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Siesta: recent developments and applications

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arXiv 2020年

作者： García, Alberto Papior, Nick Akhtar, Arsalan Artacho, Emilio Blum, Volker Bosoni, Emanuele Brandimarte, Pedro Brandbyge, Mads Cerdá, J.I. Corsetti, Fabiano Cuadrado, Ramón Dikan, Vladimir Ferrer, Jaime Gale, Julian García-Fernández, Pablo García-Suárez, V.M. García, Sandra Huhs, Georg Illera, Sergio Korytár, Richard Koval, Peter Lebedeva, Irina Lin, Lin López-Tarifa, Pablo Mayo, Sara G. Mohr, Stephan Ordejón, Pablo Postnikov, Andrei Pouillon, Yann Pruneda, Miguel Robles, Roberto Sánchez-Portal, Daniel Soler, Jose M. Ullah, Rafi Wen-zhe Yu, Victor Junquera, Javier BellaterraE-08193 Spain DTU Computing Center Technical University of Denmark 2800 Kgs Lyngby Denmark Catalan Institute of Nanoscience Nanotechnology - ICN2 CSIC and BIST Campus UAB Bellaterra08193 Spain CIC Nanogune BRTA Tolosa Hiribidea 76 San Sebastián20018 Spain Paseo Manuel de Lardizabal 4 Donostia-San Sebastian20018 Spain Ikerbasque Basque Foundation for Science Bilbao48011 Spain Theory of Condensed Matter Cavendish Laboratory University of Cambridge CambridgeCB3 0HE United Kingdom Department of Mechanical Engineering and Materials Science Duke University DurhamNC27708 United States Department of Chemistry Duke University DurhamNC27708 United States Technical University of Denmark Kgs. LyngbyDK-2800 Denmark Instituto de Ciencia de Materiales de Madrid ICMM-CSIC Cantoblanco Madrid28049 Spain Department of Physics University of Oviedo Oviedo33007 Spain Nanomaterials and Nanotechnology Research Center CSIC - Universidad de Oviedo Oviedo33007 Spain School of Molecular and Life Sciences Curtin University PO Box U1987 PerthWA6845 Australia Departamento de Ciencias de la Tierra y Física de la Materia Condensada Universidad de Cantabria Cantabria Campus Internacional Avenida de los Castros s/n Santander39005 Spain Barcelona Supercomputing Center c/ Jordi Girona 29 Barcelona08034 Spain Department of Condensed Matter Physics Faculty of Mathematics and Physics Charles University Ke Karlovu 5 Praha 2121 16 Czech Republic Simune Atomistics S.L. Tolosa Hiribidea 76 Donostia-San Sebastian20018 Spain Department of Mathematics University of California BerkeleyCA94720 United States Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Centro de Física de Materiales Centro Mixto CSIC-UPV/EHU Paseo Manuel de Lardizabal 5 Donostia-San Sebastian20018 Spain Departamento de Física de la Materia Condensada Universidad Autónoma de Madrid Madrid28049 Spain LCP-A2MC Université de Lor

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. Copyright © 2020, The Authors. All rights reserved.

关键词： Density functional theory

Zirconia and hafnia polymorphs-ground state structural properties from diffusion Monte Carlo

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arXiv 2017年

作者： Shin, Hyeondeok Benali, Anouar Luo, Ye Crabb, Emily Lopez-Bezanilla, Alejandro Ratcliff, Laura E. Jokisaari, Andrea M. Heinonen, Olle Computational Sciences Division Argonne National Laboratory ArgonneIL60439 United States Argonne Leadership Computing Facility Argonne National Laboratory LemontIL60439 United States Computational Sciences Division Argonne National Laboratory ArgonneIL60439 United States Department of Physics Massachusetts Institute of Technology CambridgeMA02139 United States Materials Science Division Argonne National Laboratory LemontIL60439 United States Department of Materials Imperial College London LondonSW7 2AZ United Kingdom Northwestern-Argonne Institute of Science and Engineering Northwestern University EvanstonIL60208 United States

Zirconia (zirconium dioxide) and hafnia (hafnium dioxide) are binary oxides used in a range of applications. Because zirconium and hafnium are chemically equivalent, they have three similar polymorphs, and it is important to understand the properties and energetics of these polymorphs. However, while density functional theory calculations can get the correct energetic ordering, the energy differences between polymorphs depend very much on the specific density functional theory approach, as do other quantities such as lattice constants and bulk modulus. We have used highly accurate quantum Monte Carlo simulations to model the three zirconia and hafnia polymorphs. We compare our results for structural parameters, bulk modulus, and cohesive energy with results obtained from density functional theory calculations. We also discuss comparisons of our results with existing experimental data, in particular for structural parameters where extrapolation to zero temperature can be attempted. We hope our results of structural parameters as well as for cohesive energy and bulk modulus can serve as benchmarks for density-functional theory based calculations and as a guidance for future experiments. Copyright © 2017, The Authors. All rights reserved.

关键词： Zirconia

Deep learning for multi-messenger astrophysics a gateway for discovery in the big data era

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arXiv 2019年

作者： Allen, Gabrielle Andreoni, Igor Bachelet, Etienne Bruce Berriman, G. Bianco, Federica B. Biswas, Rahul Kind, Matias Carrasco Chard, Kyle Cho, Minsik Cowperthwaite, Philip S. Etienne, Zachariah B. George, Daniel Gibbs, Tom Graham, Matthew Gropp, William Gupta, Anushri Haas, Roland Huerta, E.A. Jennings, Elise Katz, Daniel S. Khan, Asad Kindratenko, Volodymyr Kramer, William T.C. Liu, Xin Mahabal, Ashish McHenry, Kenton Miller, J.M. Neubauer, M.S. Oberlin, Steve Olivas, Alexander R. Rosofsky, Shawn Ruiz, Milton Saxton, Aaron Schutz, Bernard Schwing, Alex Seidel, Ed Shapiro, Stuart L. Shen, Hongyu Shen, Yue Sipocz, Brigitta M. Sun, Lunan Towns, John Tsokaros, Antonios Wei, Wei Wells, Jack Williams, Timothy J. Xiong, Jinjun Zhao, Zhizhen NCSA University of Illinois at Urbana-Champaign UrbanaIL61801 United States Department of Astronomy University of Illinois at Urbana-Champaign UrbanaIL61801 United States California Institute of Technology 1200 E California Blvd PasadenaCA91125 United States Las Cumbres Observatory 6740 Cortona Drive Suite 102 GoletaCA93117 United States Caltech/IPAC-NExScI 1200 E California Blvd PasadenaCA91125 United States Department of Physics and Astronomy University of Delaware NewarkDE19716 United States Joseph R. Biden Jr . School of Public Policy and Administration University of Delaware NewarkDE19716 United States Data Science Institute University of Delaware NewarkDE19716 United States Center for Urban Science and Progress New York University 370 Jay St BrooklynNY11201 United States The Oskar Klein Centre for Cosmoparticle Physics Stockholm University AlbaNova StockholmSE-106 91 Sweden University of Chicago ChicagoIL60605 United States IBM Systems AustinTX78717 United States Observatories of the Carnegie Institution for Science 813 Santa Barbara St. PasadenaCA91101 United States Department of Mathematics West Virginia University MorgantownWV26506 United States Center for Gravitational Waves and Cosmology West Virginia University Chestnut Ridge Research Building MorgantownWV26505 United States NVIDIA 2788 San Tomas Expressway Santa ClaraCA95050 United States Center for Data Driven Discovery Caltech PasadenaCA91125 United States Department of Computer Science University of Illinois at Urbana-Champaign UrbanaIL61801 United States Argonne National Laboratory Leadership Computing Facility LemontIL60439 United States Department of Electrical & Computer Engineering University of Illinois at Urbana-Champaign UrbanaIL61801 United States School of Information Sciences University of Illinois at Urbana-Champaign UrbanaIL61801 United States Department of Physics University of Illinois at Urbana-Champaign UrbanaIL61801 Unit

This report provides an overview of recent work that harnesses the Big Data Revolution and Large Scale computing to address grand computational challenges in Multi-Messenger Astrophysics, with a particular emphasis on real-time discovery campaigns. Acknowledging the transdisciplinary nature of Multi-Messenger Astrophysics, this document has been prepared by members of the physics, astronomy, computer science, data science, software and cyberinfrastructure communities who attended the NSF-, DOE- and NVIDIA-funded "Deep Learning for Multi-Messenger Astrophysics: Real-time Discovery at Scale" workshop, hosted at the National Center for Supercomputing Applications, October 17-19, 2018. Highlights of this report include unanimous agreement that it is critical to accelerate the development and deployment of novel, signal-processing algorithms that use the synergy between artificial intelligence (AI) and high performance computing to maximize the potential for scientific discovery with Multi-Messenger Astrophysics. We discuss key aspects to realize this endeavor, namely (i) the design and exploitation of scalable and computationally efficient AI algorithms for Multi-Messenger Astrophysics;(ii) cyberinfrastructure requirements to numerically simulate astrophysical sources, and to process and interpret Multi-Messenger Astrophysics data;(iii) management of gravitational wave detections and triggers to enable electromagnetic and astro-particle follow-ups;(iv) a vision to harness future developments of machine and deep learning and cyberinfrastructure resources to cope with the scale of discovery in the Big Data Era;(v) and the need to build a community that brings domain experts together with data scientists on equal footing to maximize and accelerate discovery in the nascent field of Multi-Messenger Astrophysics. Copyright © 2019, The Authors. All rights reserved.

关键词： Big data

Union of Intersections (UoI) for interpretable data driven discovery and prediction

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arXiv 2017年

作者： Bouchard, Kristofer E. Bujan, Alejandro F. Roosta-Khorasani, Farbod Ubaru, Shashanka Prabhat Snijders, Antoine M. Mao, Jian-Hua Chang, Edward F. Mahoney, Michael W. Bhattacharyya, Sharmodeep Biological Systems and Engineering Division Lawrence Berkeley National Laboratory Computational Research Division Lawrence Berkeley National Laboratory Redwood Center for Theoretical Neuroscience University of California at Berkeley Kavli Institute for Fundamental Neuroscience University of California at San Francisco Redwood Center for Theoretical Neuroscience University of California at Berkeley International Computer Science Institute Department of Statistics University of California at Berkeley Department of Computer Science and Engineering University of Minnesota-Twin Cities National Energy Research Super Computing Lawrence Berkeley National Laboratory Biological Systems and Engineering Division Lawrence Berkeley National Laboratory Biological Systems and Engineering Division Lawrence Berkeley National Laboratory UCSF Epilepsy Center University of California at San Francisco Department of Neurological Surgery University of California at San Francisco International Computer Science Institute Department of Statistics University of California at Berkeley Department of Statistics Oregon State University

The increasing size and complexity of scientific data could dramatically enhance discovery and prediction for basic scientific applications. Realizing this potential, however, requires novel statistical analysis methods that are both interpretable and predictive. We introduce Union of Intersections (UoI), a flexible, modular, and scalable framework for enhanced model selection and estimation. Methods based on UoI perform model selection and model estimation through intersection and union operations, respectively. We show that UoI-based methods achieve low-variance and nearly unbiased estimation of a small number of interpretable features, while maintaining high-quality prediction accuracy. We perform extensive numerical investigation to evaluate a UoI algorithm (UoILasso) on synthetic and real data. In doing so, we demonstrate the extraction of interpretable functional networks from human electrophysiology recordings as well as accurate prediction of phenotypes from genotype-phenotype data with reduced features. We also show (with the UoIL1Logistic and UoICUR variants of the basic framework) improved prediction parsimony for classification and matrix factorization on several benchmark biomedical data sets. These results suggest that methods based on the UoI framework could improve interpretation and prediction in data-driven discovery across scientific fields. Copyright © 2017, The Authors. All rights reserved.

关键词： Forecasting

High‐Pressure Synthesis of A2NiO2Ag2Se2(A=Sr, Ba) with a High‐Spin Ni2+in Square‐Planar Coordination

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Angewandte Chemie 2018年第3期131卷

作者： Yuki Matsumoto Takafumi Yamamoto Kousuke Nakano Hiroshi Takatsu Taito Murakami Kenta Hongo Ryo Maezono Hiraku Ogino Dongjoon Song Craig M. Brown Cédric Tassel Hiroshi Kageyama Graduate School of Engineering Kyoto University Kyoto 615-8510 Japan School of Information Science JAIST Asahidai 1-1 Nomi Ishikawa 923-1292 Japan Research Center for Advanced Computing Infrastructure JAIST Asahidai 1-1 Nomi Ishikawa 923-1292 Japan National Institute for Materials Science Tsukuba 305-0047 Japan PRESTO Japan Computational Engineering Applications Unit. RIKEN 2-1 Hirosawa Wako. Saitama 351-0198 Japan Electronics and Photonics Research Institute AIST Ibaraki 305-8568 Japan Center for Neutron Research NIST Gaithersburg MD 20899-6102 USA

Square‐planar coordinate Ni 2+ ions in oxides are exclusively limited to a low‐spin state (S=0) owing to extensive crystal field splitting. Layered oxychalcogenides A 2 Ni II O 2 Ag 2 Se 2 (A=Sr, Ba) with the S=1 NiO 2 square lattice are now reported. The structural analysis revealed that the Ni 2+ ion is under‐bonded by a significant tensile strain from neighboring Ag 2 Se 2 layers, leading to the reduction in crystal field splitting. Ba 2 NiO 2 Ag 2 Se 2 exhibits a G‐type spin order at 130 K, indicating fairly strong in‐plane interactions. The high‐pressure synthesis employed here possibly assists the expansion of NiO 2 square lattice by taking the advantage of the difference in compressibility in oxide and selenide layers.

关键词： Dehnung Hochdrucksynthesen Oxychalkogenide Quadratisches Gitter Spinzustände

A pulsar-based timescale from the International Pulsar Timing Array

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arXiv 2019年

作者： Hobbs, G. Guo, L. Caballero, R.N. Coles, W. Lee, K.J. Manchester, R.N. Reardon, D.J. Matsakis, D. Tong, M.L. Arzoumanian, Z. Bailes, M. Bassa, C.G. Bhat, N.D.R. Brazier, A. Burke-Spolaor, S. Champion, D.J. Chatterjee, S. Cognard, I. Dai, S. Desvignes, G. Dolch, T. Ferdman, R.D. Graikou, E. Guillemot, L. Janssen, G.H. Keith, M.J. Kerr, M. Kramer, M. Lam, M.T. Liu, K. Lyne, A. Lazio, T.J.W. Lynch, R. McKee, J.W. McLaughlin, M.A. Mingarelli, C.M.F. Nice, D.J. Oslowski, S. Pennucci, T.T. Perera, B.B.P. Perrodin, D. Possenti, A. Russell, C.J. Sanidas, S. Sesana, A. Shaifullah, G. Shannon, R.M. Simon, J. Spiewak, R. Stairs, I.H. Stappers, B.W. Swiggum, J.K. Taylor, S.R. Theureau, G. Toomey, L. van Haasteren, R. Wang, J.B. Wang, Y. Zhu, X.J. U.S. Naval Observatory WashingtonD.C. United States CSIRO Astronomy and Space Science Australia Telescope National Facility Box 76 EppingNSW1710 Australia Shanghai Astronomical Observatory CAS Shanghai200030 China Max-Planck-Institut für Radioastronomie Auf dem Hügel 69 BonnD-53121 Germany Kavli institute for Astronomy and Astrophysics Peking University Beijing100871 China Department of Electrical and Computer Engineering University of California at San Diego La JollaCA92093 United States Centre for Astrophysics and Supercomputing Swinburne University of Technology PO Box 218 HawthornVIC3122 Australia National Time Service Center CAS Xi’anShaanxi710600 China Astrophysics Science Division NASA Goddard Space Flight Center GreenbeltMD20771 United States ASTRON Netherlands Institute for Radio Astronomy Oude Hoogeveensedijk 4 PD Dwingeloo7991 Netherlands International Centre for Radio Astronomy Research Curtin University BentleyWA6102 Australia Cornell Center for Astrophysics and Planetary Science Cornell University IthacaNY14853 United States Cornell Center for Advanced Computing Cornell University IthacaNY14853 United States Department of Physics and Astronomy West Virginia University MorgantownWV26506 United States Center for Gravitational Waves and Cosmology West Virginia University Chestnut Ridge Research Building MorgantownWV26505 United States Laboratoire de Physique et Chimie de l’Environnement et de l’Espace LPC2E CNRS- Université d’Orléans OrléansF-45071 France Station de radioastronomie de Nançay Observatoire de Paris PSL University CNRS/INSU NancayF-18330 France Department of Physics Hillsdale College 33 E. College Street HillsdaleMI49242 United States University of East Anglia Norwich Research Park NorwichNR4 7TJ United Kingdom Department of Astrophysics IMAPP Radboud University P.O. Box 9010 Nijmegen6500 GL Netherlands Jodrell Bank Centre for Astrophysics University of Manchester ManchesterM13 9PL Unite

We have constructed a new timescale, TT(IPTA16), based on observations of radio pulsars presented in the first data release from the International Pulsar Timing Array (IPTA). We used two analysis techniques with independent estimates of the noise models for the pulsar observations and different algorithms for obtaining the pulsar timescale. The two analyses agree within the estimated uncertainties and both agree with TT(BIPM17), a post-corrected timescale produced by the Bureau International des Poids et Mesures (BIPM). We show that both methods could detect significant errors in TT(BIPM17) if they were present. We estimate the stability of the atomic clocks from which TT(BIPM17) is derived using observations of four rubidium fountain clocks at the US Naval Observatory. Comparing the power spectrum of TT(IPTA16) with that of these fountain clocks suggests that pulsar-based timescales are unlikely to contribute to the stability of the best timescales over the next decade, but they will remain a valuable independent check on atomic timescales. We also find that the stability of the pulsar-based timescale is likely to be limited by our knowledge of solar-system dynamics, and that errors in TT(BIPM17) will not be a limiting factor for the primary goal of the IPTA, which is to search for the signatures of nano-Hertz gravitational waves. Copyright © 2019, The Authors. All rights reserved.

关键词： Pulsars

Preparation of logically labeled pure states with only two turns for bulk quantum computation

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arXiv 2017年

作者： Xin, Tao Hao, Liang Hou, Shi-Yao Feng, Guan-Ru Long, Gui-Lu State Key Laboratory of Low-dimensional Quantum Physics and Department of Physics Tsinghua University Beijing100084 China Tsinghua National Laboratory of Information Science and Technology Beijing100084 China Institute of Applied Physics and Computational Mathematics Beijing100094 China Microsystem and Terahertz Research Center China Academy of Engineering Physics Chengdu610200 China Institute of Electronic Engineering China Academy of Engineering Physics Mianyang621999 China Institute for Quantum Computing WaterlooONN2L 3G1 Canada Department of Physics and Astronomy University of Waterloo WaterlooONN2L 3G1 Canada Innovative Center of Quantum Matter Beijing100084 China

Quantum state preparation plays an equally important role with quantum operations and measurements in quantum information processing. The previous methods of preparing initial state for bulk quantum computation all have inevitable disadvantages, such as, requiring multiple experiments, causing loss of signals, or requiring molecules with restrictive structure. In this work, three kinds of quantum circuits are introduced to prepare the pseudo-pure states of (n − 1) qubits in the Hilbert space of n coupled spins which merely need the assist of one ancilla spin and two experiments independent of n. Being without gradient fields effectively avoids the reduction of the signals. Our methods have no special requirements on the structure of the used molecules. To test these methods more comprehensively, we experimentally demonstrate the preparation of the labeled pseudo-pure states using heteronuclear 2-qubit and homonuclear 4-qubit nuclear magnetic resonance quantum information processor. Copyright © 2017, The Authors. All rights reserved.

关键词： Molecules

Procedural content generation via machine learning (PCGML)

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arXiv 2017年

作者： Summerville, Adam Snodgrass, Sam Guzdial, Matthew Holmgård, Christoffer Hoover, Amy K. Isaksen, Aaron Nealen, Andy Togelius, Julian Department of Computational Media University of California Santa CruzCA95064 United States College of Computing and Informatics Drexel University PhiladelpiaPA19104 United States School of Electrical and Computer Engineering Georgia Institute of Technology AtlantaGA30332 United States Duck and Cover Games ApS Copenhagen K1311 Denmark College of Arts Media and Design Northeastern University BostonMA02115 United States Department of Computer Science and Engineering New York University BrooklynNY11201 United States

This survey explores Procedural Content Generation via Machine Learning (PCGML), defined as the generation of game content using machine learning models trained on existing content. As the importance of PCG for game development increases, researchers explore new avenues for generating high-quality content with or without human involvement;this paper addresses the relatively new paradigm of using machine learning (in contrast with search-based, solver-based, and constructive methods). We focus on what is most often considered functional game content such as platformer levels, game maps, interactive fiction stories, and cards in collectible card games, as opposed to cosmetic content such as sprites and sound effects. In addition to using PCG for autonomous generation, co-creativity, mixed-initiative design, and compression, PCGML is suited for repair, critique, and content analysis because of its focus on modeling existing content. We discuss various data sources and representations that affect the generated content. Multiple PCGML methods are covered, including neural networks: long short-term memory (LSTM) networks, autoencoders, and deep convolutional networks;Markov models: n-grams and multi-dimensional Markov chains;clustering;and matrix factorization. Finally, we discuss open problems in PCGML, including learning from small datasets, lack of training data, multi-layered learning, style-transfer, parameter tuning, and PCG as a game mechanic. Copyright © 2017, The Authors. All rights reserved.

关键词： Knowledge representation

Quantum simulation of the non-fermi-liquid state of Sachdev-Ye-kitaev model

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arXiv 2017年

作者： Luo, Zhihuang You, Yi-Zhuang Li, Jun Jian, Chao-Ming Lu, Dawei Xu, Cenke Zeng, Bei Laflamme, Raymond Beijing Computational Science Research Center Beijing100193 China Zhuhai519082 China Shenzhen Institute for Quantum Science and Engineering Department of Physics Southern University of Science and Technology Shenzhen518055 China Institute for Quantum Computing Department of Physics and Astronomy University of Waterloo WaterlooONN2L 3G1 Canada Department of Physics Harvard University CambridgeMA02138 United States Center for Quantum Computing Peng Cheng Laboratory Shenzhen518055 China Shenzhen Key Laboratory of Quantum Science and Engineering Shenzhen518055 China Station Q Microsoft Research Santa Barbara CA93106 United States Kavli Institute of Theoretical Physics University of California Santa BarbaraCA93106 United States Department of Physics University of California Santa BarbaraCA93106 United States Department of Mathematics and Statistics University of Guelph GuelphONN1G 2W1 Canada Perimeter Institute for Theoretical Physics WaterlooONN2L 2Y5 Canada

The Sachdev-Ye-Kitaev (SYK) model incorporates rich physics, ranging from exotic non- Fermi liquid states without quasiparticle excitations, to holographic duality and quantum chaos. However, its experimental realization remains a daunting challenge due to various unnatural ingredients of the SYK Hamiltonian such as its strong randomness and fully nonlocal fermion interaction. At present, constructing such a nonlocal Hamiltonian and exploring its dynamics is best through digital quantum simulation, where state-of-the-art techniques can already handle a moderate number of qubits. Here we demonstrate a first step towards simulation of the SYK model on a nuclear-spin-chain simulator. We observed the fermion paring instability of the non-Fermi liquid state and the chaotic-nonchaotic transition at simulated temperatures, as was predicted by previous theories. As the realization of the SYK model in practice, our experiment opens a new avenue towards investigating the key features of non-Fermi liquid states, as well as the quantum chaotic systems and the AdS/CFT duality. Copyright © 2017, The Authors. All rights reserved.

关键词： Hamiltonians