Quantum Hall Phases from Dipolar Symmetry Breaking

The spontaneous breaking of multipole symmetries has been a matter of recent interest, leading to novel phases of matter such as Bose condensates without a Meissner effect and Fermi surfaces without quasiparticles [1,2]. Here, we investigate the related question of fermionic dipole symmetry-breaking orders that exhibit nontrivial topology. We compute the mean-field phase diagram of a 2-d dipole-symmetric model where the symmetry-breaking ground states are band insulators with a variable Chern number. The Chern number of the occupied band is found to determine both the counting and dispersion of the Goldstone modes of the broken dipole symmetry. At the topological phase transition from a trivial insulator to a Chern insulator, we study a novel quantum critical point featuring an emergent Dirac fermion coupled to the dipolar Goldstone modes. We additionally discuss the boundary theory of the mean-field ground states, and show that the boundary mode remains chiral but acquires a cubic dispersion.

[1] Ethan Lake, Michael Hermele, and T. Senthil. Dipolar bose-hubbard model. Phys. Rev. B, 106:064511, Aug 2022.

[2] Amogh Anakru and Zhen Bi. Non-fermi liquids from dipolar symmetry breaking. Phys. Rev. B, 108:165112, Oct 2023.