Instability of Laughlin fractional quantum Hall liquids into gapless power-law correlated states with continuous exponents in ideal Chern bands: Rigorous results from plasma mapping

We investigate the fate of Laughlin's wave function in ideal Chern bands which can be mapped to generalized zero Landau levels in spatially dependent magnetic fields. By exploiting its exact mapping onto a classical Coulomb gas and leveraging previous results of one-component plasmas in nonuniform neutralizing backgrounds, we demonstrate that the ideal Laughlin wave function undergoes a phase transition from its well-known fully gapped topologically ordered plasma state into a power-law correlated dielectric state even for the fixed filling of 1 / 3 , as the magnetic field becomes increasingly more inhomogeneous. This dielectric state is gapless even though it does not spontaneously break translational symmetry. Remarkably, for a fixed filling ν = 1 / m , the exponent governing density correlations in this state changes continuously as a function of the degree of spatial inhomogeneity of the magnetic field, and can range from 4 near a Berezinskii-Kosterlitz-Thouless transition to the plasma state, up to 2 m in the limit of fields generated by point solenoids.