Kells, G.; Kailasvuori, J.; Slingerland, J.K.; Vala, J.

Abstract:

Exactly solvable lattice models for spins and non-interacting
fermions provide fascinating examples of topological phases, some of them
exhibiting the localized Majorana fermions that feature in proposals for
topological quantum computing. The Chern invariant
ν
is an important
characterization of such phases. Here we look at the square–octagon variant
of Kitaev’s honeycomb model. It maps to spinful paired fermions and enjoys
a rich phase diagram featuring distinct Abelian and non-Abelian phases with
ν
=
0
,
±
1
,
±
2
,
±
3 and
±
4. The
ν
= ±
1 and
ν
= ±
3 phases all support localized
Majorana modes and are examples of Ising and SU
(
2
)
2
anyon theories,
respectively

Burnell, F.J.; Simon, Steven H.; Slingerland, J.K.

Abstract:

We study transitions between phases of matter with topological
order. By studying these transitions in exactly solvable lattice models we show
how universality classes may be identified and critical properties described. As
a familiar example to elucidate our results concretely, we describe in detail a
transition between a fully gapped achiral 2D
p
-wave superconductor (
p
+i
p
for pseudo-spin up/
p
−
i
p
for pseudo-spin down) to an s-wave superconductor.
We show in particular that this transition is of the 2D transverse field Ising
universality class.

We examine how best to design qubits for use in topological
quantum computation. These qubits are topological Hilbert spaces associated
with small groups of anyons. Operations are performed on these by exchanging
the anyons. One might argue that in order to have as many simple single-qubit
operations as possible, the number of anyons per group should be maximized.
However, we show that there is a maximal number of particles per qubit,
namely 4, and more generally a maximal number of particles for qudits of
dimension
d
. We also look at the possibility of having topological qubits for
which one can perform two-qubit gates without leakage into non-computational
states. It turns out that the requirement that all two-qubit gates are leakage free
is very restrictive and this property can only be realized for two-qubit systems
related to Ising-like anyon models, which do not allow for universal quantum
computation by braiding. Our results follow directly from the representation
theory of ...

Aarts, G.; Allton, C.; Kelly, A.; Skullerud, J.-I.; Kim, S.; Harris, T.; Ryan, S. M.; Lombardo, M. P.; Oktay, M. B.; Sinclair, D. K.

Abstract:

We study the temperature dependence of bottomonium for
temperatures in the range 0.4Tc < T < 2.1Tc, using non-relativistic
dynamics for the bottom quark and full relativistic lattice QCD simulations
for Nf = 2 light flavors. We consider the behaviour of the correlators in
Euclidean space, we analyze the associated spectral functions and we study
the dependence on the momentum. Our results are amenable to a successful
comparison with effective field theories. They help build a coherent picture
of the behaviour of bottomonium in the plasma, consistent which the current
LHC results.

Huijse, L.; Mehta, D.; Moran, N.; Schoutens, K.; Vala, J.

Abstract:

We study a model for itinerant, strongly interacting fermions where
a judicious tuning of the interactions leads to a supersymmetric Hamiltonian.
On the triangular lattice this model is known to exhibit a property called
superfrustration, which is characterized by an extensive ground state entropy.
Using a combination of numerical and analytical methods we study various
ladder geometries obtained by imposing doubly periodic boundary conditions
on the triangular lattice. We compare our results to various bounds on the
ground state degeneracy obtained in the literature. For all systems we find that
the number of ground states grows exponentially with system size. For two
of the models that we study we obtain the exact number of ground states by
solving the cohomology problem. For one of these, we find that via a sequence
of mappings the entire spectrum can be understood. It exhibits a gapped phase at
1/4 filling and a gapless phase at 1/6 filling and phase separation at intermediate
f...

Graham, Leigh; van der Burgt, Peter J.M.; Alexander, John; Hunniford, C. Adam; Haughey, Sean; Field, Tom A.; McCullough, Robert W.

Abstract:

Relative cross sections for the production of negatively charged fragments have been determined as a
function of ion impact energy in low-energy (0.5 - 5.5 keV) collisions of H– and O– with acetonitrile molecules.
The most abundantly produced negative ions from fragmentation by H– and O– impact are CH3CN–, CH2CN– and
CN–. Notably, the parent negative ion CH3CN– is produced abundantly.

Medina, Julieta; Huet, Idrish; O'Connor, Denjoe; Dolan, Brian P.

Abstract:

We present a manifestly Spin(5) invariant construction of s
quashed fuzzy CP3 as a fuzzy S2 bundle over fuzzy
S4 . We develop the necessary projectors and exhibit the
squashing in terms of the radii of the S2 and S4 . Our analysis allows us give both scalar
and spinor fuzzy action functionals whose low lying modes are truncated versions of those
of a commutative S4
.

We study the temperature flow of conductivities in a gated GaAs two-dimensional electron gas
(2DEG) containing self-assembled InAs dots and compare the results with recent theoretical
predictions. By changing the gate voltage, we are able to tune the 2DEG density and thus vary
disorder and spin-splitting. Data for both the spin-resolved and spin-degenerate phase
transitions are presented, the former collapsing to the latter with decreasing gate voltage
and/or decreasing spin-splitting. The experimental results support a recent theory, based on
modular symmetry, which predicts how the critical Hall conductivity varies with spin-splitting.

Sabol, D; Gleeson, M. R.; Liu, S.; Sheridan, J. T.

Abstract:

A deeper understanding of the processes, which occur during free radical photopolymerization, is
necessary in order to develop a fully comprehensive model, which represents their behavior during
exposure. One of these processes is photoinitiation, whereby a photon is absorbed by a
photosensitizer producing free radicals, which can initiate polymerization. These free radicals can
also participate in polymer chain termination primary termination, and it is therefore necessary to
understand their generation in order to predict the temporally varying kinetic effects present during
holographic grating formation. In this paper, a study of the photoinitiation mechanisms of Irgacure
784 photosensitizer, in an epoxy resin matrix, is presented. We report our experimental results and
present a theoretical model to predict the physically observed behavior.

Dolan, Brian P.; Huet, Idrish; Murray, Sean; O'Connor, Denjoe

Abstract:

We generalise the construction of fuzzy CPN in a manner that allows us to access
all noncommutative equivariant complex vector bundles over this space. We
give a simplified construction of polarization tensors on S2 that generalizes to complex
projective space, identify Laplacians and natural noncommutative covariant
derivative operators that map between the modules that describe noncommutative
sections. In the process we find a natural generalization of the Schwinger-Jordan
construction to su(n) and identify composite oscillators that obey a Heisenberg
algebra on an appropriate Fock space.

It is argued that there are strong similarities between the infra-red
physics of N=2 supersymmetric Yang-Mills and that of the quantum
Hall effect, both systems exhibit a hierarchy of vacua with a sub-group
of the modular group mapping between them. The coupling flow for
pure SU(2) N = 2 supersymmetric Yang-Mills in 4-dimensions is reexamined
and an earlier suggestion in the literature, that was singular
at strong coupling, is modified to a form that is well behaved at both
weak and strong coupling and describes the crossover in an analytic
fashion. Similarities between the phase diagram and the flow of SUSY
Yang-Mills and that of the quantum Hall effect are then described,
with the Hall conductivity in the latter playing the role of the θ-
parameter in the former. Hall plateaux, with odd denominator filling
fractions, are analogous to fixed points at strong coupling in N=2
SUSY Yang-Mills, where the massless degrees of freedom carry an
odd monopole charge.

We study the edge excitations of the Chern Simons matrix theory, describing the
Laughlin fluids for filling fraction n = 1k, with k an integer. Based on the semiclassical
solutions of the theory, we are able to identify the bulk and edge degrees of freedom.
In this way we can freeze the bulk of the theory, to the semiclassical values, obtaining
an effective theory governing the boundary excitations of the Chern Simons matrix
theory. Finally, we show that this effective theory is equal to the chiral boson theory
on the circle.

Howard, J.; van der Burgt, P.J.M.; Manil, B.; Rousseau, P.; Huber, B.A.

Abstract:

We report on two collision experiments performed on nucleobases, (i) using electron impact on nucleobases in the gas phase, and (ii) using low-energy ion impact of small nucleobase clusters. In both experiments mass-resolved positive ions were detected using time-of-flight mass spectrometers, and neutral metastable fragments were detected, also using a time-of-flight technique.

We demonstrate that the UV/IR mixing problems found recently
for a scalar ' 4 theory on the fuzzy sphere are localized to tadpole
diagrams and can be overcome by a suitable modification of the action.
This modification is equivalent to normal ordering the '
4 vertex. In
the limit of the commutative sphere, the perturbation theory of this
modified action matches that of the commutative theory.

We consider SU(2)-equivariant dimensional reduction of Yang-Mills-Dirac theory on manifolds
of the form M × CP1, with emphasis on the effects of non-trivial magnetic flux on CP1. The
reduction of Yang-Mills fields gives a chain of coupled Yang-Mills-Higgs systems on M with a
Higgs potential leading to dynamical symmetry breaking, as a consequence of the monopole
fields. The reduction of SU(2)-symmetric fermions gives massless Dirac fermions on M transforming
under the low-energy gauge group with Yukawa couplings, again as a result of the
internal U(1) fluxes. The tower of massive fermionic Kaluza-Klein states also has Yukawa interactions
and admits a natural SU(2)-equivariant truncation by replacing CP1 with a fuzzy
sphere. In this approach it is possible to obtain exactly massless chiral fermions in the effective
field theory with Yukawa interactions, without any further requirements. We work out the spontaneous
symmetry breaking patterns and determine the complete physical particl...

The present understanding of nonperturbative ground states in the
fractional quantum Hall effect is based on effective theories of the Jain \composite
fermion" excitations. We review the approach based on matrix variables, i.e. D0
branes, originally introduced by Susskind and Polychronakos. We show that the
Maxwell-Chern-Simons matrix gauge theory provides a matrix generalization of the
quantum Hall effect, where the composite-fermion construction naturally follows from
gauge invariance. The matrix ground states obtained by suitable projections of higher
Landau levels are found to be in one-to-one correspondence with the Laughlin and
Jain hierarchical states. The matrix theory possesses a physical limit for commuting
matrices that could be reachable while staying in the same phase.

Dolan, Brian P.; Huet, Idrish; Murray, Sean; O’Connor, Denjoe

Abstract:

We present a universal Dirac operator for noncommutative spin
and spinc bundles over fuzzy complex projective spaces. We give an
explicit construction of these bundles, which are described in terms
of finite dimensional matrices, calculate the spectrum and explicitly
exhibit the Dirac eigenspinors. To our knowledge the spinc spectrum
for CPn with n ≥ 3 is new.

We describe the structure of the vacuum states of quiver gauge theories obtained via dimensional
reduction over homogeneous spaces, in the explicit example of SU(3)-equivariant dimensional
reduction of Yang-Mills-Dirac theory on manifolds of the form M × CP2. We pay particular
attention to the role of topology of background gauge fields on the internal coset spaces, in
this case U(1) magnetic monopoles and SU(2) instantons on CP2. The reduction of Yang-Mills
theory induces a quiver gauge theory involving coupled Yang-Mills-Higgs systems on M with
a Higgs potential leading to dynamical symmetry breaking. The criterion for a ground state
of the Higgs potential can be written as the vanishing of a non-abelian Yang-Mills flux on the
quiver diagram, regarded as a lattice with group elements attached to the links. The reduction of
SU(3)-symmetric fermions yields Dirac fermions on M transforming under the low-energy gauge
group with Yukawa couplings. The fermionic zero modes on CP2 yield e...

It is shown that the flow diagrams for the conductivities in the quantum Hall effect, arising from two ostensibly very different proposals based on modular symmetry, are in fact identical. The β-functions are different, the rate at
which the flow lines are traversed are different, but the tangents to the flow lines are the same in both cases, hence the flow diagrams are same in all aspects.

Bayntun, Allan; Burgess, C. P.; Dolan, Brian P.; Lee, Sung-Sik

Abstract:

Transitions among quantum Hall plateaux share a suite of
remarkable experimental features, such as semicircle laws and duality relations, whose accuracy and robustness are difficult to explain directly in terms of the detailed dynamics of the microscopic electrons. They would naturally follow if the low-energy transport properties were governed by an emergent discrete duality group relating the different plateaux, but no explicit examples of interacting systems having such a group are known. Recent progress using the AdS/CFT correspondence has identified examples with similar duality groups, but without the dc ohmic conductivity characteristic of quantum Hall experiments. We use this to propose a simple holographic model for low-energy quantum Hall systems, with a nonzero dc conductivity that automatically exhibits all of the observed consequences of duality, including the existence of the plateaux and the semicircle transitions between them. The model can be regarded as a strongly ...

We have studied the production of neutral metastable fragments in electron collisions with neutral
argon clusters. The fragments are detected using a time-of-flight technique. The time-of-flight
spectra show that the metastable fragments appear in two velocity ranges. Kinetic energy
distributions are obtained, showing that the faster fragments are ejected with energies from 0.2 to
1.5 eV and that the slower fragments have energies less than 0.2 eV. It is argued that the
fragmentation of the clusters involves the excitation and decay of excitons in the clusters.The faster
fragments are produced by n52 excitons, which localize on an excimer or an excited trimer within
the cluster and upon dissociation cause the ejection of a metastable atom. The slower fragments are
produced by n51 excitons, which tend to localize on the periphery of the cluster, leading to the
ejection of a metastable atom due to weak repulsive forces with neighboring atoms. Four different
production mechanisms for n...

We demonstrate that the classical dimer model defined on a toroidal hexagonal lattice acquires holonomy phases in the thermodynamic limit. When all activities are equal the lattice sizes must be considered mod 6 in which case the finite size corrections to the bulk partition function correspond to a massless Dirac Fermion in the presence of a flat connection with nontrivial holonomy. For general
bond activities we find that the phase transition in this model is a topological one, where the torus degenerates and its modular parameter becomes real at the critical temperature. We argue that these features are generic to bipartite dimer models and we present a more general lattice whose continuum partition function is that of a massive Dirac Fermion.

A new analogue technique is proposed as a method of obtaining Fabry-Perot line profiles using an imaging photon detector. The technique employs the principle of replacing software with hardware, which increases speed and in this case removes problems due to quantisation errors. A further advantage of the system is that it allows the profile to be observed as the integration proceeds, something which was not possible using the digitised x and y coordinates. The ability to obtain the profile in real-time is of importance when recording from a light source whose intensity varies with time.

Modeling the event horizon of a black hole by a fuzzy sphere it is shown that in the classical limit, for large astrophysical black-holes, the event horizon looks locally like a non-commutative plane with non-commutative parameter dictated by the Planck length. Some suggestions in the literature concerning black hole mass spectra are used to derive a formula for the mass spectrum of quantum black holes in terms of four integers which define the area, angular momentum, electric and magnetic charge of the black hole. We also suggest how the classical bounds on extremal black holes might be modified in the quantum theory.