2:40pm - The duality between fermionic supercohomology SPT andbosonic 2-groupSPT phases in (3+1)D
Abstract: Symmetry-protectedtopological (SPT) phases of matter are described by short-range entangledstates. For each bosonic SPT phase described by the group cohomology, there isa fixed-pointstate that can be prepared by a finite depth quantum circuit (FDQC) built fromthe correspondingcohomology data. In this talk, I will describe a generalization for (3+1)D intrinsicallyinteracting fermionic SPT phases known as the supercohomology phases. The derivationof the FDQC utilizes a series of exact lattice dualities that relate bosonicSPT phases witha certain 2-group symmetry to supercohomology phases. A quick overview is thatgauging theZ2 1-form symmetry of a bosonic model gives a Z2 lattice gauge theory, andbosonizing a fermionicmodel also gives a Z2 lattice gauge theory. With careful design, these Z2lattice gauge theoriescan match, and this constructs a duality between certain bosonic and fermionicmodels. Theideas of "gauging 1-form symmetry" and "bosonization (gaugingfermion parity)" will be clearlyexplained. A primary result of this approach is that the “symmetryfractionalization” on fermionparity flux loops is immediate, which is the characteristic of supercohomologyphases. Reference:https://arxiv.org/abs/2008.05652
3:10pm - On the theoretical ability to identify topological wiresbased on transportmeasurements of three terminal and Coulomb blockaded devices
Abstract:I will report on work done in the Maryland group on modeling transportmeasurement onMajorana nanowires. While the simple single channel effective model for such awire can reproducetwo terminal end conductance qualitatively by introducing a few fit parameters,it also indicatesthat uncertainties in the potential landscape leads to the possibility of two non-topologicalscenarios (so-called "bad" and "ugly") that can potentiallyproduce qualitatively similarend conductance results as predicted for the topological case. This makes itcrucial to understandif other characterization measurements would be more reliable in being able to identifytopological nanowires. Motivated by such measurements, I will first discuss our comparisonof three terminal measurements to the topological invariant in Majoranananowires. Threeterminal devices allow measurement of 2 local and 2 non-local conductances aswell as a thermalcross-conductance. The latter two classes of measurements allow, in principle,an estimateof the "gap" of a wire. The correlation of closing and reopening of agap with the appearanceof zero-bias peaks is expected to be strong evidence for a topological phase.We examinethis claim by contrasting simulations of these measurements with a theoretical calculationof the topological invariant. I will also report on our modeling of Coulombblockade transportwhere we assume that the lead-wire coupling is weak enough to allowthermalization ofthe Majorana wire. This approximation allows an efficient calculation ofCoulomb blockade transportin a semi-realistic nanowire model that includes strong coupling effects of thewire to thebulk superconductor, end quantum dot potential landscapes, large number oflevels near the criticalpoint as well as near the end of superconductivity. In addition to themagnitude of the splittingwe attempt to extract information from the intensity profile such as the bright-dark-brightfeatures in the intensity. Reference:Based on joint works with Sankar Das Sarma and CMTC students Haining Pan andYi-Hua Lai respectively.
3:40pm - Student Introductions
4:10pm - Discussion