arXiv subjects

Lin Lin

Publications and source records attributed to Lin Lin.

At least 217 records · Page 12Linked to original sources

arXiv2020

SIESTA: recent developments and applications

A review of the present status, recent enhancements, and applicability of the SIESTA program is presented. Since its debut in the mid-nineties, SIESTA's flexibility, efficiency and free distribution has given advanced materials simulation capabilities to many groups worldwide. The core methodological scheme of SIESTA combines finite-support pseudo-atomic orbitals as basis sets, norm-conserving pseudopotentials, and a real-space grid for the representation of charge density and potentials and the computation of their associated matrix elements. Here we describe the more recent implementations on top of that core scheme, which include: full spin-orbit interaction, non-repeated and multiple-contact ballistic electron transport, DFT+U and hybrid functionals, time-dependent DFT, novel reduced-scaling solvers, density-functional perturbation theory, efficient Van der Waals non-local density functionals, and enhanced molecular-dynamics options. In addition, a substantial effort has been made in enhancing interoperability and interfacing with other codes and utilities, such as Wannier90 and the second-principles modelling it can be used for, an AiiDA plugin for workflow automatization, interface to Lua for steering SIESTA runs, and various postprocessing utilities. SIESTA has also been engaged in the Electronic Structure Library effort from its inception, which has allowed the sharing of various low level libraries, as well as data standards and support for them, in particular the PSML definition and library for transferable pseudopotentials, and the interface to the ELSI library of solvers. Code sharing is made easier by the new open-source licensing model of the program. This review also presents examples of application of the capabilities of the code, as well as a view of on-going and future developments.

physics.comp-ph↗

arXiv2020

Quenching as a Contest between Galaxy Halos and their Central Black Holes

Existing models of galaxy formation have not yet explained striking correlations between structure and star-formation activity in galaxies, notably the sloped and moving boundaries that divide star-forming from quenched galaxies in key structural diagrams. This paper uses these and other relations to ``reverse-engineer'' the quenching process for central galaxies. The basic idea is that star-forming galaxies with larger radii (at a given stellar mass) have lower black-hole masses due to lower central densities. Galaxies cross into the green valley when the cumulative effective energy radiated by their black hole equals $\sim4\times$ their halo-gas binding energy. Since larger-radii galaxies have smaller black holes, one finds they must evolve to higher stellar masses in order to meet this halo-energy criterion, which explains the sloping boundaries. A possible cause of radii differences among star-forming galaxies is halo concentration. The evolutionary tracks of star-forming galaxies are nearly parallel to the green-valley boundaries, and it is mainly the sideways motions of these boundaries with cosmic time that cause galaxies to quench. BH-scaling laws for star-forming, quenched, and green-valley galaxies are different, and most BH mass growth takes place in the green valley. Implications include: the radii of star-forming galaxies are an important second parameter in shaping their black holes; black holes are connected to their halos but in different ways for star-forming, quenched, and green-valley galaxies; and the same BH-halo quenching mechanism has been in place since $z \sim 3$. We conclude with a discussion of black hole-galaxy co-evolution, the origin and interpretation of BH scaling laws.

astro-ph.GA↗

arXiv2020

Stochastic Constrained Extended System Dynamics for Solving Charge Equilibration Models

We present a new stochastic extended Lagrangian solution to charge equilibration that eliminates self-consistent field (SCF) calculations, eliminating the computational bottleneck in solving the many-body solution with standard SCF solvers. By formulating both charges and chemical potential as latent variables, and introducing a holonomic constraint that satisfies charge conservation, the SC-XLMD method accurately reproduces structural, thermodynamic, and dynamics properties using ReaxFF, and shows excellent weak- and strong-scaling performance in the LAMMPS molecular simulation package.

physics.comp-ph↗

arXiv2020

Policy Gradient based Quantum Approximate Optimization Algorithm

The quantum approximate optimization algorithm (QAOA), as a hybrid quantum/classical algorithm, has received much interest recently. QAOA can also be viewed as a variational ansatz for quantum control. However, its direct application to emergent quantum technology encounters additional physical constraints: (i) the states of the quantum system are not observable; (ii) obtaining the derivatives of the objective function can be computationally expensive or even inaccessible in experiments, and (iii) the values of the objective function may be sensitive to various sources of uncertainty, as is the case for noisy intermediate-scale quantum (NISQ) devices. Taking such constraints into account, we show that policy-gradient-based reinforcement learning (RL) algorithms are well suited for optimizing the variational parameters of QAOA in a noise-robust fashion, opening up the way for developing RL techniques for continuous quantum control. This is advantageous to help mitigate and monitor the potentially unknown sources of errors in modern quantum simulators. We analyze the performance of the algorithm for quantum state transfer problems in single- and multi-qubit systems, subject to various sources of noise such as error terms in the Hamiltonian, or quantum uncertainty in the measurement process. We show that, in noisy setups, it is capable of outperforming state-of-the-art existing optimization algorithms.

quant-ph↗

arXiv2020

Learning the mapping $\mathbf{x}\mapsto \sum_{i=1}^d x_i^2$: the cost of finding the needle in a haystack

The task of using machine learning to approximate the mapping $\mathbf{x}\mapsto\sum_{i=1}^d x_i^2$ with $x_i\in[-1,1]$ seems to be a trivial one. Given the knowledge of the separable structure of the function, one can design a sparse network to represent the function very accurately, or even exactly. When such structural information is not available, and we may only use a dense neural network, the optimization procedure to find the sparse network embedded in the dense network is similar to finding the needle in a haystack, using a given number of samples of the function. We demonstrate that the cost (measured by sample complexity) of finding the needle is directly related to the Barron norm of the function. While only a small number of samples is needed to train a sparse network, the dense network trained with the same number of samples exhibits large test loss and a large generalization gap. In order to control the size of the generalization gap, we find that the use of explicit regularization becomes increasingly more important as $d$ increases. The numerically observed sample complexity with explicit regularization scales as $\mathcal{O}(d^{2.5})$, which is in fact better than the theoretically predicted sample complexity that scales as $\mathcal{O}(d^{4})$. Without explicit regularization (also called implicit regularization), the numerically observed sample complexity is significantly higher and is close to $\mathcal{O}(d^{4.5})$.

cs.LG↗

arXiv2020

Sparsity pattern of the self-energy for classical and quantum impurity problems

We prove that for various impurity models, in both classical and quantum settings, the self-energy matrix is a sparse matrix with a sparsity pattern determined by the impurity sites. In the quantum setting, such a sparsity pattern has been known since Feynman. Indeed, it underlies several numerical methods for solving impurity problems, as well as many approaches to more general quantum many-body problems, such as the dynamical mean field theory. The sparsity pattern is easily motivated by a formal perturbative expansion using Feynman diagrams. However, to the extent of our knowledge, a rigorous proof has not appeared in the literature. In the classical setting, analogous considerations lead to a perhaps less-known result, i.e., that the precision matrix of a Gibbs measure of a certain kind differs only by a sparse matrix from the precision matrix of a corresponding Gaussian measure. Our argument for this result mainly involves elementary algebraic manipulations and is in particular non-perturbative. Nonetheless, the proof can be robustly adapted to various settings of interest in physics, including quantum systems (both fermionic and bosonic) at zero and finite temperature, non-equilibrium systems, and superconducting systems.

math-ph↗

arXiv2020

Structural and Stellar Population Properties vs. Bulge Types in Sloan Digital Sky Survey Central Galaxies

This paper studies pseudo-bulges (P-bulges) and classical bulges (C-bulges) in Sloan Digital Sky Survey central galaxies using the new bulge indicator $ΔΣ_1$, which measures relative central stellar-mass surface density within 1 kpc. We compare $ΔΣ_1$ to the established bulge-type indicator $Δ\langleμ_e\rangle$ from Gadotti (2009) and show that classifying by $ΔΣ_1$ agrees well with $Δ\langleμ_e\rangle$. $ΔΣ_1$ requires no bulge-disk decomposition and can be measured on SDSS images out to $z = 0.07$. Bulge types using it are mapped onto twenty different structural and stellar-population properties for 12,000 SDSS central galaxies with masses 10.0 < log $M_*$/$M_{\odot}$ < 10.4. New trends emerge from this large sample. Structural parameters show fairly linear log-log relations vs. $ΔΣ_1$ and $Δ\langleμ_e\rangle$ with only moderate scatter, while stellar-population parameters show a highly non-linear "elbow" in which specific star-formation rate remains roughly flat with increasing central density and then falls rapidly at the elbow, where galaxies begin to quench. P-bulges occupy the low-density end of the horizontal arm of the elbow and are universally star-forming, while C-bulges occupy the elbow and the vertical branch and exhibit a wide range of star-formation rates at fixed density. The non-linear relation between central density and star-formation rate has been seen before, but this mapping onto bulge class is new. The wide range of star-formation rates in C-bulges helps to explain why bulge classifications using different parameters have sometimes disagreed in the past. The elbow-shaped relation between density and stellar indices suggests that central structure and stellar-populations evolve at different rates as galaxies begin to quench.

astro-ph.GA↗

arXiv2020

Convergence of Stochastic-extended Lagrangian molecular dynamics method for polarizable force field simulation

Extended Lagrangian molecular dynamics (XLMD) is a general method for performing molecular dynamics simulations using quantum and classical many-body potentials. Recently several new XLMD schemes have been proposed and tested on several classes of many-body polarization models such as induced dipoles or Drude charges, by creating an auxiliary set of these same degrees of freedom that are reversibly integrated through time. This gives rise to a singularly perturbed Hamiltonian system that provides a good approximation to the time evolution of the real mutual polarization field. To further improve upon the accuracy of the XLMD dynamics, and to potentially extend it to other many-body potentials, we introduce a stochastic modification which leads to a set of singularly perturbed Langevin equations with degenerate noise. We prove that the resulting Stochastic-XLMD converges to the accurate dynamics, and the convergence rate is both optimal and is independent of the accuracy of the initial polarization field. We carefully study the scaling of the damping factor and numerical noise for efficient numerical simulation for Stochastic-XLMD, and we demonstrate the effectiveness of the method for model polarizable force field systems.

math.NA↗

arXiv2020

Enhancing robustness and efficiency of density matrix embedding theory via semidefinite programming and local correlation potential fitting

Density matrix embedding theory (DMET) is a powerful quantum embedding method for solving strongly correlated quantum systems. Theoretically, the performance of a quantum embedding method should be limited by the computational cost of the impurity solver. However, the practical performance of DMET is often hindered by the numerical stability and the computational time of the correlation potential fitting procedure, which is defined on a single-particle level. Of particular difficulty are cases in which the effective single-particle system is gapless or nearly gapless. To alleviate these issues, we develop a semidefinite programming (SDP) based approach that can significantly enhance the robustness of the correlation potential fitting procedure compared to the traditional least squares fitting approach. We also develop a local correlation potential fitting approach, which allows one to identify the correlation potential from each fragment independently in each self-consistent field iteration, avoiding any optimization at the global level. We prove that the self-consistent solutions of DMET using this local correlation potential fitting procedure are equivalent to those of the original DMET with global fitting. We find that our combined approach, called L-DMET, in which we solve local fitting problems via semidefinite programming, can significantly improve both the robustness and the efficiency of DMET calculations. We demonstrate the performance of L-DMET on the 2D Hubbard model and the hydrogen chain. We also demonstrate with theoretical and numerical evidence that the use of a large fragment size can be a fundamental source of numerical instability in the DMET procedure.

physics.comp-ph↗

arXiv2020

Quantum Dynamics with the Parallel Transport Gauge

The dynamics of a closed quantum system is often studied with the direct evolution of the Schrodinger equation. In this paper, we propose that the gauge choice (i.e. degrees of freedom irrelevant to physical observables) of the Schrodinger equation can be generally non-optimal for numerical simulation. This can limit, and in some cases severely limit the time step size. We find that the optimal gauge choice is given by a parallel transport formulation. This parallel transport dynamics can be simply interpreted as the dynamics driven by the residual vectors, analogous to those defined in eigenvalue problems in the time-independent setup. The parallel transport dynamics can be derived from a Hamiltonian structure, thus suitable to be solved using a symplectic and implicit time discretization scheme, such as the implicit midpoint rule, which allows the usage of a large time step and ensures the long time numerical stability. We analyze the parallel transport dynamics in the context of the singularly perturbed linear Schrodinger equation, and demonstrate its superior performance in the near adiabatic regime. We demonstrate the effectiveness of our method using numerical results for linear and nonlinear Schrodinger equations, as well as the time-dependent density functional theory (TDDFT) calculations for electrons in a benzene molecule driven by an ultrashort laser pulse.

math.NA↗

arXiv2020

Split representation of adaptively compressed polarizability operator

The polarizability operator plays a central role in density functional perturbation theory and other perturbative treatment of first principle electronic structure theories. The cost of computing the polarizability operator generally scales as $\mathcal{O}(N_{e}^4)$ where $N_e$ is the number of electrons in the system. The recently developed adaptively compressed polarizability operator (ACP) formulation [L. Lin, Z. Xu and L. Ying, Multiscale Model. Simul. 2017] reduces such complexity to $\mathcal{O}(N_{e}^3)$ in the context of phonon calculations with a large basis set for the first time, and demonstrates its effectiveness for model problems. In this paper, we improve the performance of the ACP formulation by splitting the polarizability into a near singular component that is statically compressed, and a smooth component that is adaptively compressed. The new split representation maintains the $\mathcal{O}(N_e^3)$ complexity, and accelerates nearly all components of the ACP formulation, including Chebyshev interpolation of energy levels, iterative solution of Sternheimer equations, and convergence of the Dyson equations. For simulation of real materials, we discuss how to incorporate nonlocal pseudopotentials and finite temperature effects. We demonstrate the effectiveness of our method using one-dimensional model problem in insulating and metallic regimes, as well as its accuracy for real molecules and solids.

physics.comp-ph↗

arXiv2020

Efficient hybridization fitting for dynamical mean-field theory via semi-definite relaxation

We introduce a nested optimization procedure using semi-definite relaxation for the fitting step in Hamiltonian-based cluster dynamical mean-field theory (DMFT) methodologies. We show that the proposed method is more efficient and flexible than state-of-the-art fitting schemes, which allows us to treat as large a number of bath sites as the impurity solver at hand allows. We characterize its robustness to initial conditions and symmetry constraints, thus providing conclusive evidence that in the presence of a large bath, our semi-definite relaxation approach can find the correct set of bath parameters without needing to include \emph{a priori} knowledge of the properties that are to be described. We believe this method will be of great use for Hamiltonian-based calculations, simplifying and improving one of the key steps in cluster dynamical mean-field theory calculations.

cond-mat.str-el↗

arXiv2020

Variational embedding for quantum many-body problems

Quantum embedding theories are powerful tools for approximately solving large-scale strongly correlated quantum many-body problems. The main idea of quantum embedding is to glue together a highly accurate quantum theory at the local scale and a less accurate quantum theory at the global scale. We introduce the first quantum embedding theory that is also variational, in that it is guaranteed to provide a one-sided bound for the exact ground-state energy. Our method, which we call the variational embedding method, provides a lower bound for this quantity. The method relaxes the representability conditions for quantum marginals to a set of linear and semidefinite constraints that operate at both local and global scales, resulting in a semidefinite program (SDP) to be solved numerically. The accuracy of the method can be systematically improved. The method is versatile and can be applied, in particular, to quantum many-body problems for both quantum spin systems and fermionic systems, such as those arising from electronic structure calculations. We describe how the proper notion of quantum marginal, sufficiently general to accommodate both of these settings, should be phrased in terms of certain algebras of operators. We also investigate the duality theory for our SDPs, which offers valuable perspective on our method as an embedding theory. As a byproduct of this investigation, we describe a formulation for efficiently implementing the variational embedding method via a partial dualization procedure and the solution of quantum analogs of the Kantorovich problem from optimal transport theory.

physics.comp-ph↗

arXiv2019

Numerical solution of large scale Hartree-Fock-Bogoliubov equations

The Hartree-Fock-Bogoliubov (HFB) theory is the starting point for treating superconducting systems. However, the computational cost for solving large scale HFB equations can be much larger than that of the Hartree-Fock equations, particularly when the Hamiltonian matrix is sparse, and the number of electrons $N$ is relatively small compared to the matrix size $N_{b}$. We first provide a concise and relatively self-contained review of the HFB theory for general finite sized quantum systems, with special focus on the treatment of spin symmetries from a linear algebra perspective. We then demonstrate that the pole expansion and selected inversion (PEXSI) method can be particularly well suited for solving large scale HFB equations. For a Hubbard-type Hamiltonian, the cost of PEXSI is at most $\Or(N_b^2)$ for both gapped and gapless systems, which can be significantly faster than the standard cubic scaling diagonalization methods. We show that PEXSI can solve a two-dimensional Hubbard-Hofstadter model with $N_b$ up to $2.88\times 10^6$, and the wall clock time is less than $100$ s using $17280$ CPU cores. This enables the simulation of physical systems under experimentally realizable magnetic fields, which cannot be otherwise simulated with smaller systems.

physics.comp-ph↗

arXiv2019

Deep Density: circumventing the Kohn-Sham equations via symmetry preserving neural networks

The recently developed Deep Potential [Phys. Rev. Lett. 120, 143001, 2018] is a powerful method to represent general inter-atomic potentials using deep neural networks. The success of Deep Potential rests on the proper treatment of locality and symmetry properties of each component of the network. In this paper, we leverage its network structure to effectively represent the mapping from the atomic configuration to the electron density in Kohn-Sham density function theory (KS-DFT). By directly targeting at the self-consistent electron density, we demonstrate that the adapted network architecture, called the Deep Density, can effectively represent the electron density as the linear combination of contributions from many local clusters. The network is constructed to satisfy the translation, rotation, and permutation symmetries, and is designed to be transferable to different system sizes. We demonstrate that using a relatively small number of training snapshots, Deep Density achieves excellent performance for one-dimensional insulating and metallic systems, as well as systems with mixed insulating and metallic characters. We also demonstrate its performance for real three-dimensional systems, including small organic molecules, as well as extended systems such as water (up to $512$ molecules) and aluminum (up to $256$ atoms).

physics.comp-ph↗

arXiv2019

A multiscale neural network based on hierarchical matrices

In this work we introduce a new multiscale artificial neural network based on the structure of $\mathcal{H}$-matrices. This network generalizes the latter to the nonlinear case by introducing a local deep neural network at each spatial scale. Numerical results indicate that the network is able to efficiently approximate discrete nonlinear maps obtained from discretized nonlinear partial differential equations, such as those arising from nonlinear Schrödinger equations and the Kohn-Sham density functional theory.

math.NA↗

arXiv2019

Estimating the molecular gas mass of low-redshift galaxies from a combination of mid-infrared luminosity and optical properties

We present CO(J=1-0) and/or CO(J=2-1) spectroscopy for 31 galaxies selected from the ongoing MaNGA survey, obtained with multiple telescopes. This sample is combined with CO observations from the literature to study the correlation of the CO luminosities ($L_{\rm CO(1-0)}$) with the mid-infrared luminosities at 12 ($L_{12 μm}$) and 22 $μ$m ($L_{\rm 22 μm}$), as well as the dependence of the residuals on a variety of galaxy properties. The correlation with $L_{\rm 12 μm}$ is tighter and more linear, but galaxies with relatively low stellar masses and blue colors fall significantly below the mean $L_{\rm CO(1-0)}-L_{\rm 12μm}$ relation. We propose a new estimator of the CO(1-0) luminosity (and thus the total molecular gas mass) that is a linear combination of three parameters: $L_{\rm 12 μm}$, $M_\ast$ and $g-r$. We show that, with a scatter of only 0.18 dex in log $(L_{\rm CO(1-0)})$, this estimator provides unbiased estimates for galaxies of different properties and types. An immediate application of this estimator to a compiled sample of galaxies with only CO(J=2-1) observations yields a distribution of the CO(J=2-1) to CO(J=1-0) luminosity ratios ($R21$) that agrees well with the distribution of real observations, in terms of both the median and the shape. Application of our estimator to the current MaNGA sample reveals a gas-poor population of galaxies that are predominantly early-type and show no correlation between molecular gas-to-stellar mass ratio and star formation rate, in contrast to gas-rich galaxies. We also provide alternative estimators with similar scatters, based on $r$ and/or $z$ band luminosities instead of $M_\ast$. These estimators serve as cheap and convenient $M_{\rm mol}$ proxies to be potentially applied to large samples of galaxies, thus allowing statistical studies of gas-related processes of galaxies.

astro-ph.GA↗

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↗