Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session E18: Machine Learning Quantum States IFocus

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Sponsoring Units: DCOMP DCMP DAMOP Chair: Yizhuang You, Harvard University Room: BCEC 156B 
Tuesday, March 5, 2019 8:00AM  8:36AM 
E18.00001: Learning quantum states with generative models Invited Speaker: Juan Carrasquilla The technological success of machine learning techniques has motivated a research area in the condensed matter physics and quantum information communities, where new tools and conceptual connections between machine learning and manybody physics are rapidly developing. In this talk, I will discuss the use of generative models for learning quantum states. In particular, I will discuss a strategy for learning mixed states through a combination of informationally complete positiveoperator valued measures and generative models. In this setting, generative models enable accurate learning of prototypical quantum states of large size directly from measurements mimicking experimental data. 
Tuesday, March 5, 2019 8:36AM  8:48AM 
E18.00002: Machine Learning Holography in Neural Network Renormalization Group Hongye Hu, ShuoHui Li, Lei Wang, Yizhuang You Previously, people have shown the close relations between renormalization group(RG) with both deep learning and holographic duality, and how holographic geometry can emerge from deep learning the entanglement feature of a quantum manybody state. Inspired by those, we propose any boundary conformal field theory can be mapped into its holographic bulk to an operator level. In our framework, renormalization group is constructed as a hierarchical unsupervised generative model. Coarse graining direction can be viewed as an emergent direction, and it pushes boundary field theory configurations to bulk field configurations. The inverse coarse graining direction generates boundary field configurations from bulk noises. The goal is to construct optimal RG that makes bulk variables as uncorrelated as possible. The leftover of correlations between bulk variables can be used to define measure of distance in the bulk. We studied two dimensional interacting bosonic system as a boundary field theory. RG network is trained to find the effective bulk field theory and we observed the emergence of hyperbolic geometry(AdS3 spatial geometry) as we tuned system towards critical point. 
Tuesday, March 5, 2019 8:48AM  9:00AM 
E18.00003: ABSTRACT WITHDRAWN

Tuesday, March 5, 2019 9:00AM  9:12AM 
E18.00004: Analytic continuation by combining sparse modeling with the Pade approximation Yuichi Motoyama, Kazuyoshi Yoshimi, Junya Otsuki, Hiroshi Shinaoka Numerical methods based on the imaginarytime pathintegral such as the pathintegral Monte Carlo method are powerful tools to investigate a quantum manybody system both at absolute zero and finite temperatures. For example, these can calculate the imaginarytime Green's function directly, and other important quantities such as spectrum function can be transformed from this by the analytic continuation (AC) or by solving the Lehmann representation as an integral equation. In practice, however, this transformation is unstable against noise of the imaginarytime Green's function. 
Tuesday, March 5, 2019 9:12AM  9:24AM 
E18.00005: A machine learning approach to excited states of quantum manybody systems Douglas Hendry, Adrian Feiguin We present a variational Monte Carlo method for determining dynamical properties and the spectral function of quantum manybody systems. Restricted Boltzmann machines (RBMs) are used to encode the Green's function of the system. First, the ground state wave function is calculated using a standard variational approach. The dynamical correlation function is then obtained by solving two linear systems of equations. We present a variational Monte Carlo approach to do so. This process has to be repeated for each value of frequency and momentum, but it can be easily parallelized. We illustrate it with applications to the Heisenberg model in one and two dimensions. Results show remarkable agreement with exact calculations on small systems and demonstrate that RBMs can also faithfully represent excited states. 
Tuesday, March 5, 2019 9:24AM  9:36AM 
E18.00006: Machine Learning Spatial Geometry from Entanglement Features Yizhuang You Motivated by the close relations of the renormalization group with both the holography duality and the deep learning, we propose that the holographic geometry can emerge from deep learning the entanglement feature of a quantum manybody state. We develop a concrete algorithm, call the entanglement feature learning (EFL), based on the random tensor network (RTN) model for the tensor network holography. We show that each RTN can be mapped to a Boltzmann machine, trained by the entanglement entropies over all subregions of a given quantum manybody state. The goal is to construct the optimal RTN that best reproduce the entanglement feature. The RTN geometry can then be interpreted as the emergent holographic geometry. We demonstrate the EFL algorithm on 1D free fermion system and observe the emergence of the hyperbolic geometry (AdS3 spatial geometry) as we tune the fermion system towards the gapless critical point (CFT2 point). 
Tuesday, March 5, 2019 9:36AM  9:48AM 
E18.00007: Machine learning manybody localization: Search for the elusive nonergodic metal Xiao Li, YiTing Hsu, DongLing Deng The manybody localization transition in isolated quantum systems with a singleparticle mobility edge is an intriguing subject that has not yet been fully understood. In particular, whether a nonergodic metallic phase associated with a manybody mobility edge exists or not is under active debate. In this Letter, we construct a neural network classifier to investigate the existence of the nonergodic metallic phase in a prototype model using manybody entanglement spectra as the sole diagnostic. We find that such a classifier is able to identify with high confidence the nonergodic metallic phase existing between the manybody localized and the thermal phase. Our neural network based approach shows how supervised machine learning can be applied not only in locating phase boundaries, but also in providing a way to definitively examine the existence of a novel phase whose existence is unclear. 
Tuesday, March 5, 2019 9:48AM  10:00AM 
E18.00008: Machine learning of condensedmatter phases with physical interpretability Ming Han, Zonghui Wei, Erik Luijten Nature displays a vast variety of phase transitions. Detecting and quantifying these often requires creative design of order parameters, which are strongly system dependent. Thanks to recent advances in machine learning (ML), it is now possible to identify phase behavior by directly analyzing atomistic configurations via modern patternrecognition techniques. Whereas these ML approaches are universal and robust, they often suffer from the lack of physical interpretability. Here we introduce a new ML scheme, which distinguishes different condensedmatter phases by autonomously recognizing order parameters. When applied to twodimensional Ising models, our method can accurately predict the Curie and Néel temperatures and capture the corresponding critical phenomena by recognizing ferro and antiferromagnetizations, respectively. Going beyond these prototypical test cases, we analyze the nonequilibrium polymeric sol–gel transition, locating not only the transition temperature, but also discovering two classes of underlying collective behavior, the condensation and networkformation modes. Compared to existing MLs, our method offers physical insights as well as high training efficiency. 
Tuesday, March 5, 2019 10:00AM  10:12AM 
E18.00009: Interpretable Machine Learning Study of ManyBody Localization Transition in Disordered Quantum Spin Chains Wei Zhang, Lei Wang, Ziqiang Wang We develop, train, and apply a support vector machine (SVM) to study the phase transition between manybody localized and thermal phases in a disordered quantum Ising chain. We use the labeled probability density of eigenstate wavefunctions in the deeply localized and thermal regimes at two different energy densities as the training set. We find that the trained SVM is then able to predict the whole phase diagram. The obtained phase boundary qualitatively agrees with previous work using entanglement entropy to characterize these two phases. We further analyze the decision function of the SVM to interpret its physical meaning and find that it is analogous to the inverse participation ratio in the manybody configuration space. Our findings demonstrate the ability of the SVM to capture potential quantities that may characterize the manybody localization phase transition. The qualitative agreement of phase boundary obtained by SVM and by scaling entanglement entropy motivates further exploration of the relation between these two different quantities in connection to manybody localization. 
Tuesday, March 5, 2019 10:12AM  10:24AM 
E18.00010: Analytic continuation via “domainknowledge free” machine learning Hongkee Yoon, JaeHoon Sim, Myung Joon Han We present a machinelearning (ML) approach to a longstanding issue in quantum manybody physics, namely, analytic continuation. This notorious illconditioned problem of obtaining spectral function from Green’s function has been a focus of new method developments for past decades. Here we demonstrate the usefulness of modern ML techniques including convolutional neural networks and the variants of stochastic gradient descent optimizer. ML continuation kernel is successfully realized without any ‘domainknowledge’, which means that any physical ‘prior’ is not utilized in the kernel construction and the neural networks ‘learn’ the knowledge solely from ‘training’. The outstanding performance is achieved for both insulating and metallic band structure. Our MLbased approach not only provides the more accurate spectrum than the conventional methods in terms of peak positions and heights, but is also more robust against the noise which is the required key feature for any continuation technique to be successful [1]. Furthermore, its computation speed is 10^{4}–10^{5} times faster than maximum entropy method. 
Tuesday, March 5, 2019 10:24AM  10:36AM 
E18.00011: Monte Carlo Renormalization Group for Systems with Quenched Disorder Yantao Wu, Roberto Car We extend to quenched disordered systems the variational scheme for real space renormalization 
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