In this talk I will describe my work characterizing
quantum entanglement in systems with a Fermi surface. This class includes everything from Fermi
liquids to exotic spin liquids in frustrated magnets and perhaps even
holographic systems. I review my
original scaling argument and then describe in detail a number of new precise
results on entanglement in Fermi liquids.
I will also discuss recent quantum Monte Carlo calculations of Renyi
entropies and will argue that we now have a rather complete agreement between
theory and numerics for Fermi liquid entanglement. I will also discuss universal crossovers
between thermal and entanglement entropy and a class of solvable interacting
models where we can prove the universality of the Widom formula for Fermi
surface entanglement. If there is time,
I will comment on several other topics including fluctuations of conserved
quantities and connections to holography.
The existence of a
positive linear functional acting on the space of (differences between)
conformal blocks has been shown to rule out regions in the parameter space of
conformal field theories (CFTs). We argue that at the boundary of the allowed
region the extremal functional contains, in principle, enough information to
determine the dimensions and OPE coefficients of an infinite number of
operators appearing in the correlator under analysis. Based on this idea we
develop the Extremal Functional Method (EFM), a numerical procedure for
deriving the spectrum and OPE coefficients of CFTs lying on the boundary (of
solution space). We test the EFM by using it to rederive the low lying spectrum
and OPE coefficients of the 2d Ising model based solely on the dimension of a
single scalar quasi-primary -- no Virasoro algebra required. Our work serves as
a benchmark for applications to more interesting, less known CFTs in the near
future, such as the 3d Ising model.
Most applications of the density matrix renormalization
group (DMRG) have been to lattice models with short range interactions. But
recent developments in DMRG technology open the door to studying continuum
systems with long-range interactions in one dimension (1d). One key motivation
is simulating cold atom experiments, where it is possible to engineer
Hamiltonians of precisely this type.
We have been applying DMRG in the 1d continuum with
another
motivation: to investigate and improve density functional
theory (DFT). DFT has exact mathematical foundations, but in practice one must
use approximations. These approximations work incredibly well for weakly
correlated systems yet fail when correlations are strong.
Improving DFT directly for realistic 3d systems is hard
because few systems can be solved exactly. By working in the 1d continuum
instead, we can use the power of DMRG to study DFT. We can implement both the
exact DFT formalism and standard DFT approximations.
After showing how to overcome the challenges in
performing these calculations, I will discuss some of the key questions we are
investigating, for example, the ability of DFT to predict gaps of insulating
systems.
The stress-energy tensor in a conformal field theory has
zero trace.
Hence AdS boundary stress-tensors are traceless by
construction, to match this property of the dual CFT. An elegant (aka nifty)
construction based on the conformal isometry of AdS will be presented which
shows that in an asymptotically AdS spacetime, the sum of the ADM mass and the
ADM tensions is zero. This result follows strictly from the gravitational point
of view- that is, the Einstein equations and the definitions of the ADM
charges. Further, it turns out that perturbative stress-energy sources in an asymptotically
AdS spacetime must satisfy a local version of this constraint, namely that the
sum of the energy density minus the pressures equals zero. The situation with
positive cosmological constant is both similar and distinct in interesting
ways, which will be briefly discussed. The analogous (analytically continued)
conformal isometry in dS is the root of the
``k^4 “ power spectrum for causal cosmological
perturbations. Work in progress (speculations) will be presented about a
corresponding sum-rule for gravitational charges defined at future infinity in
a spacetime that approaches dS at late times.
Holographic cosmology maps cosmological time evolution to
the inverse RG flow of a dual three-dimensional QFT. In cases where this RG flow
connects two closely separated fixed points, QFT correlators may be calculated
perturbatively in terms of the conformal field theory associated with one of the
fixed points, even when the dual QFT is at strong coupling.
Realising slow-roll inflation in these terms, we show how to derive
standard slow-roll inflationary power spectra and non-Gaussianities through
purely holographic calculations. The form of slow-roll inflationary correlators
is seen to be determined by the perturbative breaking of conformal symmetry
away from the fixed point.
In
a generic quantum experiment we have a given set of devices analyzing some
physical property of a system. To each device involved in the experiment we
associate a set of random outcomes corresponding to the possible values of the
variable analyzed by the device. Devices have apertures that permit physical
systems to pass through them. Each aperture is labelled as "input" or
"output" depending on whether it is assumed that the aperture lets
the system go inside or outside the device. Assuming a particular input/output
structure for the devices involved in a generic experiment is equivalent to
assume a particular causal structure for the space-time events constituted by
the outcomes happening on devices. The joint probability distribution of these
outcomes is usually predicted assuming an absolutely defined input/output
structure of devices. This means that all observers of the experiment agree on
whether an aperture is labelled as "input" or "output". In
this talk we show that the mathematical formalism of quantum theory permits to
predict the joint probability distribution of outcomes in a generic experiment
in such a way that the input/output structure is indeed relative to an
observer. This means that two observers of the same experiment can predict the
joint probability distribution of outcomes assuming different input/output
labels for the apertures. Since input/output structure is the causal structure
of the space-time events constituting the outcomes involved in the experiment
we conclude that in quantum theory, the causal structure of events may not be
regarded as absolute but rather as relative to the observer. We finally point
out that properly extending this concept to the cosmological domain could shed
light on the problem of dark energy.
I will present recent developments in the computation of
three point functions in the AdS4/CFT3 correspondence. More specifically I will
consider two different computations for three point functions of operators
belonging to the SU(2)XSU(2) sector of ABJM. I
will discuss first the generalization of the
determinant representation, found by Foda for the three-point functions of
the SU(2) sector of N = 4 SYM, to the ABJM theory and
secondly semiclassical
computations in the case where two operators are heavy and one is light
and BPS, comparing the results obtained in the gauge theory
side using a coherent state description of the heavy operators with its string theory
counterpart calculated holographically.
After a brief overview of electroweak baryogenesis, I will show how to construct a solution of
the Dirac equation for a CP violating kink wall. This solution nicely reduces
to the known solution for a CP violating thin (step) wall. The novel solution can be helpful for studies
of baryogenesis sources at strong first order phase transitions, which is
relevant for electroweak scale baryogenesis studies.