Adiabatic Continuity of the Spinful Quantum Hall States

TL;DR

This paper demonstrates the adiabatic deformation of spinful quantum Hall states using an extended Hubbard model of anyons, confirming continuity between certain states and exploring topological invariants.

Contribution

It introduces a numerical approach to study adiabatic continuity in spinful QH states and confirms the connection between singlet states at different fillings.

Findings

Adiabatic deformation between $ u=2$ and $ u=2/5$ singlet QH states is confirmed.

The many-body Chern number remains invariant during adiabatic evolution.

The generalized Streda formula for spinful systems is validated.

Abstract

By using the extended Hubbard model of anyons, we numerically demonstrate the adiabatic deformation of the spinful quantum Hall (QH) states by transmutation of statistical fluxes. While the ground state is always spin-polarized in a series of $\nu=1$ integer QH system, the adiabatic continuity between the singlet QH states at $\nu=2$ and $\nu=2/5$ is confirmed. These results are consistent with the composite fermion theory with spin. The many-body Chern number of the ground state multiplet works as an adiabatic invariant and also explains the wild change of the topological degeneracy during the evolution. The generalized Streda formula of spinful systems is justified.