PI-UIUC Joint Workshop On Strongly Correlated Quantum Many-Body Systems
Twist defects are point-like objects that support robust non-local
storage of quantum information and non-abelian unitary operations.
Unlike quantum deconfined anyonic excitations, they rely on symmetry
rather than a non-abelian topological order. Zero energy Majorana bound
states can arise at lattice defects, such as disclinations and
dislocations, in a topological crystalline superconductor. More general
parafermion bound state can appear as twist defects in a topological
I will begin reviewing the Callan-Harvey mechanism of anomaly inflow
with particular focus on topological edge states and show how the
inflow picture naturally converts the non-covariant "consistent"
gauge anomaly of Bardeen and Zumino to the more physical "covariant"
anomaly. I will then discuss some recent derivations of the covariant
form of the gauge anomaly from classical phase space flows.
When proximity coupled to s-wave superconductors, quantum wires can
support effective p-wave superconductivity under appropriate
circumstances. The p-wave state has Majorana states at the wire ends
which can store quantum information. I will discuss some properties of
Majorana states formed in oxide and semiconductor quantum wires,
including superconducting state phase diagrams as a function of
spin-orbit coupling strength, Fermi energy, and external magnetic field
strength, and Majorana exchange properties.
We employ holographic techniques to study quantum quenches at finite
temperature, where the quenches involve varying the coupling of the
boundary theory to a relevant operator with an arbitrary conformal
dimension. The evolution of the system is studied by evaluating the
expectation value of the quenched operator and the stress tensor
throughout the process. The time dependence of the new coupling is
characterized by a fixed timescale and the response of the observables
Certain varieties of transition metal oxides possess both significant
interactions and strong spin-orbit coupling. In this talk I will
describe materials-motivated models that predict topological phases in
heterostructured and bulk transition metal oxides. We find Z2
topological insulators, Chern insulators, topological crystalline
insulators, and interaction-driven topological phases not adiabatically
connected to non-interacting topological phases.
At a quantum critical point (QCP) in two or more spatial dimensions,
leading-order contributions to the scaling of entanglement entropy
typically follow the "area" law, while sub-leading behavior contains
universal physics. Different universal functions can be access through
entangling subregions of different geometries. For example, for
polygonal shaped subregions, quantum field theories have demonstrated
that the sub-leading scaling is logarithmic, with a universal
coefficient dependent on the number of vertices in the polygon.
One of the open problems in strong correlation physics is whether or not
Luttinger's theorem works for doped Mott insulators, particularly in
the pseudo gap regime where the pole-like excitations form only a Fermi
arc. I will begin this talk by using this theorem to count particles and
show that it fails in general for the Mott state. The failure stems
from the divergent self energy that underlies Mottness. When such a
divergence is present, charged degrees of freedom are present that have