This series consists of talks in the area of Condensed Matter.
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).
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.