This series consists of talks in the area of Condensed Matter.
It has been known for some time that
a system with a filled band will have an integer quantum Hall conductance equal
to its Chern number, a toplogical index associated with the band. While this is
true for a system in a magnetic field with filled Landau Levels, even a system
in zero external field can exhibit the QHE if its band has a Chern number. I
review this issue and discuss a more recent question of whether a partially
filled Chern band can exhibit the Fractional QHE. I describe the work done with
What information can be determined about a state given
just the ground state wave function?
Quantum ground states, speaking intuitively, contain
fluctuations between many of the configurations one might want to understand.
The information about them can be organized by introducing an imaginary system,
dubbed the entanglement Hamiltonian.
What light does the dynamics of this Hamiltonian (a
precise version of the notion of "zero point motion") shed on the
actual system?
Much effort has been devoted to the study of systems with
topological order, motivated by practical issues as well as more field
theoretical and mathematical concerns. This talk will give an overview of some
of the field, describing abelian systems relevant to the search for spin
liquids, and non-abelian systems relevant to topological quantum computation. I
will focus in particular on problems not reducible to free-fermion ones;
examples include the RVB state of electrons as well as models of quantum loops
and nets.
Amorphous materials (glasses) probably
constitute >90% of the solid matter surrounding us in everyday life,yet
traditional textbooks of condensed matter physics devote virtually no space to
them.Crudely speaking,the puzzles in the behavior of glasses can be divided
into three major areas:the glass transition itself,the characteristic long-term
memory effects and the near-equilibrium thermal,dielectric and transport
properties;this talk focusses entirely on the third area.Over the last 40 years
A simple physical realization of an integer quantum Hall
state of interacting two dimensional bosons is provided. This is an example of
a "symmetry-protected topological" (SPT) phase which is a
generalization of the concept of topological insulators to systems of
interacting bosons or fermions. Universal physical properties of the boson
integer quantum Hall state are described and shown to correspond to those
expected from general classifications of SPT phases.
I will briefly review topological phases of non
interacting fermions, such as topological insulators, and discuss how ideas
from quantum information, in particular the entanglement spectrum, can be used
to characterize them.
It has long been known that a metal near an instability
to antiferromagnetism also has a weak-coupling Cooper instability to
spin-singlet d-wave-like superconductivity.
However, the theory of the antiferromagnetic quantum
critical point flows to strong-coupling in two spatial dimensions, and so the
fate of the superconductivity has also been unclear.
We discuss the thermodynamic properties of the model
exchange quantum spin ice material Yb_2Ti_2O_7. Using exchange parameters
recently determined from high-field neutron scattering measurements, we
calculate the thermodynamic properties of this model system. We find very good
agreement with the heat capacity, entropy and magnetization measurements on the
materials. We show that, in the weak quantum regime, quantum fluctuations lead
to the selection, within the spin-ice manifold, of a conventional ordered