Speaker
Description
Fractionalization and anyon superconductivity are fascinating concepts in modern condensed matter physics, dating back to the 1980s and the work of Laughlin and others. The recent experimental discovery of the zero-field fractional Chern insulator (FCI) and of superconductivity provides renewed motivation for these questions. In this talk, I will present recent work on FCIs and anyon superconductivity, with particular emphasis on the microscopic aspects. In the first part, I will show how FCIs serve as a bridge between fractional quantum Hall (FQH) and Hubbard physics. I will present a family of exact lattice FCIs stabilized by Hubbard-type interactions of arbitrary strength. These model FCIs are characterized by lattice-specific clustering rules whose underlying algebraic structure we prove to be that of Macdonald polynomials. Numerical studies reveal several features characteristic of model states. Taking the infinite-interaction limit yields exact spin-based parent Hamiltonians whose ground states are exact chiral spin liquids. In the second part, I will discuss a microscopic theory of anyon superconductivity, focusing on the second-quantized formulation of anyons and on BCS-type wave functions.