Deep Learning Topological Invariants of Band Insulators

In this work we design and train deep neural networks to predict topological invariants for one-dimensional four-band insulators in AIII class whose topological invariant is the winding number, and two-dimensional two-band insulators in A class whose topological invariant is the Chern number. Given Hamiltonians in the momentum space as the input, neural networks can predict topological invariants for both classes with accuracy close to or higher than 90%, even for Hamiltonians whose invariants are beyond the training data set. Despite the complexity of the neural network, we find that the output of certain intermediate hidden layers resembles either the winding angle for models in AIII class or the solid angle (Berry curvature) for models in A class, indicating that neural networks essentially capture the mathematical formula of topological invariants. Our work demonstrates the ability of neural networks to predict topological invariants for complicated models with local Hamiltonians as the only input, and offers an example that even a deep neural network is understandable.Comment: 8 pages, 5 figure

Efficient Learning of a One-dimensional Density Functional Theory

Density functional theory underlies the most successful and widely used numerical methods for electronic structure prediction of solids. However, it has the fundamental shortcoming that the universal density functional is unknown. In addition, the computational result---energy and charge density distribution of the ground state---is useful for electronic properties of solids mostly when reduced to a band structure interpretation based on the Kohn-Sham approach. Here, we demonstrate how machine learning algorithms can help to free density functional theory from these limitations. We study a theory of spinless fermions on a one-dimensional lattice. The density functional is implicitly represented by a neural network, which predicts, besides the ground-state energy and density distribution, density-density correlation functions. At no point do we require a band structure interpretation. The training data, obtained via exact diagonalization, feeds into a learning scheme inspired by active learning, which minimizes the computational costs for data generation. We show that the network results are of high quantitative accuracy and, despite learning on random potentials, capture both symmetry-breaking and topological phase transitions correctly.Comment: 5 pages, 3 figures; 4+ pages appendi

The Boston University Photonics Center annual report 2016-2017

This repository item contains an annual report that summarizes activities of the Boston University Photonics Center in the 2016-2017 academic year. The report provides quantitative and descriptive information regarding photonics programs in education, interdisciplinary research, business innovation, and technology development. The Boston University Photonics Center (BUPC) is an interdisciplinary hub for education, research, scholarship, innovation, and technology development associated with practical uses of light.This has undoubtedly been the Photonics Center’s best year since I became Director 10 years ago. In the following pages, you will see highlights of the Center’s activities in the past year, including more than 100 notable scholarly publications in the leading journals in our field, and the attraction of more than 22 million dollars in new research grants/contracts. Last year I had the honor to lead an international search for the first recipient of the Moustakas Endowed Professorship in Optics and Photonics, in collaboration with ECE Department Chair Clem Karl. This professorship honors the Center’s most impactful scholar and one of the Center’s founding visionaries, Professor Theodore Moustakas. We are delighted to haveawarded this professorship to Professor Ji-Xin Cheng, who joined our faculty this year.The past year also marked the launch of Boston University’s Neurophotonics Center, which will be allied closely with the Photonics Center. Leading that Center will be a distinguished new faculty member, Professor David Boas. David and I are together leading a new Neurophotonics NSF Research Traineeship Program that will provide $3M to promote graduate traineeships in this emerging new field. We had a busy summer hosting NSF Sites for Research Experiences for Undergraduates, Research Experiences for Teachers, and the BU Student Satellite Program. As a community, we emphasized the theme of “Optics of Cancer Imaging” at our annual symposium, hosted by Darren Roblyer. We entered a five-year second phase of NSF funding in our Industry/University Collaborative Research Center on Biophotonic Sensors and Systems, which has become the centerpiece of our translational biophotonics program. That I/UCRC continues to focus on advancing the health care and medical device industries

Probing criticality in quantum spin chains with neural networks

The numerical emulation of quantum systems often requires an exponential number of degrees of freedom which translates to a computational bottleneck. Methods of machine learning have been used in adjacent fields for effective feature extraction and dimensionality reduction of high-dimensional datasets. Recent studies have revealed that neural networks are further suitable for the determination of macroscopic phases of matter and associated phase transitions as well as efficient quantum state representation. In this work, we address quantum phase transitions in quantum spin chains, namely the transverse field Ising chain and the anisotropic XY chain, and show that even neural networks with no hidden layers can be effectively trained to distinguish between magnetically ordered and disordered phases. Our neural network acts to predict the corresponding crossovers finite-size systems undergo. Our results extend to a wide class of interacting quantum many-body systems and illustrate the wide applicability of neural networks to many-body quantum physics.Comment: 14pp, 9 figures, IoP clas