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Title:Disorder-driven phase transitions in weak, boundary-obstructed, and non-Hermitian topological insulators
Author(s):Claes, Jahan
Director of Research:Hughes, Taylor L
Doctoral Committee Chair(s):Vishveshwara, Smitha
Doctoral Committee Member(s):Clark, Bryan K; Gadway, Bryce
Department / Program:Physics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Topological insulators
Abstract:This thesis focuses on three main areas in quantum physics. The bulk of this thesis addresses the effects of disorder on novel classes of topological insulators. Topological insulators are states of matter that display properties (most notably, protected anomalous edge states) that are robust to symmetry-preserving disorder. While the properties of "classical" tenfold way topological insulators under disorder are well-understood, there exist other topological phases whose behavior under disorder has yet to be characterized. In this portion of the thesis, we will develop real-space methods to compute weak, boundary-obstructed, and non-Hermitian topological invariants, establish their stability at weak and strong disorder, and connect these disordered topological invariants to physical signatures. The remainder of the thesis contains an eclectic mix of other work that broadly focuses on the intersection of computational complexity and quantum mechanics. The first section addresses the problem of simulating quantum mechanics on a classical computer. While exactly simulating quantum mechanics is NP hard, in this section we develop and approximate variational method to simulate quantum systems at nite temperature. The second section develops a \randomized benchmarking" method for verifying the gates of a quantum computer, a challenging task as the output of a quantum circuit is generically di cult to simulate. Finally, the third section deals with the ability of a quantum computer to simulate condensed matter systems; we study the ability of a variational quantum circuit to approximate the ground state of the mixed-spin Sherrington-Kirkpatrick spin-glass model.
Issue Date:2021-04-01
Rights Information:Copyright 2021 Jahan Claes
Date Available in IDEALS:2021-09-17
Date Deposited:2021-05

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