Quantum Matter

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

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.

The properties of a strange metal fermion model with infinite-range

interactions turn out to be closely related to those of charged black holes

with AdS2 horizons. I show that a microscopic computation of the ground

state entropy density of the fermion model yields precisely the Bekenstein-Hawking

entropy density of the black hole. The fermion model is UV finite and has no supersymmetry