PPT-Symmetric tensor-networks and topological phases

Shenghan Jiang Boston College Benasque February 09 2017 Symmetric tensornetworks and topological phases Collaborators Ying Ran Boston College Panjin Kim Hyungyong Lee Jung Hoon. Syed. Ali . Raza. Supervisor: Dr. . Pervez. . Hoodbhoy. What are Topological insulators?. Fairly recently discovered electronic phases of matter.. Theoretically predicted in 2005 and 2007 by Zhang, . IndexTopicarraytensor,1%*t%(tensor),1%t*%(tensor),1%t*t%(tensor),1aperm,2matmult,2tensor,14 Yangian. symmetry in sigma model on squashed sphere. @. 理研 . ’10/12/18. 川口　維男（京大理）. I.K. . Kentaroh. Yoshida, arXiv:1008.0776. I.K. . Domenico. Orlando, . Kentaroh. Yoshida, in preparation . /6930-902. Scientific Visualization. TENSOR FIELD VISUALIZATION. Paul Rosen. Assistant Professor. University of South Florida. Slide credit X. . Tricoche. . Outline. Tensor basics. Tensor glyphs. Hyperstreamlines. He Zhang. 1. , He Huang. 2. , . Rui. Li. 1. , . Jie. Chen. 1. , Li-Shi Luo. 2. Jefferson Lab. Old Dominion University. FEIS-2, 05/15/2015. Outline. He Zhang. ---. 3. ---. Introduction of FMM. He Zhang. Symmetry. Topology. Interplay between symmetry and topology has led to a new understanding of . electronic phases of matter.. Conceptual simplification. Conservation laws. Distinguish phases of matter. Michael Freedman. April 23, 2009. Parsa Bonderson. Adrian Feiguin. Matthew Fisher. Michael Freedman. Matthew Hastings. Ribhu Kaul. Scott Morrison. Chetan Nayak. Simon Trebst. Kevin Walker. Zhenghan Wang. He Zhang. 1. , He Huang. 2. , . Rui. Li. 1. , . Jie. Chen. 1. , Li-Shi Luo. 2. Jefferson Lab. Old Dominion University. FEIS-2, 05/15/2015. Outline. He Zhang. ---. 3. ---. Introduction of FMM. He Zhang. Analysis . of the Topological Entanglement . Entropy. and Multipartite correlations. Kohtaro Kato (. The . University of . Tokyo). based on . PRA, 93, 022317 (2016). joint work with. Fabian Furrer (. $$ NSF, AFOSR MURI, DARPA, ARO. Harvard-MIT. Takuya Kitagawa, . Erez. Berg, Mark Rudner. Eugene . Demler. . Harvard University. Also collaboration with A. White’s group, Univ. of Queensland. Rong Ge. Duke University. Joint work with Sanjeev Arora, . Tengyu. Ma, Andrej . Risteski. “Provable Learning of Noisy-OR Networks” . STOC 2017. arxiv:1612.08795. “New practical algorithms for learning Noisy-OR networks via symmetric NMF”. Monojit . Choudhury. Microsoft Research India. monojitc@microsoft.com. . . light. color. red. blue. blood. sky. heavy. weight. 100. 20. 1. NLP vs. Computational Linguistics. Computational Linguistics is the study of . Developing efficient deep neural networks. Forrest Iandola. 1. , Albert Shaw. 2. , Ravi Krishna. 3. , Kurt Keutzer. 4. 1. UC Berkeley → DeepScale → Tesla → Independent Researcher. 2. Georgia Tech → DeepScale → Tesla. Monash University. 24. th. Canberra International Physics Summer School – Topological Matter. Lecture 2. Aims of this lecture series. Introduce electronic transport measurements. What do we measure?.