Zero-temperature continuity of the FQAHS–PSM transition

Determine whether a continuous zero-temperature phase transition exists between the fractional quantum anomalous Hall plus smectic charge-density-wave (FQAHS) state and the polar smectic metal (PSM) state in the checkerboard-lattice spinless-fermion flat Chern band at filling nu = 2/3 when tuning longer-range interactions, and, if such a transition exists, characterize its continuous topological nature beyond the traditional Ginzburg–Landau paradigm.

Background

The paper reports a continuous transition from a symmetric fractional quantum anomalous Hall (FQAH) state to an FQAHS state driven by the softening of magnetoroton modes while the charge gap remains open. It further notes that at larger interaction strengths a topologically trivial polar smectic metal (PSM) phase emerges.

Prior work with only third-neighbor interaction V3 found the ground-state FQAHS–PSM transition to be first-order, with indications that the finite-temperature transition might be continuous. This motivates the question of whether a continuous transition at zero temperature is possible and, if so, what its topological character is.