This series consists of talks in the area of Condensed Matter.
In the study of strongly-correlated insulators, a long-standing puzzle remained open for over 40 years. Some Kondo insulators (or mixed-valent insulators) display strange electrical transport that cannot be understood if one assumes that it is governed by the three-dimensional bulk. In this talk, I show that some 3D Kondo insulators have the right ingredients to be topological insulators, which we called “topological Kondo insulators”.
A quantum spin liquid is a hypothesized ground state of a
magnet without long-range magnetic order. Similar to a liquid, which is
spatially uniform and strongly correlated, a quantum spin liquid preserves all
the symmetries and exhibits strong correlations between spins. First proposed
by P. W. Anderson in 1973, it has remained a conjecture until recently. In the
past couple of years, numerical studies have provided strong evidences for
Graphene is a 2
dimensional net of strongly bonded carbon atoms. This magic carpet has taken us to new heights in the last decade. Silicene and Germanene are analogue nets, made of silicon and germanium atoms respectively, but with a relatively weaker chemical bond. I will argue that these carpets perform some new tricks by not being a carbon copy of graphene. We have suggested  that silicene and germanene are Mott insulators and potential abode for room temperature superconductivity, quantum spin liquids and more
In the first part
of this talk I will discuss how one can characterize geometry of quantum phases
and phase transitions based on the Fubini-Study metric, which characterizes the
distance between ground state wave-functions in the external parameter space.
This metric is closely related to the Berry curvature. I will show that there
are new geometric invariants based on the Euler characteristic.
We argue that dynamics of gapless Fractional Quantum Hall
Edge states is essentially non-linear and that it features fractionally
quantized solitons propagating along the edge. Observation of solitons would be
a direct evidence of fractional charges. We show that the non-linear dynamics
of the Laughlin's FQH state is governed by the quantum Benjamin-Ono equation.
Topological phases, quite generally, are
difficult to come by. They either occur under rather extreme conditions (e.g.
the quantum Hall liquids, which require high sample purity, strong magnetic
fields and low temperatures) or demand fine tuning of system parameters, as in
the majority of known topological insulators. Many perfectly sensible
topological phases, such as the Weyl semimetals and topological
superconductors, remain experimentally undiscovered. In this talk I will
Some of the key insights that led to the
development of DMRG stemmed from studying the behavior of real space RG for
single particle wavefunctions, a much simpler context than the many-particle
case of main interest. Similarly, one
can gain insight into MERA by studying wavelets. I will introduce basic wavelet theory and
show how one of the most well-known wavelets, a low order orthogonal wavelet of
Daubechies, can be realized as the fixed point of a specific MERA (in
single-particle direct-sum space).