Fig. 2: Stability of the parafermion phase and quantum geometry.
a The many-body energy spectrum gap for non-Abelian \({{\mathbb{Z}}}_{3}\) RR states at ν = 3/5 (red dotted lines, right axis) as a function of the coupling strength γ between twisted layers is shown for system sizes Ns = 20 (squares) and Ns = 25 (circles) together with the averaged quantum metric χ (blue line, left axis). The energy gap is defined as the difference between the energies of the lowest non-RR state and the highest RR state (typically the 11th and the 10th lowest energies), and it is set to zero if the difference is negative. The shaded area denotes the regime where parafermions are stable. b Quantum metric g(k)ABZ/2π of the single-particle band for γ = 0.20 and (c) γ = 3.75. ABZ is the Brillouin zone area.
