Scientific Series

Extensions of the Standard Model (SM) Higgs sector often predict the existence of new vacua and can feature novel patterns of symmetry breaking in the early universe. In this talk, I will discuss the implications of such scenarios for electroweak scale cosmology, baryogenesis, and Higgs phenomenology. I will focus on two classes of models, one involving a gauge singlet scalar field and the other an inert SU(2) doublet scalar. The former can give rise to a strong first-order electroweak phase transition, but also to rapidly expanding bubbles which can pose a problem for viable electroweak baryogenesis. In the latter, electroweak symmetry can be spontaneously broken by a first-order phase transition to an exotic vacuum, allowing for successful electroweak baryogenesis decoupled from the Standard Model-like Higgs field. Nevertheless, this class of scenarios generically predicts modifications of the SM-like Higgs couplings within reach of present-day collider experiments.

The existence of observables that are incompatible or not jointly measurable is a characteristic feature of quantum mechanics, which is the root of a number of nonclassical phenomena, such as uncertainty relations, wave--particle dual behavior, Bell-inequality violation, and contextuality.

However,  no intuitive  criterion  is available for determining  the compatibility of even two (generalized) observables, despite the overarching importance of this problem  and intensive efforts of many researchers over more than 80 years.

Here we introduce an information theoretic  paradigm together with an intuitive geometric picture for decoding incompatible observables,

starting from two simple ideas:   Every  observable can only provide

limited  information and   information is monotonic  under data

processing. By virtue of quantum estimation theory, we introduce a family of universal criteria for detecting incompatible observables and a natural measure of incompatibility, which are applicable to arbitrary number of arbitrary observables. Based on this framework, we derive a family of universal  measurement uncertainty relations, provide a simple information theoretic explanation of quantitative wave--particle duality, and offer new perspectives for understanding Bell nonlocality, contextuality, and quantum precision limit.

In this talk, we will analyze the properties of the bosonic $\nu = 1$ Moore-Read state when used to build a state
which is strongly believed to be a non-Abelian spin-1 chiral spin liquid state [1]. In this state the bosonic $\nu = 1$
Moore-Read Pfaffian wavefunction is interpreted as a wavefunction for a gas of bosons on a 2D square lattice with one flux quantum per plaquette. We investigate the properties of this wavefunction for the case of planar geometry and for the case of the system living on a torus. For the latter case, there are three distinct states corresponding to the three-fold degeneracy of the $\nu = 1$
bosonic Moore-Read state [2]. Our results show that correlation functions in these states become identical in the limit of large system size. Further issues investigated include the result that the three wavefunctions on the torus are linearly independent and orthogonal in the thermodynamic limit. Additionally, the Renyi entanglement entropy is also calculated for different system partitions in order to extract the topological entanglement entropy $\gamma$.

[1] M. Greiter and R. Thomale, Phys. Rev. Lett. 102, 207203 (2009).
[2] S. B. Chung and M. Stone, J. Phys. A: Math. Theor. 40, 4923 (2007).

A pedagogic introduction will be given to: i) Emergent Majorana fermions and Majorana zero modes in certain condensed matter models and ii) Kondo insulators. This will be followed by discussion of a remarkable Quantum Oscillation Anomaly seen in recent experiments in SmB6, a Kondo insulator, by the Cambridge group [1], as providing evidence [2] for presence of Majorana fermi sea, in an unexpected place. We show a counter intuitive result that these Majorana fermions though neutral, exhibit Landau diamagnetism.

[1] B.S. Tan et al., Science, vol.349, pp. 287-29 (2015), arXiv:1507.01129 [1] G. Baskaran, arXiv:1507.03477

Current and near-future cosmological surveys can provide powerful tests of gravity on the largest scales. However, in order to extract this information, it is essential to understand the host of parameter degeneracies which may arise. I present two approaches towards this goal, with a focus on the use of weak gravitational lensing measurements in combination with other probes. First, I discuss a novel expression for a weak lensing power spectrum under alternative theories of gravity. Obtained by considering small deviations from GR, this expression separates various physical effects of modifications to GR, thus allowing a quantitative understanding of degeneracies between gravitational parameters. Second, I present an investigation into the theoretical uncertainty inherent to the popular gravity-testing statistic E_G. By improving our understanding of the theoretical value of E_G, we can use it to make more robust statements about the viability of alternative theories of gravity on cosmological scales.

On small scales, our understanding of dark matter in galaxies is incomplete. One example is that high resolution simulations predict a large number of subhalos in dark matter halos, which should be seen in our Milky Way galaxy as a host of satellite galaxies. Many plausible astrophysical mechanisms have been proposed to explain why we don't clearly see large numbers of such satellite galaxies, but this remains a test of the cold dark matter scenario that has yet to be passed. Gravitational lensing provides a direct probe of subhalos in distant galaxies, but requires high sensitivity and angular resolution. I will talk about a search that is now started using strong lensing of the mm and submm-wave emission from dust grains in high-redshift star-forming galaxies. The properties of the dust emission are well-matched to the typical expected scales of the dark matter subhalos, and ALMA (the Atacama Large Millimeter Array) now has the sensitivity and angular resolution to start to see the lensing signature of these subhalos. We haven't found any yet in early data, but we should see some soon if the cold dark matter paradigm is correct.

Eugenio Bianchi and Matteo Smerlak have found a beautiful relationship between the Hawking radiation energy and von Neumann entropy in a conformal field emitted by a semiclassical two-dimensional black hole. Shohreh Abdolrahimi and I compared this relationship with what might be expected for unitary evolution of a quantum black hole in four and higher dimensions. If one neglects the expected increase in the radiation entropy over the decrease in the black hole Bekenstein-Hawking A/4 entropy that arises from the scattering of the radiation by the barrier near the black hole, the relation works very well, except near the peak of the radiation von Neumann entropy and near the final evaporation. These discrepancies are calculated and discussed as tiny differences between a semiclassical treatment and a quantum gravity treatment.

In describing condensed matter, some well established paradigms have allowed much progress to be made in understanding and using materials.  But in the last 15 - 20 years, new materials, such as heavy fermions, high temperature superconductors, and now charge density wave-supporting materials,  have been shown to require new paradigms in describing them.  While much progress has been achieved in that time, we still do not have  a widely accepted theoretical description of the nature of their electronic excitations.

Fractional quantum Hall effect in the sequence of filling factors n/(2np +- 1) is well understood by the integer quantum Hall effect of the composite fermions at the filling factor n. A composite fermion (CF) is a bound state of an electron and 2p number of quantized vortices. However, the experimentally observed states such as 4/11, 5/13, and 3/8 which are between 1/3 and 2/5 cannot be accommodated in the conventional noninteracting theory of composite fermions. The interaction between CFs in partially filled second effective Landau levels of CFs is important for these states. However, conventional fractional quantum Hall effect of these interacting composite fermions do not reproduce these incompressible states. By diagonalizing Coulomb Hamiltonian in a restricted Hilbert space of the CFs, we find that these states are incompressible for flux-particle relationships that are different from the conventional considerations. We interpret that 4/11 and 5/13 states occur due to fractional quamtum Hall effect of the composite fermions for Haldane Pseudopotential V_3 rather than V_1. And the panti-Pfaffian pair correlation between CFs in the half-filled second effective Landau level creates incompressible 3/8 state. The unconventional topologies of these states are reflected in anomalously low magneto-roton energies for these states.