Scientific Series

In this talk we propose a Hamiltonian approach to 2+1D gapped topological phases on an open surface with boundary. The bulk part is

(Levin-Wen) string-net models arising from a unitary fusion category (can be viewed as Hamiltonian approach to extended Turaev-Viro TQFT), while the boundary Hamiltonian is constructed using any Frobenius algebra in the input category. The combined Hamiltonian is exactly solvable and gives rise to a gapped energy spectrum which is topologically protected.

Our boundary Hamiltonians can be used to characterize and classify boundary conditions that give rise to gapped topological phase. We study the ground states and boundary excitations. Particularly, we show a correspondence between elementary excitations and the ground states on a cylinder system. Both are characterized by the category of bimodules over the Frobenius algebra that defines the  boundary Hamiltonian.

The fact that in physics concepts such as space, time, mass and energy are considered to be foundational has been conveniently serving a set of higher-level physical theories.

However, this keeps us from gaining a deeper understanding of such concepts which can in turn help us build a theory based on truly foundational concepts.

In this talk I introduce an alternate description of physical reality based on a simple foundational concept that there exist things that influence one another.

A network of objects that influence one another form a partially-ordered set (poset) that is called the influence network is considered. By consistently quantifying such a network with respect to a distinguished chain of events that is called an embedded observer, I demonstrate in relevant special cases that influence events can only be quantified by the familiar mathematics of space-time (Minkowski metric and Lorentz transformations), influence gives rise to basic concepts in Euclidean geometry such as direction, dimension and subspaces as well as the Pythagorean theorem, the dot product and geometrical figures. Thus a discrete version of some of the Euclidean geometry’s fundamental concepts is derived in this picture. Finally I talk about the concept of influence in quantum mechanics and how the case of a free particle is identical to the Feynman checkerboard problem for the electron which is known to give rise to the Dirac equation.

In this talk I will discuss a new use for conformal field theory crossing equation in the context of AdS/CFT:  the computation of loop amplitudes in AdS, dual to non-planar correlators in holographic CFTs. I will revisit this problem and the dual 1/N expansion of CFTs, in two independent ways. The first is to show how to explicitly solve the crossing equations to the first subleading order in 1/N^2, given a leading order solution. This is done as a systematic expansion in inverse powers of the spin, to all orders. These expansions can be resummed, leading to the CFT data for finite values of the spin. The second approach involves Mellin space. As an example, I’ll show how the polar part of the four-point, loop-level Mellin amplitudes can be fully reconstructed from the leading-order data. The anomalous dimensions computed with both methods agree. In the case of \phi^4 theory in AdS, the crossing solution reproduces a previous computation of the one-loop bubble diagram. I will end with a discussion on open problems and new developments.

We are currently entering the era of precision CMB polarization observations. The most exciting scientific targets are a possible detection of primordial gravitational waves and a measurement of the sum of the neutrino masses. The former depends on the extensive landscape of early Universe models, while the latter has been forecasted to present a clear, and reachable, scientific target. First, if large angular B modes are detected, we should firmly establish that these are sourced by primordial gravitational waves. I will discuss that cross correlating the B-mode signal with the curl-lensing field could help establish the nature of the detected B-modes. Second, I will propose to look beyond Gaussianity in the tensor sector. Scalar non-Gaussianities are tightly constrained by Planck, but couplings between tensors and scalars are currently not constrained and future CMB polarization surveys could open a new window into the early Universe, by searching for tensor non-Gaussianites. Finally, a detection of the normal hierarchy of the neutrino mass requires an excellent measurement of the amplitude of primordial fluctuations. The required measurement can only be achieved if we are able to measure the large angle E-mode polarization spectrum, which currently lies beyond reach, at least within the foreseeable future. I will present a possible solution and show how this simple methodology can be used to constrain exotic primordial physics at the same time.

The study of thermodynamics in the quantum regime has in recent years experienced somewhat of a renaissance in our community. This excitement is fueled both by the fundamental nature of the subject as well as the potential for heat machines designed with quantum advantages. Here, I will suggest the study of quantum thermodynamics restricted to a Gaussian regime, with two primary goals in mind. The first is to understand just how restrictive Gaussian states and operations are in a thermodynamic context; as such operations are often the most easily implemented in the laboratory it is pertinent to understand what limitations they impose on us. The second is to use the computational simplicity of Gaussian quantum mechanics to examine thermodynamics under less ideal but more realistic assumptions, such as with finite bath sizes and time scales. We will present two works in this seminar, one focusing on each of these motivations.

Near a quantum-critical point in a metal strong fermion-fermion interaction mediated by a soft collective boson gives rise to incoherent, non-Fermi liquid behavior. It also often gives rise to superconductivity which masks the non-Fermi liquid behavior. We analyze the interplay between the tendency to pairing and fermionic incoherence for a set of quantum-critical models with effective dynamical interaction between low-energy fermions. We argue that superconducting Tc is non-zero even for strong incoherence and/or weak interaction due to the fact that the self-energy from dynamic critical fluctuations vanishes for the two lowest fermionic Matsubara frequencies $\omega_m = \pm \pi T$. We obtain the analytic formula for T_c which reproduces well earlier numerical results, including the ones  for the  electron-phonon model at vanishing Debye frequency.

Hayden and Van Dam showed that starting with a separable state in Alice and Bob’s state space and a shared entangled state in a common bipartite resource space, then using local unitary operations, it is possible to produce an entangled pair in the state space while at the same time only perturbing the shared entangled state by a small amount, which can be made arbitrarily small as the dimension of the resource space grows. They referred to this as “embezzling entanglement” since numerically it “appears" that the resource state was returned exactly.

It is natural to wonder if using an infinite dimensional resource space and local operations, one can return the resource state exactly while producing an entangled state in their state space. Whether or not you can achieve this phenomenon of “perfect embezzlement of an entangled state” depends on which mathematical model one uses to describe “local”.

We prove that perfect embezzlement is impossible in the tensor model but is possible in the commuting model. We then relate this to current work on the conjectures of Connes and Tsirelson about different models for quantum conditional probabilities.

This talk is based on joint work with R. Cleve, L. Liu and S. Harris.

We will discuss how the process of superradiance, combined with
gravitational wave measurements, makes black holes into
nature's laboratories to search for new light bosons. We will present
analytic results for superradiance of light vector (spin-1) particles,
valid in the regime where the vector's Compton wavelength is much
larger than the horizon size of a black hole. If superradiance is
efficient, the occupation number of the vectors in the black hole's
vicinity grows exponentially and the black hole spins down. We will
present preliminary signatures of this process, including black hole
spin measurements and gravitational wave signals. Current measurements
of black hole spins disfavor a range of masses of (gravitationally
coupled) vectors. Vectors annihilating to gravitons would emit
strong monochromatic gravitational wave signals, which may be
visible in future LIGO observations. 

The discovery of the Higgs boson at the LHC in 2012 was a watershed in particle physics. Its existence focuses attention on the outstanding questions about physics beyond the Standard Model: is `empty' space unstable? what is the dark matter? what is the origin of matter? what is the explanation for the small masses of the neutrinos? how is the hierarchy of mass scales in physics established and stabilized? what drove inflation? how to quantize gravity Many of these issues will be addressed by future runs of the LHC, e.g., by studies of the Higgs boson, and also motivate possible future colliders.

Dicke's seminal 1954 paper introduced the notion of `superradiance' in a system of spins coupled to a common photon mode.

Certain quantum states of the spins dominate the radiation process so that the spins radiate coherently. Dicke's original thought experiment has recently been recreated in the lab using cavity-QED setups with two spins. I will explore extending this experiment to $N$ spins and show that the radiation process naturally gives rise to entangled states. This suggests a new experimental tool to create multi-particle entanglement in the lab. In particular, a null-observation (non-observation of emitted photon) can be used to collapse the wavefunction onto a dark state. Remarkably, this dark state has resonating valence bond character. We show that the probability of collapse onto RVB state scales as $N^{-1}$, making it possible to generate entangled states of more than 20 spins.

Reference: arXiv:1609.04853

In the first part of the talk, I will explain how the lengths of non-minimal geodesics in AdS3 conical defect backgrounds can be interpreted as the entanglement entropy of certain subalgebras in the dual CFT. This part will be based on 1608.02040. In the second part of the talk, I will discuss how the Ryu-Takayanagi area term seems to be the analog of a certain edge term for EE in a gauge theory, and how one might try to test this. This part is more speculative.