Continuous transition and gapless roton inside fractional quantum anomalous Hall states

Abstract

Collective excitations play a vital role in understanding the exotic phases of matter and phase transitions in quantum many-body systems. For the first time, we numerically (via exact diagonalization and density matrix renormalization group) report the microscopic realization of a transition from a translationally invariant fractional quantum anomalous Hall (FQAH) state to the same FQAH state with spontaneously broken translation symmetry, by softening the magnetoroton mode (intrinsic collective excitations in such systems) through isotropic interactions in a topological flat-band model. At the critical point, the gap of collective neutral excitations closes at finite momentum, while the charge gap remains robust. This mechanism echoes with the integer quantum Hall crystals and fractional quantum Hall nematics in Landau levels, but exhibits unique features. Further through criticality analysis, we identify that this non-trivial transition is consistent with the Ising universality class. Such spontaneous translation symmetry breaking inside the topological ordered FQAH state could serve as a generic scheme in various systems, with experimental implications to the quantum moir\'e materials and the cold-atom systems.