As part of the Program on Topological Aspects of Condensed Matter, a weekly seminar will be held on Mondays from 10:00-11:30pm in CMSA room G10.
|8/29/2018||Zeng-Cheng Gu||Title: Towards a complete classification of symmetry protected topological phases for interacting fermions in three dimensions and a general group supercohomology theory
Abstract: Classification and construction of symmetry protected topological (SPT) phases in interacting boson and fermion systems have become a fascinating theoretical direction in recent years. It has beenshown that the (generalized) group cohomology theory or cobordism theory can give rise to a complete classification of SPT phases in interacting boson/spin systems. Nevertheless, the construction and classification of SPT phases in interacting fermion systems are much more complicated, especially in 3D. In this talk, I will revisit this problem based on the equivalent class of fermionic symmetric local unitary (FSLU) transformations. I will show how to construct very general fixed point SPT wavefunctions for interacting fermion systems. I will also discuss the procedure of deriving a general group super-cohomology theoy in arbitrary dimensions.
|9/10/2018||Dominic Else, MIT||Title: Phases and topology in periodically driven (Floquet) systems
Abstract: I will give a pedagogical overview of new topological phenomena that occur in systems that are driven periodically in time (Floquet systems). As a warm-up, I will review new topological invariants in free-fermion Floquet systems. Then, I will discuss the richer physics that occurs in interacting Floquet phases, stabilized in systems with strong quenched disorder by many-body-localization (MBL). Finally, time permitting, I will explain how to realize interacting topological phenomena in a metastable (“pre-thermal”) regime of a clean system.
|9/17/2018||Adrian Po, MIT||
Abstract: There are 230 space groups and 1,651 magnetic space groups in three dimensions. Thankfully, these are finite numbers, and one might go about solving all the possible ways free electrons represent them. This is a central question in the nine-decade-old band theory, which is long-thought to be solvable if only one had the time and patience to crank through all the cases. In this talk, I would describe how this problem can be solved efficiently from the modern perspective of band topology. As a by-product, we will describe a simple method to detect topologically nontrivial band insulators using only symmetry eigenvalues, which offers great computational advantage compared to the traditional, wave-function-based definitions of topological band invariants.
|9/24/2018||Maxim Metlitski||Title: Surface Topological Order and a new ‘t Hooft Anomaly of Interaction Enabled 3+1D Fermion SPTs
Abstract: Symmetry protected topological (SPT) phases have attracted a lot of attention in recent years. A key property of SPTs is the presence of non-trivial surface states. While for 1+1D and 2+1D SPTs the boundary must be either symmetry broken or gapless, some 3+1D SPTs admit symmetric gapped surface states that support anyon excitation (intrinsic topological order). In all cases, the boundary of an SPT is anomalous – it cannot be recreated without the bulk; furthermore, the anomaly must “match” the bulk. I will review this bulk-boundary correspondence for 3d SPT phases of bosons with topologically ordered boundaries where it is fairly well understood. I will then proceed to describe recent advances in the understanding of strongly interacting 3+1D SPT phases of fermions and their topologically ordered surface states.