Topological Phases in Hydrogenated Group 13 Monolayers

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...

Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology

We propose that Symmetry Protected Topological Phases with a finite symmetry group G are classified by cobordism groups of the classifying space of G. This provides an explanation for the recent discovery of bosonic SPT phases which do not fit into the group cohomology classification. We discuss the connection of the cobordism classification of SPT phases to gauge and gravitational anomalies in...

Topological properties of geometric phases

The level crossing problem and associated geometric terms are neatly formulated by using the second quantization technique both in the operator and path integral formulations. The analysis of geometric phases is then reduced to the familiar diagonalization of the Hamiltonian. If one diagonalizes the Hamiltonian in one specific limit, one recovers the conventional formula for geometric phases. O...

Neural Networks Identify Topological Phases

A detailed characterization of phases of matter is at the forefront of research in condensed-matter and statistical physics. Although physicists have made incredible progress in the characterization of a wide variety of phases, the identification of novel topological phases remains challenging. Now, Yi Zhang and Eun-Ah Kim from Cornell University, New York [1], have taken a big-data approach to...

Topological phases and quantum computation