Interaction-robust probes of Fermi-surface topology in higher dimensions

Identify observables in higher-dimensional interacting Fermi liquids that retain interaction-independent information about Fermi-surface topology, potentially through kinematic structures such as the coadjoint-orbit Wess–Zumino–Witten term rather than through density correlations alone.

Background

The paper shows that interactions generate an additional band-curvature-dependent nonanalytic contribution to the equal-time density three-point function in a two-dimensional Fermi liquid. Consequently, although the noninteracting topology-sensitive structure can persist, the full density correlator is no longer determined solely by the topology of the Fermi sea. The authors therefore leave unresolved the broader problem of finding observables whose topological information remains independent of interaction-dependent Hamiltonian parameters. They suggest that observables governed by the kinematic sector of the coadjoint-orbit theory, including the Wess–Zumino–Witten term, may provide suitable candidates, by analogy with the interaction-independent stress-tensor correlator in one-dimensional Luttinger liquids.