Stiefel–Whitney classes and topological phases in band theory

Topological Phases in Narrow-band syst(

I discuss several novel topological phases in correlated electron systems, realized through spin-orbit interactions and lattice effects especially narrow-band systems. The first realizes the fractional quantum Hall effect using geometric frustration and ferromagnetism to obtain a nearly flat band with a large bandgap and non-zero Chern number. This system can support this effect at high tempera...

Self-consistent phases in topological particle theory.

Equivariant Topological Quantum Field Theory and Symmetry Protected Topological Phases

Short-range entangled topological phases of matter are closely connected to Topological Quantum Field Theory. We use this connection to classify Symmetry Protected Topological Phases in low dimensions, including the case when the symmetry involves time-reversal. To accomplish this, we generalize Turaev’s description of equivariant TQFT to the unoriented case. We show that invertible unoriented ...

Gauge theory of topological phases of matter

We study the response of quantum many-body systems to coupling some of their degrees of freedom to external gauge fields. This serves to understand the current Green functions and transport properties of interacting many-body systems. Our analysis leads to a “gauge theory of states of matter” complementary to the well-known Landau theory of order parameters. We illustrate the power of our appro...

Entanglement in Topological Phases

In this report, the research conducted on entanglement in topological phases is detailed and summarized. This includes background developed and an explanation of the structure of the code written it MATLAB to compute various aspects of entanglement for topological systems. Topological phases are generally those that cannot be described by Landau symmetry-breaking, including the fractional quant...