This series consists of talks in the area of Quantum Matter.
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.
Utilizing a variety and also
constraints offered by quantum and solid
state chemistry, we discuss
possibilities of unconventional quantum
magnetism and superconductivity
in doped 3 dimensional Mott insulators.
Some of the possibilities are
quantum spin liquid states having pseudo
fermi surface coexisting with
long range magnetic order, 3 dimensional
emergent gauge fields and
unconventional superconducting order parameter
Recent advances in analytical theory and numerical methods
enable some long-standing questions about transport in one dimension to be
answered; these questions are closely related to transport experiments in
quasi-1D compounds. The spinless fermion chain with nearest-neighbor
interactions at half-filling, or equivalently the XXZ model in zero magnetic
field, is an example of an integrable system in which no conventional conserved
quantity forces dissipationless transport (Drude weight); we show that there is
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
data. Despite the existence of a Fermi surface, this spin liquid state has
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,