Geometric response of fractional quantum Hall states to anisotropy

Fractional quantum Hall states possess a geometric degree of freedom that is usually hidden in the case of rotationally symmetric Hamiltonians. When this symmetry is broken, for example by means of an anisotropic electron band mass or electron-electron interaction, the many-body wavefunction optimizes over this degree of freedom to obtain the lowest energy. This is manifested as a partial transference of the anisotropy of Hamiltonian to observable properties of the ground state. In some cases, the fractional quantum Hall phase is unstable to the application of anisotropy and there is a transition to a broken symmetry phase. We use a combination of exact diagonalization and the infinite density matrix renormalization group (iDMRG) algorithm to quantify the extent of the anisotropic response and find a remarkable dependence on filling fraction, Landau level index, interaction type and particle statistics [1].
[1] Krishna et al, Phys. Rev. B 100, 085129 (2019)