Abstract

We examine a partial sum-rule for the inverse frequency-weighted optical conductivity restricted to low energies in correlated insulating phases. Using solvable limits of magic-angle twisted bilayer graphene, fractional Chern insulators, and topologically trivial flat-band models, we derive a projected optical absorption sum-rule and show that it is governed by many-body projected operators and low-energy geometry rather than the full band quantum geometry. The work also connects the projected sum-rule to interaction-renormalized many-body projected quantum geometry and to the quantum Fisher information of the projected many-body position operator.

Abstract

We examine a partial sum-rule for the inverse frequency-weighted optical conductivity restricted to low energies in correlated insulating phases. Using solvable limits of magic-angle twisted bilayer graphene, fractional Chern insulators, and topologically trivial flat-band models, we derive a projected optical absorption sum-rule and show that it is governed by many-body projected operators and low-energy geometry rather than the full band quantum geometry. The work also connects the projected sum-rule to interaction-renormalized many-body projected quantum geometry and to the quantum Fisher information of the projected many-body position operator.

Abstract

We examine a partial sum-rule for the inverse frequency-weighted optical conductivity restricted to low energies in correlated insulating phases. Using solvable limits of magic-angle twisted bilayer graphene, fractional Chern insulators, and topologically trivial flat-band models, we derive a projected optical absorption sum-rule and show that it is governed by many-body projected operators and low-energy geometry rather than the full band quantum geometry. The work also connects the projected sum-rule to interaction-renormalized many-body projected quantum geometry and to the quantum Fisher information of the projected many-body position operator.

Abstract

We examine a partial sum-rule for the inverse frequency-weighted optical conductivity restricted to low energies in correlated insulating phases. Using solvable limits of magic-angle twisted bilayer graphene, fractional Chern insulators, and topologically trivial flat-band models, we derive a projected optical absorption sum-rule and show that it is governed by many-body projected operators and low-energy geometry rather than the full band quantum geometry. The work also connects the projected sum-rule to interaction-renormalized many-body projected quantum geometry and to the quantum Fisher information of the projected many-body position operator.