As part of the Program on Topological Aspects of Condensed Matter, a weekly seminar will be held on Mondays from 10:0011:30pm in CMSA room G10.
Date  Speaker  Title/Abstract 
8/29/2018  ZengCheng 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 supercohomology 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 warmup, I will review new topological invariants in freefermion Floquet systems. Then, I will discuss the richer physics that occurs in interacting Floquet phases, stabilized in systems with strong quenched disorder by manybodylocalization (MBL). Finally, time permitting, I will explain how to realize interacting topological phenomena in a metastable (“prethermal”) regime of a clean system. 
9/17/2018  Adrian Po, MIT  Title: A modern solution to the old problem of symmetries in band theory
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 ninedecadeold band theory, which is longthought 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 byproduct, 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, wavefunctionbased 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 nontrivial 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 bulkboundary 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. 
10/1/2018  Cancelled  
10/9/2018
Tuesday 3:004:30pm 
Sagar Vijay  Title: Fracton Phases of Matter
Abstract: Fracton phases are new kinds of highlyentangled quantum matter in three spatial dimensions that are characterized by gapped, pointlike excitations (“fractons”) that are strictly immobile at zero temperature, and by degenerate groundstates that are locally indistinguishable. Fracton excitations provide an alternative to Fermi or Bose statistics in three spatial dimensions, and these states of matter are a gateway for exploring mechanisms for quantum information storage, and for studying “slow” dynamical behavior in the absence of disorder. I will review exactly solvable models for these phases, constructions of these states using wellstudied twodimensional topological phases, and a model in which the fracton excitations carry a protected internal degeneracy, which provides a natural generalization of nonAbelian anyons to three spatial dimensions. I will then describe recent advances in categorizing these states of matter using finitedepth unitary transformations. 
10/15/2018  Ethan Lake  Title: A primer on higher symmetries
Abstract: The notion of a higher symmetry, namely a symmetry whose charged objects have a dimension greater than zero, is proving to be very useful for organizing our understanding of gauge theories and topological phases of matter. Just like regular symmetries, higher symmetries can be gauged, spontaneously broken, and can have anomalies. I will review these aspects of higher symmetries and motivate why beyond their conceptual utility, they are often an indispensable tool for making statements about dualities and phase diagrams of theories with gauge fields. 
10/22/2018
Room G02 
YinChen He, Perimeter  Title: Emergent QED3 and QCD3 in condensed matter system
Abstract: QED3ChernSimons and QCD3ChernSimons theories are interesting critical theories in the 2+1 dimension. These theories are described by gapless Dirac fermions interacting with dynamical gauge fields (U(1), SU(N), U(N), etc.) with a possible ChernSimon term. These theories have fundamental importance as it will flow to the 3D conformal field theories and have interesting dualities in the infrared. Various of condensed matter system are described by these critical theories. I will introduce several examples including the Dirac spin liquid in the frustrated magnets (kagome, triangular lattice), quantum phase transitions in the fractional quantum Hall systems and Kitaev materials. 
10/29/2018  Dominic Williamson, Yale  Title: Symmetry and topological order in tensor networks
Abstract: I will present an overview of how topological states of matter with global symmetries can be described using tensor networks. First reviewing the classification of 1D symmetryprotected topological phases with matrix product states, before moving on to the description of 2D symmetryenriched topological phases with projectedentangled pair states. 
11/13/2018
Tuesday 3:004:30pm 
Jason Alicea, Caltech  Title: Timecrystalline topological superconductors 
11/19/2018  X. G. Wen, MIT  Title: A classification of 3+1D topological orders
Abstract: I will discuss a classification of 3+1D topological orders in terms of fusion 2 category. The 3+1D topological orders can be divided into two classes: the ones without emergent fermions and the ones with emergent fermions. The 3+1D topological orders with emergent fermions can be further divided into two classes: the ones without emergent Majorana zero mode and the ones with emergent Majorana zero mode. I will present pictures to understand those 3+1D topological orders. 
12/3/2018
*Room G02* 
Claudio Chamon, Boston University  Title: Manybody scar states with topological properties in 1D, 2D, and 3D.
Abstract: We construct (some) exact excited states of a class of nonintegrable quantum manybody Hamiltonians in 1D, 2D and 3D. These high energy manybody “scar” states have area law entanglement entropy, and display properties usually associated to gapped ground states of symmetry protected topological phases or topologically ordered phases of matter, including topological degeneracies. 
12/10/2018
Room G02 
Anders Sandvik, Boston University and Institute of Physics, CAS, Beijing  Title: Quantum Monte Carlo simulations of exotic states in 2D quantum magnets
Abstract: Some exotic ground states of 2D quantum magnets can be accessed through signfree quantum Monte Carlo simulations of certain “designer Hamiltonians”. I will discuss recent examples within the JQ family of models, where the standard Heisenberg exchange J on the square lattice is supplemented by multispin terms Q projecting correlated singlets, such that dimer (columnar valencebond) order is favored. In addition to a possible deconfined quantum critical point separating the Neel and dimer phases, I will discuss recent work on a modified model where a rather strongly firstorder transition between the Neel state and a plaquettesingletsolid is associated with emergent O(4) symmetry up to length scales of at least 100 lattice spacings. This type of transition may be realized in SrCu2(BO3)2 under pressure. I will also discuss a randomsinglet state obtained when randomness is introduced in a system with dimerized ground state. This type of state may be realized in some frustrated disordered quantum magnets. 
1/8/2019  Lukasz Fidkowski, Univ. of Washington 
Abstract: Motivated by studying the entanglement structure of certain symmetry protected topological phases, we construct a nontrivial quantum cellular automaton in a Hilbert space for a 3d lattice of spin 1/2 degrees of freedom. This is an operator which takes local operators to nearby local operators, but is not locally generated. We discuss implications for the classification of SPT phases in equilibrium and Floquet settings.
