This series consists of talks in the area of Condensed Matter.
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).
A fundamental
open problem in condensed matter physics is how the dichotomy between conventional and topological band insulators is modified in the presence
of strong electron interactions. In this talk I describe recent work
showing that there are 6 new electronic topological insulators that have
no non-interacting counterpart. Combined with the previously known
band-insulators, these produce a total of 8 topologically distinct
phases. Two of the new topological insulators have a simple physical
We present a set of models which realize interacting topological phases. The models are constructed in 2 dimensions for a system with U(1)xU(1) symmetry. We demonstrate that the models are topological by measuring their Hall conductivity, and demonstrating that they have gapless edge modes. We have also studied the models numerically.
In this talk, I will present recent work aimed at tackling two cornerstone problems in the field of strongly correlated electrons---(1) conducting non-Fermi liquid electronic fluids and (2) the continuous Mott metal-insulator transition---via controlled numerical and analytical studies of concrete electronic models in quasi-one-dimension. The former is motivated strongly by the enigmatic "strange metal" central to the cuprates, while the latter is pertinent to, e.g., the spin-liquid candidate 2D triangular
The decomposition of the magnetic moments in spin ice into freely moving magnetic monopoles has added a new dimension to the concept of fractionalization, showing that geometrical frustration, even in the absence of quantum fluctuations, can lead to the apparent reduction of fundamental objects into quasi particles of reduced dimension [1]. The resulting quasi-particles map onto a Coulomb gas in the grand canonical ensemble [2]. By varying the chemical potential one can drive the ground state from a vacuum to a monopole crystal with the Zinc blend structure [3].
Many of the topological insulators, in their naturally
available form are not insulating in the bulk. It has been shown that some of these metallic compounds,
become superconductor at low enough temperature and the nature of their
superconducting phase is still widely debated. In this talk I show that even
the s-wave superconducting phase of doped topological insulators, at low
doping, is different from ordinary s-wave superconductors and goes through a
topological phase transition to an ordinary s-wave state by increasing the
The existence of three generations of neutrinos and their mass mixing is a deep mystery of our universe. Majorana's elegant work on the real solution of Dirac equation predicted the existence of Majorana particles in our nature, unfortunately, these Majorana particles have never been observed. In this talk, I will begin with a simple 1D condensed matter model which realizes a T^2=-1time reversal symmetry protected superconductors and then discuss the physical property of its boundary Majorana zero modes.