arXiv subjects

Lin Lin

Publications and source records attributed to Lin Lin.

At least 235 records · Page 13Linked to original sources

arXiv2019

Influence of point defects on the electronic and topological properties of monolayer WTe$_2$

In some topological insulators, such as graphene and WTe$_2$, band inversion originates from chemical bonding and space group symmetry, in contrast to materials such as Bi$_2$Se$_3$, where the band inversion derives from relativistic effects in the atoms. In the former, band inversion is susceptible to changes of the chemical environment, e.g. by defects, while the latter are less affected by defects due to the larger energy scale associated with atomic relativistic effects. Motivated by recent experiments, we study the effect of Te-vacancies and Te-adatoms on the electronic properties of WTe$_2$. We find that the Te-vacancies have a formation energy of $2.21$ eV, while the formation energy of the Te-adatoms is much lower with $0.72$ eV. The vacancies strongly influence the band structure and we present evidence that band inversion is already reversed at the nominal composition of WTe$_{1.97}$. In contrast, we show that the adatoms do not change the electronic structure in the vicinity of the Fermi level and thus the topological properties. Our findings indicate that Te-adatoms should be present in thin films that are grown in a Te-rich environment, and we suggest that they have been observed in scanning tunneling microscopy experiments.

cond-mat.mtrl-sci↗

arXiv2019

Robust Control Optimization for Quantum Approximate Optimization Algorithm

Quantum variational algorithms have garnered significant interest recently, due to their feasibility of being implemented and tested on noisy intermediate scale quantum (NISQ) devices. We examine the robustness of the quantum approximate optimization algorithm (QAOA), which can be used to solve certain quantum control problems, state preparation problems, and combinatorial optimization problems. We demonstrate that the error of QAOA simulation can be significantly reduced by robust control optimization techniques, specifically, by sequential convex programming (SCP), to ensure error suppression in situations where the source of the error is known but not necessarily its magnitude. We show that robust optimization improves both the objective landscape of QAOA as well as overall circuit fidelity in the presence of coherent errors and errors in initial state preparation.

quant-ph↗

arXiv2019

Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller-Plesset Perturbation Theory

We present a systematically improvable tensor hypercontraction (THC) factorization based on interpolative separable density fitting (ISDF). We illustrate algorithmic details to achieve this within the framework of Becke's atom-centered quadrature grid. A single ISDF parameter $c_\text{ISDF}$ controls the tradeoff between accuracy and cost. In particular, $c_\text{ISDF}$ sets the number of interpolation points used in THC, $N_\text{IP} = c_\text{ISDF}\times N_\text{X}$ with $N_\text{X}$ being the number of auxiliary basis functions. In conjunction with the resolution-of-the-identity (RI) technique, we develop and investigate the THC-RI algorithms for cubic-scaling exact exchange for Hartree-Fock and range-separated hybrids (e.g., $ω$B97X-V) and quartic-scaling second- and third-order Møller-Plesset theory (MP2 and MP3). These algorithms were evaluated over the W4-11 thermochemistry (atomization energy) set and A24 non-covalent interaction benchmark set with standard Dunning basis sets (cc-pVDZ, cc-pVTZ, aug-cc-pVDZ, and aug-cc-pVTZ). We demonstrate the convergence of THC-RI algorithms to numerically exact RI results using ISDF points. Based on these, we make recommendations on $c_\text{ISDF}$ for each basis set and method. We also demonstrate the utility of THC-RI exact exchange and MP2 for larger systems such as water clusters and $\text{C}_{20}$. We stress that more challenges await in obtaining accurate and numerically stable THC factorization for wavefunction amplitudes as well as the space spanned by virtual orbitals in large basis sets and implementing sparsity-aware THC-RI algorithms.

physics.chem-ph↗

arXiv2019

Low-rank representation of tensor network operators with long-range pairwise interactions

Tensor network operators, such as the matrix product operator (MPO) and the projected entangled-pair operator (PEPO), can provide efficient representation of certain linear operators in high dimensional spaces. This paper focuses on the efficient representation of tensor network operators with long-range pairwise interactions such as the Coulomb interaction. For MPOs, we find that all existing efficient methods exploit a peculiar "upper-triangular low-rank" (UTLR) property, i.e. the upper-triangular part of the matrix can be well approximated by a low-rank matrix, while the matrix itself can be full-rank. This allows us to convert the problem of finding the efficient MPO representation into a matrix completion problem. We develop a modified incremental singular value decomposition method (ISVD) to solve this ill-conditioned matrix completion problem. This algorithm yields equivalent MPO representation to that developed in [Stoudenmire and White, Phys. Rev. Lett. 2017]. In order to efficiently treat more general tensor network operators, we develop another strategy for compressing tensor network operators based on hierarchical low-rank matrix formats, such as the hierarchical off-diagonal low-rank (HODLR) format, and the $\mathcal{H}$-matrix format. Though the pre-constant in the complexity is larger, the advantage of using the hierarchical low-rank matrix format is that it is applicable to both MPOs and PEPOs. For the Coulomb interaction, the operator can be represented by a linear combination of $\mathcal{O}(\log(N)\log(N/ε))$ MPOs/PEPOs, each with a constant bond dimension, where $N$ is the system size and $ε$ is the accuracy of the low-rank truncation. Neither the modified ISVD nor the hierarchical low-rank algorithm assumes that the long-range interaction takes a translation-invariant form.

physics.comp-ph↗

arXiv2019

Discontinuous Galerkin discretization for quantum simulation of chemistry

Methods for electronic structure based on Gaussian and molecular orbital discretizations offer a well established, compact representation that forms much of the foundation of correlated quantum chemistry calculations on both classical and quantum computers. Despite their ability to describe essential physics with relatively few basis functions, these representations can suffer from a quartic growth of the number of integrals. Recent results have shown that, for some quantum and classical algorithms, moving to representations with diagonal two-body operators can result in dramatically lower asymptotic costs, even if the number of functions required increases significantly. We introduce a way to interpolate between the two regimes in a systematic and controllable manner, such that the number of functions is minimized while maintaining a block diagonal structure of the two-body operator and desirable properties of an original, primitive basis. Techniques are analyzed for leveraging the structure of this new representation on quantum computers. Empirical results for hydrogen chains suggest a scaling improvement from $O(N^{4.5})$ in molecular orbital representations to $O(N^{2.6})$ in our representation for quantum evolution in a fault-tolerant setting, and exhibit a constant factor crossover at 15 to 20 atoms. Moreover, we test these methods using modern density matrix renormalization group methods classically, and achieve excellent accuracy with respect to the complete basis set limit with a speedup of 1-2 orders of magnitude with respect to using the primitive or Gaussian basis sets alone. These results suggest our representation provides significant cost reductions while maintaining accuracy relative to molecular orbital or strictly diagonal approaches for modest-sized systems in both classical and quantum computation for correlated systems.

quant-ph↗

arXiv2019

Projected Density Matrix Embedding Theory with Applications to the Two-Dimensional Hubbard Model

Density matrix embedding theory (DMET) is a quantum embedding theory for strongly correlated systems. From a computational perspective, one bottleneck in DMET is the optimization of the correlation potential to achieve self-consistency, especially for heterogeneous systems of large size. We propose a new method, called projected density matrix embedding theory (p-DMET), which achieves self-consistency without needing to optimize a correlation potential. We demonstrate the performance of p-DMET on the two-dimensional Hubbard model.

physics.chem-ph↗

arXiv2019

Parallel Transport Time-Dependent Density Functional Theory Calculations with Hybrid Functional on Summit

Real-time time-dependent density functional theory (rt-TDDFT) with hybrid exchange-correlation functional has wide-ranging applications in chemistry and material science simulations. However, it can be thousands of times more expensive than a conventional ground state DFT simulation, hence is limited to small systems. In this paper, we accelerate hybrid functional rt-TDDFT calculations using the parallel transport gauge formalism, and the GPU implementation on Summit. Our implementation can efficiently scale to 786 GPUs for a large system with 1536 silicon atoms, and the wall clock time is only 1.5 hours per femtosecond. This unprecedented speed enables the simulation of large systems with more than 1000 atoms using rt-TDDFT and hybrid functional.

physics.comp-ph↗

arXiv2019

Projection based embedding theory for solving Kohn-Sham density functional theory

Quantum embedding theories are playing an increasingly important role in bridging different levels of approximation to the many body Schrödinger equation in physics, chemistry and materials science. In this paper, we present a linear algebra perspective of the recently developed projection based embedding theory (PET) [Manby et al, J. Chem. Theory Comput. 8, 2564, 2012], restricted to the context of Kohn-Sham density functional theory. By partitioning the global degrees of freedom into a `system' part and a `bath' part, and by choosing a proper projector from the bath, PET is an in principle exact formulation to confine the calculation to the system part only, and hence can be carried out with reduced computational cost. Viewed from the perspective of the domain decomposition method, one particularly interesting feature of PET is that it does not enforce a boundary condition explicitly, and remains applicable even when the discretized Hamiltonian matrix is dense, such as in the context of the planewave discretization. In practice, the accuracy of PET depends on the accuracy of the projector for the bath. Based on the linear algebra reformulation, we develop a first order perturbation correction to the projector from the bath to improve its accuracy. Numerical results for real chemical systems indicate that with a proper choice of reference system, the perturbatively corrected PET can be sufficiently accurate even when strong perturbation is applied to very small systems, such as the computation of the ground state energy of a SiH$_3$F molecule, using a SiH$_4$ molecule as the reference system.

physics.comp-ph↗

arXiv2019

A multiscale neural network based on hierarchical nested bases

In recent years, deep learning has led to impressive results in many fields. In this paper, we introduce a multi-scale artificial neural network for high-dimensional non-linear maps based on the idea of hierarchical nested bases in the fast multipole method and the $\mathcal{H}^2$-matrices. This approach allows us to efficiently approximate discretized nonlinear maps arising from partial differential equations or integral equations. It also naturally extends our recent work based on the generalization of hierarchical matrices [Fan et al. arXiv:1807.01883] but with a reduced number of parameters. In particular, the number of parameters of the neural network grows linearly with the dimension of the parameter space of the discretized PDE. We demonstrate the properties of the architecture by approximating the solution maps of non-linear Schr{ö}dinger equation, the radiative transfer equation, and the Kohn-Sham map.

math.NA↗

arXiv2019

Linking bar- and interaction-driven molecular gas concentration with centrally-enhanced star formation in EDGE-CALIFA galaxies

We study the spatially resolved star formation history and molecular gas distribution of 58 nearby galaxies, using integral field spectroscopy from the CALIFA survey and CO $J=1\rightarrow 0$ intensity mapping from the CARMA EDGE survey. We use the 4000 Å break (D$_n$4000), the equivalent width of the H$δ$ absorption line (EW H$δ_A$), and the equivalent width of the H$α$ emission line (EW H$α$) to measure the recent star formation history (SFH) of these galaxies. We measure radial profiles of the three SFH indicators and molecular gas mass surface density, from which we measure the level of centrally enhanced star formation and the molecular gas concentration. When we separate our galaxies into categories of barred (17 galaxies), unbarred (24 galaxies), and merging/paired (17 galaxies) we find that the galaxies which have centrally-enhanced star formation (19/58) are either barred (13/19) or in mergers/pairs (6/19) with relatively high molecular gas concentrations. A comparison between our barred galaxies and a snapshot of a hydrodynamic $N$-body simulation of a barred galaxy shows that the current theory of bar formation and evolution can qualitatively reproduce the main features of the observed galaxies in our sample, including both the sharp decrease of stellar age in the galactic center and the gradual decrease of age with increasing distance from center. These findings provide substantial evidence for a picture in which cold gas is transported inward by a bar or tidal interaction, which leads to the growth and rejuvenation of star formation in the central region.

astro-ph.GA↗

arXiv2019

Fast real-time time-dependent hybrid functional calculations with the parallel transport gauge and the adaptively compressed exchange formulation

We present a new method to accelerate real time-time dependent density functional theory (rt-TDDFT) calculations with hybrid exchange-correlation functionals. For large basis set, the computational bottleneck for large scale calculations is the application of the Fock exchange operator to the time-dependent orbitals. Our main goal is to reduce the frequency of applying the Fock exchange operator, without loss of accuracy. We achieve this by combining the recently developed parallel transport (PT) gauge formalism and the adaptively compressed exchange operator (ACE) formalism. The PT gauge yields the slowest possible dynamics among all choices of gauge. When coupled with implicit time integrators such as the Crank-Nicolson (CN) scheme, the resulting PT-CN scheme can significantly increase the time step from sub-attoseconds to 10-100 attoseconds. At each time step $t_{n}$, PT-CN requires the self-consistent solution of the orbitals at time $t_{n+1}$. We use ACE to delay the update of the Fock exchange operator in this nonlinear system, while maintaining the same self-consistent solution. We verify the performance of the resulting PT-CN-ACE method by computing the absorption spectrum of a benzene molecule and the response of bulk silicon systems to an ultrafast laser pulse, using the planewave basis set and the HSE functional. We report the strong and weak scaling of the PT-CN-ACE method for silicon systems ranging from 32 to 1024 atoms, with up to 2048 computational cores. Compared to standard explicit time integrators such as the 4th order Runge-Kutta method (RK4), the PT-CN-ACE can reduce the Fock exchange operator application by nearly 70 times, thus reduce the overall wall clock time time by 46 times for the system with 1024 atoms. Hence our work enables hybrid functional rt-TDDFT calculations to be routinely performed with a large basis set for the first time.

physics.comp-ph↗

arXiv2019

Interpreting the star formation - extinction relation with MaNGA

We investigate the resolved relation between local extinction and star formation surface density within nearby star-forming galaxies selected from the MaNGA survey. Balmer decrement measurements imply an extinction of the Hα line emission which scales approximately linearly with the logarithm of the star formation surface density: $ A_{Hα} = 0.46 \log(Σ_{SFR}) + 1.53$. Secondary dependencies are observed such that, at a given $Σ_{SFR}$, regions of lower metallicity and/or enhanced Hα equivalent width (EW) suffer less obscuration than regions of higher metallicity and/or lower Hα EW. Spaxels lying above the mean relation also tend to belong to galaxies that are more massive, larger and viewed under higher inclination than average. We present a simple model in which the observed trends can be accounted for by a metallicity-dependent scaling between $Σ_{SFR}$ and $Σ_{dust}$ via a super-linear Kennicutt-Schmidt relation ($n_{KS} \sim 1.47$) and a dust-to-gas ratio which scales linearly with metallicity (DGR($Z_{\odot}$) = 0.01). The relation between the resulting total dust column and observed effective extinction towards nebular regions requires a geometry for the relative distribution of Hα emitting regions and dust that deviates from a uniform foreground screen and also from an entirely homogeneous mixture of dust and emitting sources. The best-fit model features an Hα EW and galactocentric distance dependent fraction of the dust mass in a clumpy foreground screen in front of a homogeneous mixture.

astro-ph.GA↗

arXiv2018

Physics and astrophysics of strong magnetic field systems with eXTP

In this paper we present the science potential of the enhanced X-ray Timing and Polarimetry (eXTP) mission for studies of strongly magnetized objects. We will focus on the physics and astrophysics of strongly magnetized objects, namely magnetars, accreting X-ray pulsars, and rotation powered pulsars. We also discuss the science potential of eXTP for QED studies. Developed by an international Consortium led by the Institute of High Energy Physics of the Chinese Academy of Sciences, the eXTP mission is expected to be launched in the mid 2020s.

astro-ph.HE↗

arXiv2018

A General Framework for Enhancing Sparsity of Generalized Polynomial Chaos Expansions

Compressive sensing has become a powerful addition to uncertainty quantification when only limited data is available. In this paper we provide a general framework to enhance the sparsity of the representation of uncertainty in the form of generalized polynomial chaos expansion. We use alternating direction method to identify new sets of random variables through iterative rotations such that the new representation of the uncertainty is sparser. Consequently, we increases both the efficiency and accuracy of the compressive sensing-based uncertainty quantification method. We demonstrate that the previously developed iterative method to enhance the sparsity of Hermite polynomial expansion is a special case of this general framework. Moreover, we use Legendre and Chebyshev polynomials expansions to demonstrate the effectiveness of this method with applications in solving stochastic partial differential equations and high-dimensional (O(100)) problems.

math.NA↗

arXiv2018

Explaining Deep Learning Models - A Bayesian Non-parametric Approach

Understanding and interpreting how machine learning (ML) models make decisions have been a big challenge. While recent research has proposed various technical approaches to provide some clues as to how an ML model makes individual predictions, they cannot provide users with an ability to inspect a model as a complete entity. In this work, we propose a novel technical approach that augments a Bayesian non-parametric regression mixture model with multiple elastic nets. Using the enhanced mixture model, we can extract generalizable insights for a target model through a global approximation. To demonstrate the utility of our approach, we evaluate it on different ML models in the context of image recognition. The empirical results indicate that our proposed approach not only outperforms the state-of-the-art techniques in explaining individual decisions but also provides users with an ability to discover the vulnerabilities of the target ML models.

cs.LG↗

arXiv2018

Fast real-time time-dependent density functional theory calculations with the parallel transport gauge

Real-time time-dependent density functional theory (RT-TDDFT) is known to be hindered by the very small time step (attosecond or smaller) needed in the numerical simulation due to the fast oscillation of electron wavefunctions, which significantly limits its range of applicability for the study of ultrafast dynamics. In this paper, we demonstrate that such oscillation can be considerably reduced by optimizing the gauge choice using the parallel transport formalism. RT-TDDFT calculations can thus be significantly accelerated using a combination of the parallel transport gauge and implicit integrators, and the resulting scheme can be used to accelerate any electronic structure software that uses a Schrödinger representation. Using absorption spectrum, ultrashort laser pulse, and Ehrenfest dynamics calculations for example, we show that the new method can utilize a time step that is on the order of $10\sim 100$ attoseconds in a planewave basis set, and is no less than $5\sim 10$ times faster when compared to the standard explicit 4th order Runge-Kutta time integrator. Thanks to the significant increase of the size of the time step, we also demonstrate that the new method is more than 10 times faster in terms of the wall clock time when compared to the standard explicit 4th order Runge-Kutta time integrator for silicon systems ranging from 32 to 1024 atoms

physics.comp-ph↗

arXiv2018

Direct observation of ferroelectricity in Ca$_3$Mn$_2$O$_7$ and its prominent light absorption

Layered perovskites $A_3M_2$O$_7$ are known to exhibit the so-called hybrid improper ferroelectricity. Despite experimentally confirmed cases (e.g. nonmagnetic $M$=Ti and Sn), the ferroelectricity in magnetic Ca$_3$Mn$_2$O$_7$ remains a puzzle. Here, the structural, ferroelectric, magnetoelectric, and optical properties of Ca$_3$Mn$_2$O$_7$ are systematically investigated. Switchable polarization is directly measured, demonstrating its ferroelectricity. In addition, magnetoelectric response is also evidenced, implying the coupling between magnetism and ferroelectricity. Furthermore, strong visible light absorption is observed, which can be understood from its electronic structure. Its direct and appropriate band gap, as well as wide conducting bands, makes Ca$_3$Mn$_2$O$_7$ a potential candidate for ferroelectric photoelectric applications.

cond-mat.mtrl-sci↗

arXiv2018

Bold Feynman diagrams and the Luttinger-Ward formalism via Gibbs measures. Part I: Perturbative approach

Many-body perturbation theory (MBPT) is widely used in quantum physics, chemistry, and materials science. At the heart of MBPT is the Feynman diagrammatic expansion, which is, simply speaking, an elegant way of organizing the combinatorially growing number of terms of a certain Taylor expansion. In particular, the construction of the `bold Feynman diagrammatic expansion' involves the partial resummation to infinite order of possibly divergent series of diagrams. This procedure demands investigation from both the combinatorial (perturbative) and the analytical (non-perturbative) viewpoints. In Part I of this two-part series, we illustrate how the combinatorial properties of Feynman diagrams in MBPT can be studied in the simplified setting of Gibbs measures (known as the Euclidean lattice field theory in the physics literature) and provide a self-contained explanation of Feynman diagrams in this setting. We prove the combinatorial validity of the bold diagrammatic expansion, with methods generalizable to several types of field theories and interactions. Our treatment simplifies the presentation and numerical study of known techniques in MBPT such as the self-consistent Hartree-Fock approximation (HF), the second-order Green's function approximation (GF2), and the GW approximation. The bold diagrams are closely related to the Luttinger-Ward (LW) formalism, which was proposed in 1960 but whose analytic properties have not been rigorously established. The analytical study of the LW formalism in the setting of Gibbs measures will be the topic of Part II.

math-ph↗