This series consists of talks in the area of Condensed Matter.
A non-perturbative definition of anomaly-free chiral fermions and bosons in 1+1D spacetime as finite quantum systems on 1D lattice is proposed. In particular, any 1+1D anomaly-free chiral matter theory can be defined as finite quantum systems on 1D lattice with on-site symmetry, if we include strong interactions between matter fields. Our approach provides another way, apart from Ginsparg-Wilson fermions approach, to avoid the fermion-doubling challenge.
Quantum spin liquid (QSL) is an exotic phase of matter and provides an interesting example of emergent non-locality. Even though many materials have been proposed as candidates for QSLs, there is no direct confirmation of QSLs in any of these systems. Quantum spin ice (QSI) is a physical realization of U(1) QSLs on the pyrochlore lattice. We consider a class of electron systems in which dipolar-octupolar Kramers doublets arise on the pyrochlore lattice. In the localized limit, the Kramers doublets are described by the effective spin 1/2 pseudospins.
The amplitude mode is a ubiquitous phenomenon in systems with broken continuous symmetry and effective relativistic dynamics, and has been observed in magnets, charge density waves, cold atom systems, and superconductors. It is a simple analog of the Higgs boson of particle physics. I will discuss the properties of the amplitude mode and its somewhat surprising visibility in two-dimensional systems, recently confirmed in cold atom experiments.
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.