This series consists of talks in the area of Condensed Matter.
The quantum spin liquid is an emergent new state of matter, which has attracted a lot of recent attention. In particular, the time reversal symmetry broken spin liquid (Kalmeyer et. al. and Wen et. al.), characterized by the chiral ordering and fractionalized quasi-particle as a realization of the fractional quantum Hall state had been proposed for more than 20 years, but never identified as the true ground state in any more generic (e.g. Heisenberg spin exchange) models with time reversal symmetry.
What is the price of naturalness? In minimal extensions of the standard model, stringent limits on new colored particles and measurements of Higgs properties from the LHC severely challenge the hypothesis of naturalness of the electroweak scale. However, these measurements also provide unprecedented guidance in exploring non-minimal models of new electroweak physics.
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.