This series consists of talks in the area of Condensed Matter.
In
this talk, I will construct a symmetry protected topological phase of bosons in
3d with particle number conservation and time reversal symmetries, which is the
direct bosonic analogue of the familiar electron topological insulator. The
construction employs a parton decomposition of bosons, followed by condensation
of parton-monopole composites. The surface of the resulting state supports a
gapped symmetry respecting phase with intrinsic toric code topological order
where both e and m anyons carry charge 1=2.
In the first part of my talk I describe a search for
possible quantum spin liquid ground states for spin S=1 Heisenberg models on
the triangular lattice which was motivated by recent experiments on
Ba3NiSb2O9. We use representation of
spin-1 via three flavors of fermionic spinon operators. The ground state where
one gapless flavor of spinons with a Fermi surface coexists with d+id
topological pairing of the two other flavors can explain available experimental
Quantum number fractionalization is a remarkable property
of topologically ordered states of matter, such as fractional quantum Hall
liquids, and quantum spin liquids. For a given type of topological order, there
are generally many ways to fractionalize the quantum numbers of a given
symmetry. What does it mean to have different types of fractionalization? Are
different types of fractionalization a universal property that can be used to
distinguish phases of matter? In this talk, I will answer these questions,
In this talk we will discuss both the one-photon and
two-photon switching mechanisms in hybrid nanomaterials made from two or more
semiconductor, metallic and optical nanostructures. The most prominent examples
of these nanostructures are graphene, semiconductor quantum dots, metallic
nanoparticles, and photonic and polaritonic crystals. Advances in nanoscience
have allowed for the construction of these new classes of hybrid nanomaterials.
Optical excitations in semiconductor nanostructures are electron-hole pairs
Since the quantum Hall effect, the notion of topological
phases of matter has been extended to those that are well-defined (or:
``protected'') in the presence of a certain set of
symmetries, and that exist in dimensions higher than two. In the (fractional)
quantum Hall effects (and in ``chiral'' topological phases in general),
Laughlin's thought experiment provides a key insight into their topological
characterization; it shows a close connection between topological phases and
quantum anomalies.
I will present a density-matrix renormalization group
(DMRG) study of the S=1/2 Heisenberg antiferromagnet on the kagome lattice to
identify the conjectured spin liquid ground state. Exploiting SU(2) spin
symmetry, which allows us to keep up to 16,000 DMRG states, we consider
cylinders with circumferences up to 17 lattice spacings and find a spin liquid
ground state with an estimated per site energy of -0.4386(5), a spin gap of
0.13(1), very short-range decay in spin, dimer and chiral correlation functions
We construct in the K matrix formalism concrete examples
of symmetry enriched topological phases, namely intrinsically topological
phases with global symmetries. We focus on the Abelian and non-chiral
topological phases and demonstrate by our examples how the interplay between
the global symmetry and the fusion algebra of the anyons of a topologically
ordered system determines the existence of gapless edge modes protected by the
symmetry and that a (quasi)-group structure can be defined among these phases.
The density matrix renormalization group (DMRG), which
has proved so successful in one dimension, has been making the push into higher
dimensions, with the fractional quantum Hall (FQH) effect an important target.
I'll briefly explain how the infinite DMRG algorithm can be adapted to find the
degenerate ground states of a microscopic FQH Hamiltonian on an infinitely long
cylinder, then focus on two applications. To characterize the topological order
We have used a recently proposed quantum Monte Carlo
algorithm [1] to study spinons (emergent S = 1/2 excitations) in 2D
Resonating-Valence-Bond (RVB) spin liquids and in a J-Q model hosting a Neel –
Valence Bond Solid (VBS) phase transition at zero temperature [2]. We confirm
that spinons are well defined quasi-particles with finite intrinsic size in the
RVB spin liquid. The distance distribution between two spinons shows signatures
of deconfinement.
Two types of topological phases have attracted a lot of
attention in condensed matter physics:
symmetry protected