Interaction driven quantum phase transition in fractional quantum spin Hall effects

TL;DR

This paper uses exact diagonalization to study a checkerboard lattice model, revealing a quantum phase transition between two topologically distinct fractional quantum spin Hall states driven by spin-dependent interactions.

Contribution

It identifies and characterizes a quantum phase transition between two fractional quantum spin Hall phases with different degeneracies and demonstrates the topological nature of these phases through numerical analysis.

Findings

Two topological quantum phases with ninefold and threefold degeneracy identified.

Quantum phase transition confirmed by energy spectrum and quasispin excitation spectrum analysis.

Counting rules of spin excitations serve as fingerprints of fractionalized quantum spin Hall states.

Abstract

By means of finite size exact diagonalization we theoretically study the electronic many-body effects on the nearly flat-band structure with time-reversal symmetry in a checkerboard lattice model and identify the topological nature of two quantum phases, with ninefold and threefold degeneracy, that appear, respectively, at small and large values $\lambda$ of a nearest neighbor spin dependent interaction. Numerical evidences from the evolution of low-lying energy spectra and Berry phases with both spin-independent and spin-dependent twisted boundary conditions reveal that these two different ground states share the same topological spin Chern number. Quantum phase transition between these two states by tuning $\lambda$ is confirmed by evaluating the energy spectra and quasispin excitation spectra closing. At last, the counting rules of spin excitation spectra are demonstrated as the fingerprints of the fractionalized quantum spin Hall states.