We present a family of three-dimensional local
quantum codes with pairs of fractal logical operators. It has two polynomials
over finite fields as input parameters
which generate fractal shapes of anti-commuting logical operators, and
possesses exotic topological order with quantum glassiness which is beyond
descriptions of conventional topological field theory. A necessary and
sufficient condition for being free from string-like logical operators is
obtained under which the model works as marginally self-correcting quantum
memory. We also provide theoretical tools to analyze physical and coding properties
of translation symmetric stabilizer Hamiltonians.
In the context of holography applied to condensed matter
theory, I will present an analysis of transport properties of p-wave
superfluids by means of a gravity dual. Fluctuations modes in the SU(2)
Einstein-Yang-Mills theory are considered, and phenomenological implications
are derived. Due to the spatial anisotropy of the system, a non-universal shear
viscosity is obtained, along with a new coefficient associated to normal stress
differences. I will also discuss how the transport phenomena in this model is
related to the thermoelectric, flexoelectric and piezoelectric effects (mixing
of electric current, heat flux and mechanical stress), which have been observed
in some superconductors and crystal liquids.
Recent experiments in BEC
quantum magnets exhibit a dramatic evolution of
the thermal conductivity of these materials in
magnetic field. By considering various relaxation mechanisms of
bosonic excitations in the vicinity of the BEC quantum-critical point at
finite temperature we provide a detailed explanation of several
unusual features of the data. We identify the leading impurity-scattering
interaction and demonstrate that its renormalization due to quantum fluctuations
of the paramagnetic state compensates the related mass renormalization
effect. This explains the enigmatic absence of the asymmetry between the
two critical points in the low-T thermal conductivity data, while such an
asymmetry is prominent in many other physical quantities. The observed
characteristic "migration'' of the peak in thermal conductivity away from
the transition points as a function of temperature is explained as due to a
competition between an increase in the number of heat carriers and an
enhancement of their mutual scattering. An important role of the three-boson
scattering processes within the ordered phase of these systems is
also discussed. Other qualitative and quantitative features of the
experiment are clarified and the future directions are sketched.
The study of the worldsheet S-matrix for AdS_5×S^5
strings was a key step in
the complete determination of the non-pertubrative planar
spectrum of anomalous
dimensions for N=4 super-Yang-Mills. To go beyond
the spectral problem it is
important to consider higher-point
worldsheet correlation functions and, as is
standard in many integrable models, one approach is
the study of form factors.
We will discuss a set of consistency conditions appropriate
to form factors in
the light-cone gauge
fixed AdS_5×S^5 string theory. We further
discuss the
form factors in the weakly coupled dual description,
verifying that the relevant conditions naturally hold for the one-loop Heisenberg
spin-chain.
Dark energy coupled to Standard Model fermions and gauge
bosons gives rise to fifth forces and new particles, which are readily
accessible to experiments from laboratory to cosmological scales. I will discuss chameleon and symmetron
models, whose fifth forces are screened locally through large effective masses
and symmetry-restoring phase transitions, respectively. Fifth force experiments such as the Eot-Wash
torsion balance will test chameleons with small quantum corrections and
gravitation-strength fifth forces, as well as symmetrons with coupling energies
just beyond the Standard Model scale. A
dark energy coupling to electromagnetism would imply that photons passing
through a magnetic field will oscillate into particles of dark energy, a
phenomenon studied by afterglow experiments such as CHASE. After constraining dark energy using
laboratory experiments, I proceed to astrophysical probes. Particles of a photon-coupled dark energy
could be produced in the Sun and detected in magnetic helioscopes such as CAST,
while fifth forces may alter the dynamics of variable stars and the growth of
large-scale structure.
In this talk we will present results on all one-loop scattering amplitudes in N=6 Chern-Simons matter theories. Especially we will discuss connection between certain triple-cut diagrams and tree-level recursive diagrams, and a general formula capturing the multi-particle factorization of arbitrary one-loop amplitudes in the theories is obtained from this connection. Furthermore a recursion relation for the supercoefficients of one-loop amplitudes will be derived, which leads the solution for all one-loop amplitudes.
In this talk I will sketch a project which aims at the
design of systematic and efficient procedures to infer quantum models from
measured data. Progress in experimental control have enabled an increasingly
fine tuned probing of the quantum nature of matter, e.g., in superconducting
qubits. Such experiments have shown that we not always have a good
understanding of how to model the experimentally performed measurements via
POVMs. It turns out that the ad hoc postulation of POVMs can lead to
inconsistencies. For example, when doing asymptotic state tomography via linear
inversion, one sometimes recovers density operators which are significantly not
positive semidefinite. Assuming the asymptotic regime, we suggest an
alternative procedure where we do not make a priori assumptions on the quantum
model, i.e., on the Hilbert space dimension, the prepared states or the
measured POVMs. In other words, we simultaneously estimate the dimension of the
underlying Hilbert space, the quantum states and the POVMs. We are guided by
Occam's razor, i.e., we search for the minimal quantum model consistent with
the data.
In this talk, I'll give a brief summary of how one-loop
bulk effects
renormalize both bulk and brane effective interactions for geometries sourced by codimension-two
branes. I'll then discuss what these results imply for a six-dimensional
supergravity model which aims to capture the features that make extra-dimensional
physics attractive for understanding naturalness issues in particle physics.
I'll also emphasize the role that brane back-reaction plays in yielding
unexpected results, and present a one-loop contribution to the 4D vacuum energy
whose size is set by the KK scale.
I will review some problems of the black hole paradigm and explore other possibilities for the final state of stellar collapse other than an evaporating black hole. In particular I will use the so-called transplanckian problem as a guide in this search for a compelling scenario for the evaporation of ultracompact objects.
It is widely known in the
quantum information community that the states that satisfy strong subadditivity
of entropy with equality have the form of quantum Markov chain. Based on a
recent strengthening of strong subadditivity of entropy, I will describe how
such structure can be exploited in the studies of gapped quantum many-body
system. In particular, I will describe a diagrammatic trick to i) give a
quantitative statement about the locality of entanglement spectrum ii)
perturbatively bound changes of topological entanglement entropy under generic
perturbation.
The Rosenbluth Method is a classical kinetic growth Monte
Carlo algorithm for growing a self-avoiding walk by appending steps to its
endpoint.
This algorithm
can be generalised by the implementation of more general
elementary moves (for example, BFACF elementary moves) to realise kinetic
growth algorithms for lattice polygons.
This generalises the counting principle that underlies the Rosenbluth
method and the result is a widely applicable class of algorithms which may be
used for microcanonical sampling in discrete models. In addition to self-avoiding walks, several
applications of kinetic growth and canonical Monte Carlo algorithms will be
presented, including the sampling of trivial words in abstract groups, as well
as knotted lattice polygons and discrete lattice spin systems such as the Potts
model.
This is work was done in collaboration with Andrew
Rechnitzer of the Mathematics Department at the University of British Columbia.