I will present a density-matrix renormalization group
(DMRG) study of the S=1/2 Heisenberg antiferromagnet on the kagome lattice to
identify the conjectured spin liquid ground state. Exploiting SU(2) spin
symmetry, which allows us to keep up to 16,000 DMRG states, we consider
cylinders with circumferences up to 17 lattice spacings and find a spin liquid
ground state with an estimated per site energy of -0.4386(5), a spin gap of
0.13(1), very short-range decay in spin, dimer and chiral correlation functions
and finite topological entanglement consistent with the logarithm of 2, ruling
out gapless, chiral or non-topological spin liquids. All this would provide
strong evidence for a gapped topological Z_2 spin liquid.
Last year strong evidence was
claimed for a 130 GeV gamma ray line from the galactic center in the FERMI
telescope data. In the first half of the talk I will review the status of
the evidence, including recent suggestions which call it into question.
In the second half of the talk, under the bold assumption that the line
is a genuine signature of dark matter, I will review some of the properties
required of dark matter to explain the line and the general features of models
proposed to explain it. This second half will include material from
recent work with Francesco D'Eramo and Jesse Thaler (arxiv:1210.7817), which
suggests that the line is readily explained by dark matter
"semi-annihilation" rather than the standard annihilation
interpretation.
Newton’s inferences from phenomena realize an ideal of
empirical success that’s richer than prediction. To realize Newton’s richer
conception of empirical success a theory needs to do more than to accurately
predict the phenomena it purports to explain: in addition it needs to have the
phenomena accurately measure parameters of the theory. Newton’s method aims to
turn theoretical questions into ones which can be empirically answered by
measurements from phenomena.
Propositions inferred from phenomena are provisionally
accepted as guides to further research.
Newton’s ideal of empirical success as agreeing
measurements from diverse phenomena is appealed to in support of the radical
inference to dark energy in cosmology today. Robert Kirshner (two of his PhDs
share one half of 2011’s Nobel Prize in physics) gave an account of the role of
cosmic microwave background measurements, to back up the supernova measurements
and measurements from galaxy clustering in supporting the transition of dark
energy from a wild hypothesis into an accepted background assumption that
guides further research in cosmology today. This illustrates a feature of
agreeing measurements from diverse phenomena that is especially important for
turning data into evidence. To the extent that the sources of systematic error
of the different measurements can be regarded as independent, their agreement
contributes additional support for counting them as accurate rather than as
mere artifacts of systematic error.
A mixed state can be expressed as a sum of D tensor product matrices, where D is its operator Schmidt rank, or as the result of a purification with a purifying state of Schmidt rank D', where D' is its purification rank. The question whether D' can be upper bounded by D is important theoretically (to establish a description of mixed states with tensor networks), as well as numerically (as the first decomposition is more efficient, but the second one guarantees positive-semidefiniteness after truncation). Here we show that no upper bounds of the purification rank that depend only on operator Schmidt rank exist, but provide upper bounds that also depend on the number of eigenvalues. In addition, we formulate the approximation problem as a Semidefinite Program. Joint work with N. Schuch, D. Perez-Garcia, and J. I. Cirac.
In the last few years there has been a burst of
progress in the field of massive gravity. The construction of consistent
theories in which the graviton has a small mass has in turn led to the
development a new family of compelling, consistent low-energy modifications of
General Relativity. These theories improve our understanding of the
interplay between gravity and particle physics and provide new approaches to
solving the cosmological constant problem. In this talk I will review
these recent developments. I will discuss the search among these new
theories for a symmetry that has the potential to address the cosmological
constant problem.
Gamma Rays at 130 GeV and How They Might Come from Dark
Matter"
I'll discuss the exciting (but somewhat controversial)
new discovery of a sharp gamma ray feature at 130 GeV from near the galactic
center and review some other evidence that might link it to annihilation of
dark matter. I will then explain the challenges in understanding how dark
matter might produce this signal and explain a model or two that overcome these
difficulties.
While the luminosity and mass distributions of quasars
has evolved dramatically with cosmic time, the physical properties of quasars
of a given luminosity are remarkably independent of redshift. I will describe recent results on the spectra
of luminous quasars, the dark matter halos in which they sit, and the
intergalactic medium of their host galaxies, that are essentially
indistinguishable from moderate redshifts to z>6.
The one property apparently unique to the
highest-redshift quasars is that some small fraction show evidence for having
very little infrared excess from hot dust.
Dust obscuration is another theme in quasar studies; an appreciable
fraction of the growth of black holes may be hidden at optical wavelengths by
dust. I will describe searches for
obscured quasars at high redshift and low, and studies of their demographics
and physical properties.
We construct in the K matrix formalism concrete examples
of symmetry enriched topological phases, namely intrinsically topological
phases with global symmetries. We focus on the Abelian and non-chiral
topological phases and demonstrate by our examples how the interplay between
the global symmetry and the fusion algebra of the anyons of a topologically
ordered system determines the existence of gapless edge modes protected by the
symmetry and that a (quasi)-group structure can be defined among these phases.
Our examples include phases that display charge fractionalization and more
exotic non-local anyon exchange under global symmetry that correspond to
general group extensions of the global symmetry group.
We start with a one-slide review of the Kontsevich-Soibelman
(KS) solution to the wall-crossing problem and then proceed to direct and comprehensive physics counting of BPS states that eventually connects to KS. We also asks what input data is needed for either approaches to produce complete BPS spectra, and this naturally leads to the BPS quiver representation of BPS states and the new notion of quiver invariants.
We propose a simple geometrical conjecture that can segregate BPS states in Higgs phases of the BPS quiver dynamics to those that experience wall-crossing and those that do not, and give
proofs for all cyclice Abelian quivers. We close with explanation of how physics distinguishes two such classes of BPS states.
The
interpretation of events with jets is often ambiguous, especially for the sort
of highly complex events one encounters at the LHC. One often finds that
an event interpreted as signal-like using one choice of jet algorithm and
radius parameter is no longer signal-like with another, even if the two are
very similar. Here we present an extension of the Qjets procedure
designed to account for this ambiguity and assign each plausible interpretation
of an event a weight, so that events which are unambiguously signal-like carry
more influence on one's results than events which are only marginally so.
This procedure can be used with any existing analysis employing a
sequential recombination algorithm like anti-kT and we will show that through
its use the statistical power of an analysis often increases. In
particular, we will see that a up to a 20\% improvement in statistical
significance can be realized for a Higgs-like analysis searching for a
resonance recoiling against an associated vector boson.