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

Erez Berg Weizmann Institute of Science
May 07, 2013

PIRSA:13050029
Condensed Matter
A 3d Boson Topological Insulator and the “Statistical Witten Effect”

Matthew Fisher University of California, Santa Barbara
May 07, 2013

PIRSA:13050028
Condensed Matter
Asymmetry protected emergent E8 symmetry

Brian Swingle Brandeis University
May 06, 2013

PIRSA:13050027
Quantum Fields and Strings
Protected edge modes without symmetry

Michael Levin University of Chicago
May 06, 2013

PIRSA:13050026
Quantum Fields and Strings
Emergent Fermionic Strings in Bosonic He4 Crystal

Baskaran Ganapathy Institute of Mathematical Sciences
May 06, 2013

PIRSA:13050025
Condensed Matter
Topological Order with a Twist: Ising Anyons from an Abelian Model

Hector Bombin PsiQuantum Corp.
May 06, 2013

PIRSA:13050024
Quantum Information
Quantum spin liquid phases in the absence of spin-rotation symmetry

Yong-Baek Kim University of Toronto
May 06, 2013

PIRSA:13050023
Condensed Matter
TQFTs and Topological Phases of Matter

Zhenghan Wang Microsoft Corporation
May 06, 2013

PIRSA:13050022
Mathematical physics
3d boson topological insulators and quantum spin liquids

Senthil Todadri Massachusetts Institute of Technology (MIT) - Department of Physics
May 06, 2013

PIRSA:13050021
Condensed Matter
From Pauli's Principle to Fermionic Entanglement

Matthias Christandl ETH Zurich
May 03, 2013

PIRSA:13050005
Quantum Information

Quantum Foundations
AMS02 results support the secondary origin of cosmic ray positrons

Kfir Blum
May 03, 2013

PIRSA:13050015
Particle Physics
An Infalling Observer in AdS/CFT and the Information Paradox

Suvrat Raju
May 03, 2013

PIRSA:13050016
Quantum Fields and Strings

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

Erez Berg Weizmann Institute of Science
May 07, 2013

PIRSA:13050029
Condensed Matter
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. We find that each interface between a region on the edge coupled to a superconductor and a region coupled to a ferromagnet corresponds to a non-abelian anyon of quantum dimension $\sqrt{2m}$. We calculate the unitary transformations that are associated with braiding of these anyons, and show that they are able to realize a richer set of non-abelian representations of the braid group than the set realized by non-abelian anyons based on Majorana fermions. We carry out this calculation both explicitly and by applying general considerations. Finally, we show that topological manipulations with these anyons cannot realize universal quantum computation.
A 3d Boson Topological Insulator and the “Statistical Witten Effect”

Matthew Fisher University of California, Santa Barbara
May 07, 2013

PIRSA:13050028
Condensed Matter
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. Using a 3d parton-gauge theory construction, we have recently developed a dyon condensation approach to access exotic new phases including some 3d bosonic SPT’s. A bosonic SPT with both time-reversal and charge conservation symmetries, is thereby obtained, a phase which supports a gapped, symmetry-unbroken 2d surface with topological order - a toric code with charge one-half anyons. The 3d electromagnetic response of this bosonic SPT phase is quite remarkable - an external magnetic monopole can remain charge neutral, but is statistically transmuted becoming a fermion - a “statistical Witten effect” that characterizes the phase.
Asymmetry protected emergent E8 symmetry

Brian Swingle Brandeis University
May 06, 2013

PIRSA:13050027
Quantum Fields and Strings
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 does not have conformal symmetry. We show that by considering the most general microscopic Hamiltonian, in particular by relaxing the constraint of translation invariance and adding disorder, conformal symmetry remerges in the low energy limit. The disordered fixed point has all velocities equal and is the E8 level 1 WZW model. Hence a highly entangled and highly symmetric system emerges, but only when the microscopic Hamiltonian is completely asymmetric.
Protected edge modes without symmetry

Michael Levin University of Chicago
May 06, 2013

PIRSA:13050026
Quantum Fields and Strings
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. A basic problem is to predict, for general interacting systems, when such edge modes are present or absent, and to identify the different physical mechanisms that underlie their stability. In this talk, I will discuss this problem in the simplest case: interacting fermion systems without any symmetry.
Emergent Fermionic Strings in Bosonic He4 Crystal

Baskaran Ganapathy Institute of Mathematical Sciences
May 06, 2013

PIRSA:13050025
Condensed Matter
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. This leads to profound consequences: i) statistics transmutation of He4 atoms into fermions for c-axis dynamics, arising from restricted one dimensional motion and hard core repulsion, ii) resulting `fermionic strings' undergo Peierls instability (an atom density wave formation) in a staggered fashion and help regain the original hcp crystal symmetry, iii) `particle-hole' type excitations iv) emergence of `confined' `half atom' domain wall excitations, and so on. Known anomalies of solid He4 gets a natural qualitative explanation in the present scenario.
Topological Order with a Twist: Ising Anyons from an Abelian Model

Hector Bombin PsiQuantum Corp.
May 06, 2013

PIRSA:13050024
Quantum Information
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.
Quantum spin liquid phases in the absence of spin-rotation symmetry

Yong-Baek Kim University of Toronto
May 06, 2013

PIRSA:13050023
Condensed Matter
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.
TQFTs and Topological Phases of Matter

Zhenghan Wang Microsoft Corporation
May 06, 2013

PIRSA:13050022
Mathematical physics
In two spatial dimensions, there is a good correspondence between TQFTs and topological phases of matter for spin systems. I will discuss this correspondence in one and three spatial dimensions for spin systems. If time permits, I will also discuss the situation for fermion systems.
3d boson topological insulators and quantum spin liquids

Senthil Todadri Massachusetts Institute of Technology (MIT) - Department of Physics
May 06, 2013

PIRSA:13050021
Condensed Matter
I will discuss recent work on 3d Symmetry Protected Topological (SPT) phases of bosonic systems, and their implications for understanding the more exotic quantum spin liquid phases. First I will describe various characterizations of these 3d SPT phases, in particular their surface effective theories and (when applicable) bulk electromagnetic response. Next I will show how this understanding leads to several new insights into the theory of both 2d and 3d quantum spin liquids. Finally I will provide an explicit construction of several 3d SPT phases in a system of `coupled layers'. This includes a 3d SPT state that is beyond the existing cohomology classification of such states.
From Pauli's Principle to Fermionic Entanglement

Matthias Christandl ETH Zurich
May 03, 2013

PIRSA:13050005
Quantum Information

Quantum Foundations
The Pauli exclusion principle is a constraint on the natural occupation numbers of fermionic states. It has been suspected for decades, and only proved very recently, that there is a multitude of further constraints on these numbers, generalizing the Pauli principle. Surprisingly, these constraints are linear: they cut out a geometric object known as a polytope. This is a beautiful mathematical result, but are there systems whose physics is governed by these constraints? In order to address this question, we studied a system of a few fermions connected by springs. As we varied the spring constant, the occupation numbers moved within the polytope. The path they traced hugs very close to the boundary of the polytope, suggesting that the generalized constraints affect the system. I will mention the implications of these findings for the structure of few-fermion ground states and then discuss the relation between the geometry of the polytope and different types of fermionic entanglement.
AMS02 results support the secondary origin of cosmic ray positrons

Kfir Blum
May 03, 2013

PIRSA:13050015
Particle Physics
We show that the recent AMS02 positron fraction measurement is perfectly consistent with a secondary origin for positrons, and does not require additional primary sources such as pulsars or dark matter. Within the secondary model the AMS02 data imply a cosmic ray propagation time in the
Galaxy of about one Myr and an average traversed interstellar matter density of about 1/cc at a rigidity of 300 GV. These results may hint that high energy cosmic rays are confined to a thin halo of scale height similar to the gaseous disk.
An Infalling Observer in AdS/CFT and the Information Paradox

Suvrat Raju
May 03, 2013

PIRSA:13050016
Quantum Fields and Strings
We reconstruct the experience of an infalling observer using the AdS/CFT correspondence. We write operators both outside and inside the black hole in terms of CFT operators. Our construction provides a natural realization of black hole complementarity, and a way of preserving information without the need for firewalls.

Title	Date	Collection	Type	Info
Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states	2013‑05‑07	Emergence & Entanglement II 2013	Conference	View details
A 3d Boson Topological Insulator and the “Statistical Witten Effect”	2013‑05‑07	Emergence & Entanglement II 2013	Conference	View details
Asymmetry protected emergent E8 symmetry	2013‑05‑06	Emergence & Entanglement II 2013	Conference	View details
Protected edge modes without symmetry	2013‑05‑06	Emergence & Entanglement II 2013	Conference	View details
Emergent Fermionic Strings in Bosonic He4 Crystal	2013‑05‑06	Emergence & Entanglement II 2013	Conference	View details
Topological Order with a Twist: Ising Anyons from an Abelian Model	2013‑05‑06	Emergence & Entanglement II 2013	Conference	View details
Quantum spin liquid phases in the absence of spin-rotation symmetry	2013‑05‑06	Emergence & Entanglement II 2013	Conference	View details
TQFTs and Topological Phases of Matter	2013‑05‑06	Emergence & Entanglement II 2013	Conference	View details
3d boson topological insulators and quantum spin liquids	2013‑05‑06	Emergence & Entanglement II 2013	Conference	View details
From Pauli's Principle to Fermionic Entanglement	2013‑05‑03	Colloquium	Scientific Series	View details
AMS02 results support the secondary origin of cosmic ray positrons	2013‑05‑03		Scientific Series	View details
An Infalling Observer in AdS/CFT and the Information Paradox	2013‑05‑03	Quantum Fields and Strings	Scientific Series	View details

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