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In this talk, I will describe a tensor network states in two space dimensions, made of isometric tensors, known as the isometric tensor network states (isoTNS). I will sketch its past algorithmic results and explain some new advances in the last two years including its generalization to infinite systems, fermionic systems, and Gaussian states. In addition, based on inspiration from sequential quantum circuits, I will explain a newer version of isoTNS, which in many ways better represents the physical systems one typically encounters. If time permits, I will sketch our on-going algorithmic work on two dimensional DMRG and variational Monte Carlo of isoTNS.
Yantao Wu is currently a postdoctoral fellow jointly employed by the physics department of UC Berkeley and RIKEN iTHEMS. He did his graduate study in Princeton University and undergraduate study in Harvey Mudd College. During Ph. D, he used Monte Carlo simulations to study the renormalization group properties of statistical mechanical systems. Currently he is interested in tensor network states in two dimensions. He is interested in the algorithms and theory of isometric tensor network states (isoTNS), with an application to many-body condensed matter systems. He is also interested in the incarnation of isoTNS as sequential circuits, with application to the understanding of quantum computing. Recently, he developed an interest in using tensor network states to simulate lattice gauge theory with dynamical gauge and matter fields in (2+1) D.