arXiv subjects

Lin Lin

Publications and source records attributed to Lin Lin.

At least 253 records · Page 14Linked to original sources

arXiv2018

Bold Feynman diagrams and the Luttinger-Ward formalism via Gibbs measures. Part II: Non-perturbative analysis

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 II of this two-part series, we approach the analytical investigation of the bold diagrammatic expansion in the simplified setting of Gibbs measures (known as the Euclidean lattice field theory in the physics literature). Using non-perturbative methods, we rigorously construct the Luttinger-Ward formalism for the first time, and we prove that the bold diagrammatic series can be obtained directly via an asymptotic expansion of the Luttinger-Ward functional, circumventing the partial resummation technique. Moreover we prove that the Dyson equation can be derived as the Euler-Lagrange equation associated with a variational problem involving the Luttinger-Ward functional. We also establish a number of key facts about the Luttinger-Ward functional, such as its transformation rule, its form in the setting of the impurity problem, and its continuous extension to the boundary of the domain of physical Green's functions.

math-ph↗

arXiv2018

Structured Quasi-Newton Methods for Optimization with Orthogonality Constraints

In this paper, we study structured quasi-Newton methods for optimization problems with orthogonality constraints. Note that the Riemannian Hessian of the objective function requires both the Euclidean Hessian and the Euclidean gradient. In particular, we are interested in applications that the Euclidean Hessian itself consists of a computational cheap part and a significantly expensive part. Our basic idea is to keep these parts of lower computational costs but substitute those parts of higher computational costs by the limited-memory quasi-Newton update. More specically, the part related to Euclidean gradient and the cheaper parts in the Euclidean Hessian are preserved. The initial quasi-Newton matrix is further constructed from a limited-memory Nyström approximation to the expensive part. Consequently, our subproblems approximate the original objective function in the Euclidean space and preserve the orthogonality constraints without performing the so-called vector transports. When the subproblems are solved to sufficient accuracy, both global and local q-superlinear convergence can be established under mild conditions. Preliminary numerical experiments on the linear eigenvalue problem and the electronic structure calculation show the effectiveness of our method compared with the state-of-art algorithms.

math.OC↗

arXiv2018

Multi-color blackbody emission in GRB 081221

The radiation mechanism of the prompt emission of gamma-ray bursts (GRBs) remains an open question. Although their spectra are usually well fitted with the empirical Band function, which is widely believed to be fully non-thermal and interpreted as an optically thin synchrotron emission, accumulating evidence shows that a thermal component actually exists. In this paper, a multi-color blackbody (mBB) model is proposed for the time-integrated spectrum of GRB 081221 by assuming a power-law distribution of the thermal luminosities with temperature, which manifests photospheric emissions from a different radius and/or angle. The effects of the minimum temperature $kT_{\min }$, the maximum temperature $kT_{\max }$ and the power law index $m$ of the luminosity distribution of an mBB are discussed. The fitting to the time-integrated spectrum during the bright phase (from 20s to 30s since the trigger) of GRB 081221 by the mBB model yields $kT_{\min }$ = $4.4\pm 0.3$ keV, $kT_{\max }$ = 57.0 $_{-1.4}^{+1.6}$ keV, and $m=-0.46_{-0.06}^{+0.05}$. When the time bin is small enough, the time-resolved spectra of GRB 081221 are well fitted with a series of single-temperature blackbodies. Our results imply the prompt emission of GRB 081221 is dominated by the photosphere emission and its time-integrated spectrum is a superposition of pure blackbody components at different times, indicating that some empirical Band spectra may be interpreted as mBB if the temperature is widely distributed.

astro-ph.HE↗

arXiv2018

Disentanglement via entanglement: A unified method for Wannier localization

The Wannier localization problem in quantum physics is mathematically analogous to finding a localized representation of a subspace corresponding to a nonlinear eigenvalue problem. While Wannier localization is well understood for insulating materials with isolated eigenvalues, less is known for metallic systems with entangled eigenvalues. Currently, the most widely used method for treating systems with entangled eigenvalues is to first obtain a reduced subspace (often referred to as disentanglement) and then to solve the Wannier localization problem by treating the reduced subspace as an isolated system. This is a multi-objective nonconvex optimization procedure and its solution can depend sensitively on the initial guess. We propose a new method to solve the Wannier localization problem, avoiding the explicit use of an an optimization procedure. Our method is robust, efficient, relies on few tunable parameters, and provides a unified framework for addressing problems with isolated and entangled eigenvalues.

physics.comp-ph↗

arXiv2018

Globally Constructed Adaptive Local Basis Set for Spectral Projectors of Second Order Differential Operators

Spectral projectors of second order differential operators play an important role in quantum physics and other scientific and engineering applications. In order to resolve local features and to obtain converged results, typically the number of degrees of freedom needed is much larger than the rank of the spectral projector. This leads to significant cost in terms of both computation and storage. In this paper, we develop a method to construct a basis set that is adaptive to the given differential operator. The basis set is systematically improvable, and the local features of the projector is built into the basis set. As a result the required number of degrees of freedom is only a small constant times the rank of the projector. The construction of the basis set uses a randomized procedure, and only requires applying the differential operator to a small number of vectors on the global domain, while each basis function itself is supported on strictly local domains and is discontinuous across the global domain. The spectral projector on the global domain is systematically approximated from such a basis set using the discontinuous Galerkin (DG) method. The global construction procedure is very flexible, and allows a local basis set to be consistently constructed even if the operator contains a nonlocal potential term. We verify the effectiveness of the globally constructed adaptive local basis set using one-, two- and three-dimensional linear problems with local potentials, as well as a one dimensional nonlinear problem with nonlocal potentials resembling the Hartree-Fock problem in quantum physics.

math.NA↗

arXiv2018

The evolution of galaxy shapes in CANDELS: from prolate to oblate

We model the projected b/a-log a distributions of CANDELS main sequence star-forming galaxies, where a (b) is the semi-major (semi-minor) axis of the galaxy images. We find that smaller-a galaxies are rounder at all stellar masses M and redshifts, so we include a when analyzing b/a distributions. Approximating intrinsic shapes of the galaxies as triaxial ellipsoids and assuming a multivariate normal distribution of galaxy size and two shape parameters, we construct their intrinsic shape and size distributions to obtain the fractions of prolate, oblate and spheroidal galaxies in each redshift and mass bin. We find that galaxies tend to be prolate at low m and high redshifts, and oblate at high M and low redshifts, qualitatively consistent with van der Wel et al. (2014), implying that galaxies tend to evolve from prolate to oblate. These results are consistent with the predictions from simulations (Ceverino et al. 2015, Tomassetti et al. 2016) that the transition from prolate to oblate is caused by a compaction event at a characteristic mass range, making the galaxy center baryon dominated. We give probabilities of a galaxy's being prolate, oblate or spheroidal as a function of its M, redshift, projected b/a and a, which can facilitate target selections of galaxies with specific shapes at hight redshifts. We also give predicted optical depths of galaxies, which are qualitatively consistent with the expected correlation that AV should be higher for edge-on disk galaxies in each log a slice at low redshift and high mass bins.

astro-ph.GA↗

arXiv2018

New iron-based multiferroics with improper ferroelectricity

In this contribution to the special issue on magnetoelectrics and their applications, we focus on some single phase multiferroics theoretically predicted and/or experimentally discovered by the authors in recent years. In these materials, iron is the common core element. However, these materials are conceptually different from the mostly-studied BiFeO$_3$, since their ferroelectricity is improper. Our reviewed materials are not simply repeating one magnetoelectric mechanism, but cover multiple branches of improper ferroelectricity, including the magnetism-driven ferroelectrics, geometric ferroelectric, as well as electronic ferroelectric driven by charge ordering. In this sense, these iron-based improper ferroelectrics can be an encyclopaedic playground to explore the comprehensive physics of multiferroics and magnetoelectricity. Furthermore, the unique characteristics of iron's $3d$ orbitals make some of their magnetoelectric properties quite prominent, comparing with the extensively-studied Mn-based improper multiferroics. In addition, these materials establish the crossover between multiferroics and other fields of functional materials, which enlarges the application scope of multiferroics.

cond-mat.mtrl-sci↗

arXiv2018

M101: Spectral Observations of HII Regions and Their Physical Properties

By using the Hectospec 6.5 m Multiple Mirror Telescope (MMT) and the 2.16 m telescope of National Astronomical Observatories, Chinese Academy of Sciences (NAOC), we obtained 188 high signal-to-noise ratio (S/N) spectra of HII regions in the nearby galaxy M101, which are the largest spectroscopic sample of HII regions for this galaxy so far. These spectra cover a wide range of regions on M101, which enables us to analyze two dimensional distributions of its physical properties. The physical parameters are derived from emission lines or stellar continuum, including stellar population age, electron temperature, oxygen abundance and etc. The oxygen abundances are derived using two empirical methods based on O3N2 and R$_{23}$ indicators, as well as the direct Te method when OIII$\lambda4363$ is available. By applying the harmonic decomposition analysis to the velocity field, we obtained line-of-sight rotation velocity of 71 km s$^{-1}$ and a position angle of 36 degree. The stellar age profile shows an old stellar population in galaxy center and a relative young stellar population in outer regions, suggesting an old bulge and a young disk. Oxygen abundance profile exhibits a clear break at $\sim$18 kpc, with a gradient of $-$0.0364 dex kpc$^{-1}$ in the inner region and $-$0.00686 dex kpc$^{-1}$ in the outer region. Our results agree with the "inside-out" disk growth scenario of M101.

astro-ph.GA↗

arXiv2018

SDSS-IV MaNGA: Star formation cessation in low-redshift galaxies I. Dependence on stellar mass and structural properties

We investigate radial gradients in the recent star formation history (SFH) using 1917 galaxies with $0.01<z<0.14$ and integral-field spectroscopy from the ongoing MaNGA survey. For each galaxy, we obtain two-dimensional maps and radial profiles for three spectroscopically-measured parameters that are sensitive to the recent SFH: D$_n$(4000) (the 4000Å break), EW(H$δ_A$) (equivalent width of the H$δ$ absorption line), and EW(H$α$) (equivalent width of the H$α$ emission line). We find the majority of the spaxels in these galaxies are consistent with models with continuously declining star formation rate, indicating that starbursts occur rarely in local galaxies. We classify the galaxies into three classes: fully star-forming (SF), partly quenched (PQ) and totally quenched (TQ), according to the fraction of quenched area within 1.5 times the effective radius, $f_Q(1.5R_e)$. We find that galaxies less massive than $10^{10}$M$_{\odot}$ present at most weak radial gradients in all the diagnostic parameters. In contrast, galaxies with stellar mass above $10^{10}$M$_{\odot}$ present significant gradients in all the three diagnostic parameters if classified as SF or PQ, but show weak gradients in D$_n$(4000) and EW(H$δ_A$) and no gradients in EW(H$α$) if in the TQ class. This implies the existence of a critical stellar mass, at $\sim10^{10}$M$_{\odot}$, above which the star formation in a galaxy gets shutdown from the inside out. Galaxies tend to evolve synchronously from inner to outer regions before their mass reaches the critical value. We have further divided the sample at fixed mass by both bulge-to-total luminosity ratio and morphological type, finding that our conclusions hold regardless of these factors: it appears that the presence of a central dense object is not a driving parameter, but rather a byproduct of the star formation cessation process.

astro-ph.GA↗

arXiv2018

Two-level Chebyshev filter based complementary subspace method: pushing the envelope of large-scale electronic structure calculations

We describe a novel iterative strategy for Kohn-Sham density functional theory calculations aimed at large systems (> 1000 electrons), applicable to metals and insulators alike. In lieu of explicit diagonalization of the Kohn-Sham Hamiltonian on every self-consistent field (SCF) iteration, we employ a two-level Chebyshev polynomial filter based complementary subspace strategy to: 1) compute a set of vectors that span the occupied subspace of the Hamiltonian; 2) reduce subspace diagonalization to just partially occupied states; and 3) obtain those states in an efficient, scalable manner via an inner Chebyshev-filter iteration. By reducing the necessary computation to just partially occupied states, and obtaining these through an inner Chebyshev iteration, our approach reduces the cost of large metallic calculations significantly, while eliminating subspace diagonalization for insulating systems altogether. We describe the implementation of the method within the framework of the Discontinuous Galerkin (DG) electronic structure method and show that this results in a computational scheme that can effectively tackle bulk and nano systems containing tens of thousands of electrons, with chemical accuracy, within a few minutes or less of wall clock time per SCF iteration on large-scale computing platforms. We anticipate that our method will be instrumental in pushing the envelope of large-scale ab initio molecular dynamics. As a demonstration of this, we simulate a bulk silicon system containing 8,000 atoms at finite temperature, and obtain an average SCF step wall time of 51 seconds on 34,560 processors; thus allowing us to carry out 1.0 ps of ab initio molecular dynamics in approximately 28 hours (of wall time).

physics.comp-ph↗

arXiv2018

Accelerating Optical Absorption Spectra and Exciton Energy Computation for Nanosystems via Interpolative Separable Density Fitting

We present an efficient way to solve the Bethe-Salpeter equation (BSE), a model for the computation of absorption spectra in molecules and solids that includes electron-hole excitations. Standard approaches to construct and diagonalize the Bethe-Salpeter Hamiltonian require at least $Ø(N_e^5)$ operations, where $N_e$ is proportional to the number of electrons in the system, limiting its application to small systems. Our approach is based on the interpolative separable density fitting (ISDF) technique to construct low rank approximations to the bare and screened exchange operators associated with the BSE Hamiltonian. This approach reduces the complexity of the Hamiltonian construction to $Ø(N_e^3)$ with a much smaller pre-constant. Here, we implement the ISDF method for the BSE calculations within the Tamm-Dancoff approximation (TDA) in the BerkeleyGW software package. We show that ISDF-based BSE calculations in molecules and solids reproduce accurate exciton energies and optical absorption spectra with significantly reduced computational cost.

physics.comp-ph↗

arXiv2018

Internal Variations in Empirical Oxygen Abundances for Giant HII Regions in the Galaxy NGC 2403

This paper presents a spectroscopic investigation of 11 HII regions in the nearby galaxy NGC 2403. The HII regions are observed with a long-slit spectrograph mounted on the 2.16 m telescope at XingLong station of National Astronomical Observatories of China. For each of the HII regions, spectra are extracted at different nebular radii along the slit-coverage. Oxygen abundances are empirically estimated from the strong-line indices R23, N2O2, O3N2, and N2 for each spectrophotometric unit, with both observation- and model-based calibrations adopted into the derivation. Radial profiles of these diversely estimated abundances are drawn for each nebula. In the results, the oxygen abundances separately estimated with the prescriptions on the basis of observations and models, albeit from the same spectral index, systematically deviate from each other; at the same time, the spectral indices R23 and N2O2 are distributed with flat profiles, whereas N2 and O3N2 exhibit apparent gradients with the nebular radius. Because our study naturally samples various ionization levels which inherently decline at larger radii within individual HII regions, the radial distributions indicate not only the robustness of R23 and N2O2 against ionization variations but also the sensitivity of N2 and O3N2 to the ionization parameter. The results in this paper provide observational corroboration of the theoretical prediction about the deviation in the empirical abundance diagnostics. Our future work is planned to investigate metal-poor HII regions with measurable T_e, in an attempt to recalibrate the strong-line indices and consequently disclose the cause of the discrepancies between the empirical oxygen abundances.

astro-ph.GA↗

arXiv2018

Variational formulation for Wannier functions with entangled band structure

Wannier functions provide a localized representation of spectral subspaces of periodic Hamiltonians, and play an important role for interpreting and accelerating Hartree-Fock and Kohn-Sham density functional theory calculations in quantum physics and chemistry. For systems with isolated band structure, the existence of exponentially localized Wannier functions and numerical algorithms for finding them are well studied. In contrast, for systems with entangled band structure, Wannier functions must be generalized to span a subspace larger than the spectral subspace of interest to achieve favorable spatial locality. In this setting, little is known about the theoretical properties of these Wannier functions, and few algorithms can find them robustly. We develop a variational formulation to compute these generalized maximally localized Wannier functions. When paired with an initial guess based on the selected columns of the density matrix (SCDM) method, our method can robustly find Wannier functions for systems with entangled band structure. We formulate the problem as a constrained nonlinear optimization problem, and show how the widely used disentanglement procedure can be interpreted as a splitting method to approximately solve this problem. We demonstrate the performance of our method using real materials including silicon, copper, and aluminum. To examine more precisely the localization properties of Wannier functions, we study the free electron gas in one and two dimensions, where we show that the maximally-localized Wannier functions only decay algebraically. We also explain using a one dimensional example how to modify them to obtain super-algebraic decay.

physics.comp-ph↗

arXiv2017

A Stochastic Generalized Ginzburg-Landau Equation Driven by Jump Noise

This paper is concerned with the stochastic generalized Ginzburg-Landau equation driven by a multiplicative noise of jump type. By a prior estimate, weak convergence and monotonicity technique, we prove the existence and uniqueness of the solution of an initial-boundary value problem with homogeneous Dirichlet boundary condition. However, for the generalized Ginzburg-Landau equation, such a locally monotonic condition of the nonlinear term can not be satisfied in a straight way. For this, we utilize the characteristic structure of nonlinear term and refined analysis to overcome this gap.

math.AP↗

arXiv2017

Convergence of adaptive compression methods for Hartree-Fock-like equations

The adaptively compressed exchange (ACE) method provides an efficient way for solving Hartree-Fock-like equations in quantum physics, chemistry, and materials science. The key step of the ACE method is to adaptively compress an operator that is possibly dense and full-rank. In this paper, we present a detailed study of the adaptive compression operation and establish rigorous convergence properties of the adaptive compression method in the context of solving linear eigenvalue problems. Our analysis also elucidates the potential use of the adaptive compression method in a wide range of problems.

math.NA↗

arXiv2017

Variational structure of Luttinger-Ward formalism and bold diagrammatic expansion for Euclidean lattice field theory

The Luttinger-Ward functional was proposed more than five decades ago to provide a link between static and dynamic quantities in a quantum many-body system. Despite its widespread usage, the derivation of the Luttinger-Ward functional remains valid only in the formal sense, and even the very existence of this functional has been challenged by recent numerical evidence. In a simpler and yet highly relevant regime, namely the Euclidean lattice field theory, we rigorously prove that the Luttinger-Ward functional is a well-defined universal functional over all physical Green's functions. Using the Luttinger-Ward functional, the free energy can be variationally minimized with respect to Green's functions in its domain. We then derive the widely used bold diagrammatic expansion rigorously, without relying on formal arguments such as partial resummation of bare diagrams to infinite order.

math-ph↗

arXiv2017

Interpolative Separable Density Fitting through Centroidal Voronoi Tessellation With Applications to Hybrid Functional Electronic Structure Calculations

The recently developed interpolative separable density fitting (ISDF) decomposition is a powerful way for compressing the redundant information in the set of orbital pairs, and has been used to accelerate quantum chemistry calculations in a number of contexts. The key ingredient of the ISDF decomposition is to select a set of non-uniform grid points, so that the values of the orbital pairs evaluated at such grid points can be used to accurately interpolate those evaluated at all grid points. The set of non-uniform grid points, called the interpolation points, can be automatically selected by a QR factorization with column pivoting (QRCP) procedure. This is the computationally most expensive step in the construction of the ISDF decomposition. In this work, we propose a new approach to find the interpolation points based on the centroidal Voronoi tessellation (CVT) method, which offers a much less expensive alternative to the QRCP procedure when ISDF is used in the context of hybrid functional electronic structure calculations. The CVT method only uses information from the electron density, and can be efficiently implemented using a K-Means algorithm. We find that this new method achieves comparable accuracy to the ISDF-QRCP method, at a cost that is negligible in the overall hybrid functional calculations. For instance, for a system containing $1000$ silicon atoms simulated using the HSE06 hybrid functional on $2000$ computational cores, the cost of QRCP-based method for finding the interpolation points costs $434.2$ seconds, while the CVT procedure only takes $3.2$ seconds. We also find that the ISDF-CVT method also enhances the smoothness of the potential energy surface in the context of \emph{ab initio} molecular dynamics (AIMD) simulations with hybrid functionals.

physics.comp-ph↗

arXiv2017

Strong Edge Magnetism and Tunable Energy Gaps in Zigzag Graphene Quantum Dots with High Stability

Graphene is a nonmagnetic semimetal and cannot be directly used as electronic or spintronic devices. We demonstrate that graphene quantum dots (GQDs) can exhibit strong edge magnetism and tunable energy gaps due to the presence of localized edge states. By using large-scale first principle density functional theory (DFT) calculations and detailed analysis based on model Hamiltonians, we can show that the zigzag edge states in GQDs become much stronger and more localized as the system size increases. The enhanced edge states induce strong electron-electron interactions along the edges of GQDs, ultimately resulting in a magnetic phase transition from nonmagnetic to intra-edge ferromagnetic and inter-edge antiferromagnetic, when the diameter is larger than 4.5 nm. Our analysis shows that the inter-edge superexchange interaction of antiferromagnetic states between two nearest-neighbor zigzag edges in GQDs is much stronger than that exists between two parallel zigzag edges in GQDs and graphene nanoribbons. Furthermore, such strong and localized edge states also induce GQDs semiconducting with tunable energy gaps, mainly controlled by adjusting the system size. Our results show that the quantum confinement effect, inter-edge superexchange (antiferromagnetic), and intra-edge direct exchange (ferromagnetic) interactions are crucial for the electronic and magnetic properties of zigzag GQDs at the nanoscale.

cond-mat.mtrl-sci↗