Scientific Series

Fathoming interplay between symmetry and topology of many-electron wave-functions has deepened understanding of quantum many body systems, especially after the discovery of topological insulators. Topology of electron wave-functions enforces and protects emergent gapless excitations, and symmetry is intrinsically tied to the topological protection in a certain class. Namely, unless the symmetry is broken, the topological nature is intact. We show novel interplay phenomena between symmetry and topology in topological phase transitions associated with line-nodal superconductors. The interplay may induce an exotic universality class in sharp contrast to that of the phenomenological Landau-Ginzburg theory. Hyper-scaling violation and emergent relativistic scaling are main characteristics, and the interplay even induces unusually large quantum critical region. We propose characteristic experimental signatures around the phase transitions in three spatial dimensions, for example, a linear phase boundary in a temperature-tuning parameter phase-diagram. 

Radio pulsars are Nature's most perfect clock and hence are useful for precision work on a wide variety of physical and astrophysical topics, ranging from sensitive tests of relativistic gravity to constraining the equation of state of ultradense matter. I will describe current ongoing surveys for radio pulsars using the two largest radio telescopes in the world, and how these surveys are also valuable for searching for Fast Radio Bursts, a newly recognized astrophysical phenomenon of unknown origin. 

Based on first-principle calculations, we show that a family of nonmagnetic materials including TaAs, TaP, NbAs, and NbP are Weyl semimetals (WSM) without inversion centers. We find twelve pairs of Weyl points in the whole Brillouin zone (BZ) for each of them. In the absence of spin-orbit coupling (SOC), band inversions in mirror-invariant planes lead to gapless nodal rings in the energy-momentum dispersion. The strong SOC in these materials then opens full gaps in the mirror planes, generating nonzero mirror Chern numbers and Weyl points off the mirror planes. The transport properties obtained by the Boltzmann equation combined with the semiclassical treatments of the unique electronic structure in these materials will also be discussed in comparison with the most recent experimental data.

The discovery of postquantum nonlocality, i.e. the existence of nonlocal correlations stronger than any quantum correlations but nevertheless consistent with the no-signaling principle, has deepened our understanding of the foundations quantum theory. In this work, we investigate whether the phenomenon of Einstein-Podolsky-Rosen steering, a different form of quantum nonlocality, can also be generalized beyond quantum theory. While postquantum steering does not exist in the bipartite case, we prove its existence in the case of three observers. Importantly, we show that post-quantum steering is a genuinely new phenomenon, fundamentally different from postquantum nonlocality. Our results provide new insight into the nonlocal correlations of multipartite quantum systems.

 

For a CFT perturbed by a relevant operator, the entanglement entropy of a spherical region may be computed as a perturbative expansion in the coupling.  A similar perturbative expansion applies for excited states near the vacuum.  I will describe a method due to Faulkner for calculating these entanglement entropies, and apply it in the limit of small sphere size.  The motivation for these calculations is a recent proposal by Jacobson suggesting an equivalence between the Einstein equation and the "maximal vacuum entanglement hypothesis" for quantum gravity.  This proposal relies on a conjecture about the behavior of entanglement entropies for small spheres.  The calculations presented here suggest that this conjecture must be modified, but I will discuss how Jacobson's derivation still applies under the modified conjecture.  

A simple way to trivially satisfy precision-electroweak and flavor constraints in composite Higgs models is to require a large global symmetry breaking scale, f > 10 TeV. This leads to a tuning of order 10^-4 to obtain the observed Higgs mass, but gives rise to a 'split' spectrum where the strong-sector resonances with masses greater than 10 TeV are separated from the pseudo Nambu-Goldstone bosons, which remain near the electroweak scale. To preserve gauge-coupling unification (due to a composite top quark), the symmetry breaking scale satisfies an upper bound f < 100-1000 TeV, which implies that the resonances are not arbitrarily heavy and may be accessible at future colliders. Furthermore, by identifying dark matter with a pseudo Nambu-Goldstone boson, the smallest coset space containing a stable, scalar singlet and an unbroken SU(5) symmetry is SU(7) / SU(6) x U(1). Interestingly, this coset space also contains a metastable color-triplet pseudo Nambu-Goldstone boson that can decay via a displaced vertex when produced at colliders, leading to a distinctive signal of unnaturalness.

The Atacama Cosmology Telescope (ACT) has been pushing our measurements of the Cosmic Microwave Background on small scales to high resolution and deeper sensitivity since 2008. While ACT stopped taking temperature-only measurements in 2010, ACTPol is now operating with polarisation-sensitive detectors. I will present some of the current ACTPol results in terms of the power spectrum constraints. In addition, I'll highlight some of our recent results using ACTPol data, including detections of both the thermal and the kinetic Sunyaev- Zel'dovich effects through cross-correlation with other probes. I'll discuss the lensing of the small-scale microwave sky as measured by ACT and discus how cross-correlating CMB lensing with other probes gives us a handle on galaxy properties like bias. Finally, I'll discuss the next stage in small-scale CMB cosmology: Advanced ACTPol, which will improve our understanding of the reionisation of the universe - arguably our least constrained epoch to date.

In this talk, I will discuss correlations that can be generated by performing local measurements on bipartite quantum systems. I'll present an algebraic characterization of the set of quantum correlations which allows us to identify an easy-to-compute lower bound on the smallest Hilbert space dimension needed to generate a quantum correlation. I will then discuss some examples showing the tightness of our lower bound. Also, the algebraic characterization can be used to express the set of quantum correlations as the projection of an affine section of the cone of completely positive semidefinite matrices. Using this, we identify a semidefinite programming outer approximation to the set of quantum correlations which is contained in the first level of the Navascués, Pironio and Acín hierarchy, and a linear conic programming problem formulating exactly the quantum value of a nonlocal game. Time permitting, I will discuss other consequences of these conic formulations and some interesting special cases.

This talk is based on work with Antonios Varvitsiotis and Zhaohui Wei, arXiv:1507.00213 and arXiv:1506.07297.

I will describe ongoing work with Miguel Paulos, Joao Penedones, Jon Toledo and  Balt van Rees. We are attempting to bootstrap massive quantum field theories. 

We formulate a massive S-matrix bootstrap which we analyze both numerically and analytically. We confront our findings with the conformal theory results of lecture 1. We will derive analytic bounds for the couplings in massive 2d QFTs and observe that the Ising field theory with magnetic field lies precisely at the boundary of these bounds.  We conclude with higher dimensional speculations.   

We will discuss a (conjectural) explicit presentation for the equivariant cohomology of Nakajima quiver varieties of type ADE.  This presentation arises as a shadow of the expected symplectic duality between slices to Schubert varieties in the affine Grassmannian and Nakajima quiver varieties (a.k.a. the expected Coulomb and Higgs branches for a quiver gauge theory). 

I will describe ongoing work with Miguel Paulos, Joao Penedones, Jon Toledo and  Balt van Rees. We are attempting to bootstrap massive quantum field theories. 

A massive quantum field theory can be put in a large AdS space, i.e. in a box. Its correlators define, as they approach the boundary, a conformal theory. The bootstrap of the latter can pose strong constraints on the former as we will describe. We will then initiate a presentation of the general and of the peculiar features of S-matrices in two dimensions.

We studied a holographic superconductor model with a momentum relaxation by employing a linear massless scalar field, which is expected to play a role of impurity via holographic correspondence. By fixing a ratio of impurity/chemical potential, we observed the complex scalar field condensation depending on temperature and computed an electric, thermoelectric, and thermal conductivities. Interestingly, in the presence of the linear massless scalar field, Drude behaviour was shown near a zero frequency regime and the numerical data for the conductivities satisfied Ferrell-Glover-Tinkham (FGT) sum rule. We also numerically checked that the holographic Ward Identity is hold and tried to find if universal law such as Homes law or Uemura’s law is present in our model. However, Homes law was not discovered and Uemera’s law was seen when the charge of the scalar field is 3 and the ratio of the impurity/chemical potential is smaller than about 1/2.