【直播】【粤港澳大湾区“强纠缠拓扑量子物质态”报告会】费米子拓扑序三重奏
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12月1日
Speaker: Yu-An Chen, University of Maryland, College ParkTime: 10:30 am, December 1Title: Classification of invertible fermionic topological phases by G-crossed braided tensor categoryAbstract: The integer quantum Hall states, the quantum spin Hall insulator, and the p-wave topological superconductor each have an important place in condensed matter physics due to their quantized symmetry-protected topological invariants. These systems have a unique ground state on any closed manifold in (2+1) dimensions and are examples of 'invertible' topological phases of fermions. Here I will describe a general theory describing the universal properties of invertible phases, and classifies them based on their symmetries. This approach is 'categorical': it does not depend on microscopic models. Our theories can be considered as the symmetry-enriched Kitaev's 16-fold way. Some new applications of the theory include an interacting version of the 'tenfold way' classification of topological insulators and superconductors, and also the prediction of an interesting invertible phase.
Bio: Yu-An Chen is a Postdoctoral Researcher and condensed matter theorist at the University of Maryland. He is interested in studying topological phases of matter and quantum information. His previous work focuses on bosonization, a mapping between fermionic and bosonic systems, which is useful for quantum simulation of fermions and the construction of fermionic topological phases. This approach utilizes tools in algebraic topology. He recently studies the bosonization shadow theories of fermionic invertible topological phases using G-crossed crossed braided tensor categories, and classify all chiral phases with symmetry in (2+1)D. Yu-An Chen's research style is the hybridization of math, condensed matter, and quantum information.
12月2日
Speaker: Danny Bulmash, University of Maryland, College Park
Time: 10:30 am, December 2
Title: An algebraic description of (2+1)D fermionic symmetry-enriched topological phases
Abstract: The key property of fermionic topological order is that fermions can be created by local operators; any action of a global symmetry group $G_f$ must respect this property. We construct an algebraic formalism for symmetry fractionalization in fermionic symmetry-enriched topological phases (FSETs). Our formalism is similar to a bosonic theory of $G_b = G_f/Z_2^F$ symmetry fractionalization, where $Z_2^F$ is the group generated by fermion parity symmetry, but with constraints that enforce the locality of the fermion. We characterize the obstructions to and classification of fermionic symmetry fractionalization. We then algebraically describe the ‘t Hooft anomaly of an FSET, that is, the obstruction to gauging $G_f$. To do so, we first gauge fermion parity, and then find a four-step sequence of obstructions to extending $G_b$ symmetry to the parity-gauged theory. We discuss an anomaly inflow argument characterizing some anomalous (2+1)D FSETs as surface theories for (3+1)D fermionic symmetry-protected topological phases.
Bio: Danny Bulmash is currently a postdoctoral researcher at University of Maryland at College Park. He got his PhD from Stanford University in 2017. He has been working on and made important contributions to various aspects of topological phases of matter including fractons, higher-rank gauge theories, and quantum anomalies.
12月6日
Speaker: Shangqiang Ning, Chinese University of Hong Kong
Time: 10:30 am, December 6
Title: Enforced symmetry breaking by invertible topological order
Abstact: It is well known that two-dimensional fermionic systems with a nonzero Chern number must break the time reversal symmetry, manifested by the appearance of chiral edge modes on an open boundary. Such an incompatibility between topology and symmetry can occur more generally. We will refer to this phenomenon as enforced symmetry breaking by topological orders. In this work, we systematically study enforced breaking of a general finite group Gf by a class of topological orders, namely 0D, 1D and 2D fermionic invertible topological orders. In this talk, we will discuss a series of criteria on the existence or non-existence of enforced symmetry breaking by the fermionic invertible topological orders. Using these criteria, we discover many examples that are not known previously. We also study enforced breaking of some continuous group by 2D invertible topological orders through a different argument. For 2D systems, we define the physical quantities to describe symmetry- enriched invertible topological orders and derive some obstruction functions using both fermionic and bosonic languages. In the latter case which is done via gauging the fermion parity, we find that some obstruction functions are consequences of conditional anomalies of the bosonic symmetry-enriched topological states, with the conditions inherited from the original fermionic system.
Bio: Shangqiang Ning is now a post-doctoral fellow at the Department of physics of The Chinese University of Hong Kong. He received his BS degree at Shandong University in 2014, and then move to Tsinghua University where he received his PhD degree in 2019. He was the post-doctoral fellow from Sept, 2019 to Sept, 2021 at the Department of Physics in The University of Hong Kong. His research area focus on the symmetry and topology in strongly correlated condensed matter systems.
背景介绍
自从20世纪80年代铜氧高温超导和分数量子霍尔效应发现以来，强关联电子体系已成为凝聚态物理中超越朗道范式、发现由相互作用导致的新奇物质态的重要的理论和实验研究平台。由于强相互作用（比如分数量子霍尔态里面电子之间的库伦相互作用能标远大于朗道能级的有效动能）的存在，电子体系的强关联拓扑物态完全无法用能带图像来解释。近年来，多体纠缠的引入，比如拓扑纠缠熵和局域幺正变换等概念，对强关联拓扑物态、或更加准确地讲，“强纠缠拓扑量子物态”的研究产生了深远的影响。研究强纠缠拓扑量子物态需要全新的物理理论、数学语言和数值计算方法，在国际上，该方面的研究已经引起了多学科的关注，比如凝聚态物理、量子信息、超冷原子物理、高能物理和数学物理。在这个背景下，本报告会由粤港澳大湾区的相关领域的科研工作者倡议创立，拟邀请国内外相关领域的物理学家、数学家作报告，以促进国内外学术交流和学术创新。组委会成员
陈 钢（香港大学）
陈伟强（南方科技大学）
顾正澄（香港中文大学）
孔 良（南方科技大学）
兰 天（香港中文大学）
梅佳伟（南方科技大学）
王晨杰（香港大学）
叶 鹏（中山大学）
粤港澳大湾区“强纠缠拓扑量子物质态”报告会专题直播&回放链接：
https://www.koushare.com/topicIndex/i/HETQM
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