fractional quantum Hall phase to a trivial insulating phase. On the contrary, at $f=1/2$ where a compressible composite fermion sea is present at zero disorder, the entropy derivative exhibits much greater, almost chaotic, finite-size effects, without a clear phase transition signal for system sizes within our exact diagonalization limit. However, the dependence of entanglement entropy with system size changes with increasing disorder, consistent with the expectation of a phase transition from a composite fermion sea to an insulator. Finally, we consider $f=1/7$ where compressible Wigner crystals are quite competitive at zero disorder, and analyze the level statistics of entanglement spectrum at $f=1/3$.

cond-mat.str-el↗