Many-Body Quantum Geometric Dipole

Collective excitations of electron systems may host internal structure tied to their quantum geometric structure. Recently this has been shown to result in electric dipole moments associated with neutral, two-body excitations, including excitons [1] and plasmons in two-dimensional [2] and quasi-one-dimensional [3] metals. We demonstrate that these properties can be formulated without reference to two-body wavefunctions. The approach relies on a set of momentum-labeled density matrices constructed from the many-body states, from which “hole-hosting” and “particle-hosting” single-particle states may be extracted, allowing a gauge-independent quantum geometric dipole (QGD) to be defined. This corresponds to the electric dipole moment of the excitation. As a concrete example, we analyze magnetoplasmon excitations above the Laughlin ground states of the fractional quantized Hall effect. The relevant single-particle states are constructed using composite-fermions. In the limit of very strong magnetic fields an exact result may be derived, which is equivalent to the QGD of a magnetoplasmon in the integral quantized Hall effect. This simple result is shown to be an outcome of the state fully lying in the lowest Landau level of the original electron degrees of freedom.