Download 25 – 27 MAY 2016, ATHENS, GREECE

20TH SYMPOSIUM ON TOPOLOGICAL QUANTUM INFORMATION
25 – 27 MAY 2016, ATHENS, GREECE
Wednesday, May 25th
Thursday, May 26th
Friday, May 27th
09:15 – 09:30
Welcome
09:30 – 10:30
Peter Stano
Mark S. Rudner
Mark S. Rudner
Fractional charges in quantum dot arrays with
density modulation
Topological phenomena in periodically-driven
systems – part I
Topological phenomena in periodically-driven
systems – part II
10:30 – 11:00
Contributed talk: Christos Christides
11:00 – 11:30
Coffee break
Coffee break
Coffee break
11:30 – 12:30
David Jennings
Christopher Mudry
Christopher Mudry
12:30 – 13:00
Contributed talk: Petros Wallden
13:00 – 15:00
Lunch
Lunch
Lunch
15:00 – 16:00
Jens H. Bardarson
Johannes Knolle
Eleftherios Papantonopoulos
16:00 – 17:00
Emil J. Bergholtz
Liviu Hozoi
Gavin Brennen
Weyl gets real: flipped, high and dirty
Huge anisotropic exchange and exotic
magnetism in honeycomb and pyrochlore
iridates
Realisations of the bulk/boundary
correspondence in quantum many-body systems
17:00 – 17:30
Coffee break
Coffee break
Coffee break
17:30 – 18:30
Igor F. Herbut
Stephan Rachel
Spiros N. Evangelou
18:30 – 19:30
Contributed talk: Alex Bullivant
Contributed talk: Konstantinos
Meichanetzidis
Contributed talk: Antoine Sterdyniak
Contributed talk: Zhao Liu
Contributed talk: Dimitris Kosmopoulos
19:30 – 20:30
Discussion session w/ drinks
Discussion session w/ drinks
20:30 –
Dinner
Dinner
Symmetry, irreversibility and information flow
Weyl semimetals – from chiral anomaly to
fractional chiral metal
Interactions and phase transition in Dirac
systems in two and three dimensions
A constructive approach to topological insulators A constructive approach to topological insulators
and topological order – part I
and topological order – part II
Dynamics of Abelian and non-Abelian quantum
spin liquids
Landau levels of Majorana fermions in a spin
liquid
Entanglement entropy as a probe of the
proximity effect in holographic superconductors
Parity-dependent localization in coupled chains
ABSTRACTS
Jens H. Bardarson (MPI-PKS Dresden)
Gavin Brennen (Macquarie University)
Weyl semimetals – from chiral anomaly to fractional chiral metal
Realisations of the bulk/boundary correspondence in quantum many-body
systems
Quantum anomalies is the phenomena that a symmetry classically present
is broken in the quantum theory. The chiral anomaly, in particular, refers
to the non-conservation of chiral charge or current, and has been
discussed for example in the context of the electroweak interactions and
neutral superfluid helium. In the solid state, it has recently been realized
that Weyl and Dirac semimetals, in which the conduction and valence
points touch in a set of non-degenerate Weyl nodes, have a chiral anomaly.
In this context electrons with different chirality belong to a different Weyl
node, and the chiral anomaly is a mechanism by which parallel electric and
magnetic field pump charge between different Weyl nodes. Due to
disorder scattering a characteristic non-equilibrium steady state is
obtained. In this talk I will discuss how this state is obtained, what are its
defining features, and how they can be experimentally observed. I will also
discuss recent experiments [1] on negative magnetoresistance in Weyl
semimetals and their relation to the chiral anomaly. Finally, I will briefly
talk about an interacting generalization of the Weyl semimetal, the
fractional chiral metal, whose electromagnetic response is characterized by
a fractional chiral anomaly [2].
[1] F. Arnold et al., arXiv:1506.06577v2
[2] T. Meng, A. G. Grushin, K.
arXiv:1602.08856
Shtengel,
J.
H.
A bulk/boundary correspondence relates a (d+1)-dimensional quantum
system to another quantum system that lives on the (d)-dimensional
boundary of the bulk space such that the physical properties of one system
can be derived from the other. In this talk I'll introduce two new
approaches to the bulk/boundary correspondence for quantum manybody systems. The first applies to ground states of quantum many-body
systems described by local Hamiltonians, and is based on encoding the
ground state as a multi-scale entanglement renormalization ansatz
(MERA) --- a tensor network decomposition of the ground state
wavefunction, which has been used as a successful ansatz for several
quantum lattice models. Our correspondence relates a boundary theory
with a global on-site symmetry to a bulk theory with a local gauge
symmetry. The second is based on a recently described exact holographic
mapping using wavelets. We generalize this method to an entire family of
Daubeschies wavelets and show by example how a boundary CFT can be
encoded in a bulk with negative curvature. An experimental realisation of
this mapping could be achieved using multi-mode entangled Gaussian
states of continuous variable systems using e.g. photonic networks or
trapped ions.
Bardarson,
Spiros N. Evangelou (University of Ioannina)
Emil J. Bergholtz (Freie Universität Berlin)
Parity-dependent localization in coupled chains
Weyl gets real: flipped, high and dirty
TBA
In this talk I will review the basics of Weyl fermions and pay special
attention to key features distinguishing their recently realised condensed
matter incarnations from their elusive high-energy relatives. In particular,
I will discuss the addition of Lorentz in breaking terms leading to flipped
“type-II” Weyl fermions, the possibility of having a higher topological
charge, and the influence of disorder, as well as experimental implications
of these aspects. If time permits, I will also discuss the bulk-boundary
correspondence in the light of exactly solvable lattice models.
Igor F. Herbut (Simon Fraser University)
Interactions and phase transition in Dirac systems in two and three
dimensions
I will review recent advances in our understanding of the effects of
electron-electron interactions in systems that exhibit band crossing or
touching at the Fermi level. Two study cases will be covered in detail: 1)
interacting electrons on the honeycomb or π-flux lattice, 2) and the
electronic systems with the quadratic band touching in two and three
dimensions, such as bilayer graphene and mercury telluride, for example.
I will discuss the universal physics of the semimetal-Mott insulator
transition in the Hubbard model for the former case, as uncovered by
field-theoretic and Monte Carlo methods. Three dimensional systems with
quadratic band touching will be argued to be precious examples of the
elusive non-Fermi liquid physics, ultimately giving way to new symmetry
broken, and possibly topologically non-trivial states at low temperatures.
L. Hozoi, I. Rousochatzakis, and J. van den Brink, Nat. Commun. 7, 10273
(2016).
[2] R. Yadav, N. A. Bogdanov, V. M. Katukuri, S. Nishimoto, J. van den
Brink, and L. Hozoi, arXiv:1604.04755.
[3] M. Pereiro, D. Yudin, J. Chico, C. Etz, O. Eriksson, and A. Bergman,
Nat. Commun. 5, 4815 (2014).
David Jennings (Imperial College London)
Symmetry, irreversibility and information flow
What kind of irreversibly can be present within a system displaying gauge
dynamics? Here I will describe a programme of research that combines
symmetry principles with quantum information-theoretic notions of
irreversibility. Central to this approach is a theory of asymmetry, and the
resultant framework is found to have a surprisingly complex structure.
This framework provides a powerful new tool-set that connects with
quantum metrology and recent approaches to quantum thermodynamics.
Liviu Hozoi (IFW Dresden)
Huge anisotropic exchange and exotic magnetism in honeycomb and
pyrochlore iridates
Johannes Knolle (University of Cambridge)
Dynamics of Abelian and non-Abelian quantum spin liquids
Large anisotropic exchange couplings in 5d oxide compounds open the
door to new types of magnetic ground states and excitations,
inconceivable a decade ago. In honeycomb Na 2IrO3, e.g., the intersite
spin-coupling anisotropy shows up in the form of bond-dependent Kitaev
interaction terms; this symmetric anisotropic exchange (K) defines in
Na2IrO3 the leading magnetic interaction term. For nearest-neighbor IrO6
octahedra in Sr2IrO4, on the other hand, the key anisotropy is the
antisymmetric contribution (D); it reaches impressively large values of
about 15 meV, orders of magnitude larger than in, e.g., the isostructural
'214' cuprates. We discuss the promise for exciting Kitaev-Heisenberg
physics in 5d (Ir) and 4d (Rh, Ru) oxide and halide honeycomb systems.
In particular, the dependence of the Kitaev K and Heisenberg J couplings
on bond angles is analyzed, by using truly ab initio many-body
calculations [1,2]. We also explore computationally ways of achieving
large D/J ratios in pyrochlore iridates and predict a regime in which D>5
meV and J→0. Such iridates provide thus ideal playgrounds to investigate
for instance skyrmionic states of the type anticipated by the Uppsala
group [3].
[1] S. Nishimoto, V. M. Katukuri, V. Yushankhai, H. Stoll, U. K. Roessler,
Topological states of matter present a wide variety of striking new
phenomena, most prominently is the fractionalization of electrons. Their
detection, however, is fundamentally complicated by the lack of any local
order. While there are now several instances of candidate topological spin
liquids, their identification remains challenging. Here, we address one of
the key questions: How can a quantum spin liquid phase be diagnosed in
experiments? We find that the dynamical response can serve as a valuable
tool for diagnosing quantum spin liquids. We provide a complete and
rarely available exact theoretical study of the dynamical structure factor
and the inelastic Raman scattering response of a two- and threedimensional quantum spin liquid in Abelian and non-Abelian phases. We
show that there are salient signatures of the Majorana fermions and gauge
fluxes emerging in Kitaev’s honeycomb models. Our analysis identifies
new varieties of the venerable X-ray edge problem and explores
connections to the physics of quantum quenches. A number of proposals
suggest that some materials with strong spin-orbit coupling, e.g.
{Na/Li}2IrO3 or α-RuCl3 compounds, realize some of the physics of the
Kitaev model. We discuss the current experimental situation and recent
measurements.
Christopher Mudry (Paul Scherrer Institute)
Mark S. Rudner (Niels Bohr Institute)
A constructive approach to topological insulators and topological order
Topological phenomena in periodically-driven systems
In these lectures, I will show how the technique of bosonization in onedimensional space can be used to construct Hamiltonians in ddimensions (d=2,3,...) realizing noninteracting topological insulators as
well as strongly interacting phases of matter with or without topological
order.
The past decade brought great progress in both our collective theoretical
understanding of topological phenomena, and in experimental
capabilities for controlling the quantum dynamics of solid state, optical,
and cold atomic systems. These experimental advances bring new
opportunities both for accessing topological phenomena that have
remained elusive in natural systems, and also for opening entirely new
regimes of non-equilibrium many-body dynamics. In this pair of talks I
will give an overview of recent progress in characterizing, understanding,
and controlling topological phenomena in periodically driven systems.
The discrete (rather than continuous) time-translation invariance
associated with periodic driving leads to a richer topological structure
than that of non-driven systems. At the same time, driving brings new
challenges that must be overcome. I will outline these new features and
challenges, and the approaches being explored so far to address them.
Eleftherios Papantonopoulos (National Technical University of Athens)
Entanglement entropy as a probe of the proximity effect in holographic
superconductors
We study the entanglement entropy as a probe of the proximity effect of a
superconducting system by using the gauge/gravity duality in a fully backreacted gravity system. While the entanglement entropy in the
superconducting phase is less than the entanglement entropy in the
normal phase, we find that near the contact interface of the
superconducting to normal phase the entanglement entropy has a
different behavior due to the leakage of Cooper pairs to the normal phase.
We verify this behavior by calculating the conductivity near the boundary
interface.
Stephan Rachel (TU Dresden)
Landau levels of Majorana fermions in a spin liquid
Majorana fermions, originally proposed as elementary particles acting as
their own antiparticles, can be realized in condensed-matter systems as
emergent quasiparticles, a situation often accompanied by topological
order. Here we propose a physical system which realizes Landau levels highly degenerate single-particle states usually resulting from an orbital
magnetic field acting on charged particles - for Majorana fermions. This is
achieved in a variant of a quantum spin system due to Kitaev which is
distorted by triaxial strain. This strained Kitaev model displays a spinliquid phase with charge-neutral Majorana-fermion excitations whose
spectrum corresponds to that of Landau levels, here arising from a
tailored pseudomagnetic field. We show that measuring the dynamic spin
susceptibility reveals the Landau-level structure by a remarkable
mechanism of probe-induced bound-state formation.
Peter Stano (RIKEN)
Fractional charges in quantum dot arrays with density modulation
I will discuss fractional charges which can be realized at the ends of an
array of coupled quantum dots in the presence of a periodically modulated
onsite potential. While the charge fractionalization mechanism is similar
to the one in polyacetylene, here the values of fractional charges can be
tuned to arbitrary values by varying the phase of the onsite potential or
the total number of dots in the array. I will explain why the fractional
boundary charges are stable to disorder fluctuations, unlike the boundary
electronic states. Finally, I will show how these results connect to the
currently popular language of topological phases, Chern numbers, Berry
curvature, etc.
CONTRIBUTED TALK ABSTRACTS
Alex Bullivant (University of Leeds)
Discrete lattice models for higher symmetry topological phases
We present a class of exactly solvable models of topological phases in
3+1D. The model generalises the 3+1D Kitaev quantum double replacing
the finite group with a finite 2-group. Such a model describes a lattice
realisation of BF-CG theory which is proposed to describe topological
gauge theories which are both partially Higgsed and partially confined.
Furthermore we present a relation for a subclass of models with a certain
class of deconfined Walker-Wang models.
Christos Christides (University of Patras)
Side-jump scattering from surface states in nanogranular Bi thin films
Co-author: P. Athanasopoulos (University of Patras)
Nanogranular thin films of Bismuth with nominal thicknesses 15nm and
50nm were deposited by magnetron sputtering on Si(100)/SiN x (100nm)
substrates. Hall effect measurements between 5K and 300K reveal two
conduction channels, and the observed curves of Hall resistivity ρ Η(Β) can
be formulated as: ρΗ(Β) = ρΗSurf + R∞Bulk∙B, where ρΗSurf is the intersection
point with ρΗ-axis and R∞Bulk is the slope of ρ Η(Β) curve for B>3T, that is
assigned to a bulk Hall coefficient: R ∞Bulk ~ (e∙neff)-1 with neff an effective
carrier concentration. The temperature dependence of film resistivity
ρxx(T,B=0) varies according to a fitting function: ρ xx(T,B=0) = ρxx(5K,B=0)
e−(λΤ)n, that is related to a phase coherence length LΦ(Τ) ~ T−n. A connection
has been revealed among ρΗ(T), ρxx(T,B=0) and R∞Bulk(T) indicating that:
ρHSurf(Τ, B = 0) ~ ρxx2(Τ,Β=0) ~ R∞Bulk(T) ~ (neff)-1. Surprisingly, a scaling
relationship: ρHSurf = α ρxx + β ρxx2 = RS, is obtained. Most important is the
contribution of the side-jump term: ρ HSurf ~ ρxx2, that is unlikely to be due
to intrinsic mechanism inside non-magnetic Bi. The origin of a ρ HSurf ~ ρxx2
term can be attributed to extrinsic contribution from a combination of
surface roughness plus electronic confinement inside grains, and metallic
edge states in nanogranular structure of Bi(15nm) and Bi(50nm) films. W.
Ning et al [Nature Scientific Reports|4:7086|DOI: 10.1038/srep07086]
reported that the metallic surface states of Bi single-crystal nanoribbons
were robust to the oxidation although the carrier density in the surface
states are modified after the exposures, indicating that metallic surface
states in Bi nanoribbons are topologically protected. A topological
insulator (TI) does not conduct electrons in its interior, but guarantees
robust metallic conduction on its surface. V. Sacksteder et al [Phys. Rev.
Applied 3, 064006 (2015)] predicted that, by introducing a layer of strong
surface disorder, and patterning that layer’s depth, a TI’s surface
conduction can be focused, directed along particular channels, and
switched—all of the requirements for a “topological integrated circuit”.
Our aim is to perform such experiments by introducing disorder on edge
conduction channel of nanogranular Bi thin film, induced from grain
boundaries between Co and Bi composite nanostructures.
Dimitris Kosmopoulos (University of Athens)
A perturbative approach to the concurrence of interacting qubits in a
correlated environment
We study the concurrence in a system of two interacting qubits exposed in
a classical correlated stochastic environment described by a random
telegraph process. We find that the environment's classical correlations
induce an oscillatory behaviour in the concurrence with frequency
depending on the amplitude of the external classical field. We develop a
perturbative scheme to calculate the concurrence analytically and we find
a satisfactory agreement with the numerical results for a wide range of
the parameters characterizing the composite system. The developed
perturbative approach captures the observed concurrence oscillations and
enlightens their origin.
Zhao Liu (Freie Universität Berlin)
Diagnosis of phase transitions in disordered fractional quantum Hall
liquids using quantum entanglement
Co-author: R. Bhatt (Princeton University)
The conventional method to study ground-state phase transitions from
fractional quantum Hall (FQH) liquids to localized phases induced by
disorder has relied on the collapse of the mobility gap and Hall
conductance. Here, we scrutinize this issue from the perspective of
quantum entanglement. We consider electrons in the disordered lowest
Landau level at Laughlin filling fractions ν=1/3 interacting by Haldane's
pseudopotentials. We first compute the orbital-cut entanglement of the
ground states. We find that the entanglement decays with the increase of
the disorder strength, and its derivative with respect to the disorder
strength has a sharp valley which diverges with system size, providing a
clear fingerprint of the transition from FQH liquids to a localized phase.
The minimally entangled states obtained by superposing the ground states
also suggest the same critical point. Considering the entanglement
spectrum usually contains more information than the entanglement itself,
we also investigate the evolution of the ground-state entanglement
spectrum (ES). We observe a development of localization in the ES that
starts from the low-energy region and expands to the high-energy region
with the increase of the disorder strength. In the non-interacting limit, we
argue that the ES should have a two-component structure with Poisson
and Gaussian unitary ensemble level statistics respectively. We expect
that our method can be applied to study the disorder-driven phase
transitions in other topological systems.
fractional topological insulators and as a realization outside of semiconductor physics is still missing. In this talk, I will describe realizations
of strongly interacting chiral phases in cold atoms gases. I will first
introduce optical flux lattices, which are continuous models that exhibit
topological flat bands with a tunable Chern number. Then, I will show that
they host fractional states beyond the FQHE when the partially filled band
Chern number is higher than 1. At last, I will report the emergence of the
bosonic integer quantum Hall effect for a filled C=2 band. This is a typical
example of a symmetry-protected topological phase that cannot be
realized in the absence of interaction.
Petros Wallden (University of Edinburgh)
Recent developments in verification of quantum computation
Konstantinos Meichanetzidis (University of Leeds)
Topological edge states are monogamous
We propose an alternative approach to assessing topologically induced
edge states in free and interacting fermionic systems. We do so by
focussing on the fermionic covariance matrix of the ground state. This
matrix is often tractable either analytically or numerically and it captures
the relevant correlations. By invoking the concept of monogamy of
entanglement we show that highly entangled states supported across a
system bi-partition are largely disentangled from the rest of the system.
We then define an entanglement qualifier that identifies the presence of
topological edge states in terms of singular values of the covariance
matrix. We demonstrate the versatility of this qualifier by applying it to
free and interacting fermionic topological systems.
Antoine Sterdyniak (Max-Planck Institute for Quantum Optics)
Interacting chiral topological phases beyond fractional quantum-Hall
states on optical flux lattices
Co-Authors: N.R. Cooper (University of Cambridge), N. Regnault, and
B.A. Bernevig (Princeton University)
While fractional quantum Hall effect (FQHE) was realized experimentally
thirty years ago in semiconductor heterostructures, strongly interacting
chiral topological phases are still at the center of an important research
effort, both as they serve as building blocks of more exotic phases such as
Abstract: Quantum devices are expected to outperform classical devices. It
becomes more pressing for a number of applications, to develop
techniques to be able to verify the correctness of a quantum computation
without having access to a full quantum computer. There are a number of
different techniques. Here we report some recent developments in one
such approach, the verifiable blind quantum computation (VBQC). We
give an efficient VBQC protocol, where we reduce the required qubits
from O(N2) to O(N). Then we give device-independent and one-sided
device-independent VBQC protocols, where we exploit non-local and
steering correlations to reduce the trust assumptions on verifier's devices.
[1] A. Gheorghiu, E. Kashefi, and P. Wallden, New J. Phys. 17, 083040
2015 .
[2] A. Gheorghiu, P. Wallden and E. Kashefi, arXiv:1512.07401 (2015).
[3] E. Kashefi and P. Wallden, arXiv:1510.07408 (2015)