# Emergence & Entanglement II 2013

Emergence & Entanglement II 2013

## Field theory, Wave function, and Defects of Symmetry Protected Topological Phases

Tuesday May 07, 2013
Speaker(s):
Scientific Areas:

## 3D bosonic topological insulator and its exotic electromagnetic response

Tuesday May 07, 2013
Speaker(s):

Recently, many new types of bosonic symmetry-protected topological phases, including bosonic topological insulators, were predicted using group cohomology theory.  The bosonic topological insulators have  both  U(1) symmetry (particle number conservation) and time-reversal symmetry, described by symmetry group $U(1)\rtimes Z_2^T$.  In this paper, we propose a projective construction of three-dimensional correlated gapped bosonic state with $U(1)\rtimes Z_2^T$ symmetry.  The gapped bosonic insulator is formed by eight kinds of charge-1 bosons.

Scientific Areas:

## Majorana Ghosts: From topological superconductor to the origin of neutrino mass, three generations and their mass mixing

Tuesday May 07, 2013
Speaker(s):

The existence of three generations of neutrinos and their mass mixing is a deep mystery of our universe. On the other hand, Majorana's elegant work on the real solution of Dirac equation predicted the existence of Majorana particles in our nature, unfortunately, these Majorana particles have never been observed. In this talk, I will begin with a simple 1D condensed matter model which realizes a T^2=-1 time reversal symmetry protected superconductors and then discuss the physical property of its boundary Majorana zero modes.

Scientific Areas:

## Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states

Tuesday May 07, 2013
Speaker(s):

We study the non-abelian statistics characterizing systems where counter-propagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity-coupling to superconductors and ferromagnets. The most transparent example is that of a fractional quantum spin Hall state, in which electrons of one spin direction occupy a fractional quantum Hall state of $\nu= 1/m$, while electrons of the opposite spin occupy a similar state with $\nu = -1/m$. However, we also propose other examples of such systems, which are easier to realize experimentally.

Scientific Areas:

## A 3d Boson Topological Insulator and the “Statistical Witten Effect”

Tuesday May 07, 2013
Speaker(s):

Electron topological insulators are members of a broad class of “symmetry protected topological” (SPT) phases of fermions and bosons which possess distinctive surface behavior protected by bulk symmetries. For 1d and 2d SPT’s the surfaces are either gapless or symmetry broken, while in 3d, gapped symmetry-respecting surfaces with (intrinsic) 2d topological order are also possible. The electromagnetic response of (some) SPT’s can provide an important characterization, as illustrated by the Witten effect in 3d electron topological insulators.

Scientific Areas:

## Asymmetry protected emergent E8 symmetry

Monday May 06, 2013
Speaker(s):

The E8 state of bosons is a 2+1d gapped phase of matter which has no topological entanglement entropy but has protected chiral edge states in the absence of any symmetry.  This peculiar state is interesting in part because it sits at the boundary between short- and long-range entangled phases of matter.  When the system is translation invariant and for special choices of parameters, the edge states form the chiral half of a 1+1d conformal field theory - an E8 level 1 Wess-Zumino-Witten model.  However, in general the velocities of different edge channels are different and the system

Scientific Areas:

## Protected edge modes without symmetry

Monday May 06, 2013
Speaker(s):

Some 2D quantum many-body systems with a bulk energy gap support gapless edge modes which are extremely robust. These modes cannot be gapped out or localized by general classes of interactions or disorder at the edge: they are "protected" by the structure of the bulk phase. Examples of this phenomena include quantum Hall states and 2D topological insulators, among others. Recently, much progress has been made in understanding protected edge modes in non-interacting fermion systems. However, less is known about the interacting case.

Scientific Areas:

## Emergent Fermionic Strings in Bosonic He4 Crystal

Monday May 06, 2013
Speaker(s):

Large zero point motion of light atoms in solid Helium 4 leads to several anomalous properties, including a supersolid type behavior. We suggest an `anisotropic quantum melted' atom density wave model for solid He4 with hcp symmetry. Here, atoms preferentially quantum melt along the c-axis and maintain self organized crystallinity and confined dynamics along ab-plane.

Scientific Areas:

## Topological Order with a Twist: Ising Anyons from an Abelian Model

Monday May 06, 2013
Speaker(s):

Anyon models can be symmetric under some permutations of their topological charges. One can then conceive topological defects that, under monodromy, transform anyons according to a symmetry. We study the realization of such defects in the toric code model, showing that a process where defects are braided and fused has the same outcome as if they were Ising anyons.

Scientific Areas:

## Quantum spin liquid phases in the absence of spin-rotation symmetry

Monday May 06, 2013
Speaker(s):

We investigate possible quantum spin liquid phases in the presence of a variety of spin-rotational-symmetry breaking perturbations. Projective symmetry group analysis on slave-particle representations is used to understand possible spin liquid phases on the Kagome lattice. The results of this analysis are used to  make connections to the exiting and future experiments on  Herbertsmithites. Applications to other systems are also discussed.

Scientific Areas:

## RECENT PUBLIC LECTURE

### Art McDonald: A Deeper Understanding of the Universe from 2 km Underground

Speaker: Arthur B McDonald