Lucila PERALTA GAVENSKY, The Streda Formula and its Remarkable Consequences: From Strongly Correlated to Topological Floquet Systems

Lucila PERALTA GAVENSKY, Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles

Contact: andrej.mesaros@universite-paris-saclay.fr

Le résumé :

The Streda formula is a remarkable thermodynamic relation linking the topological Hall conductivity of insulating states of matter to their density response under a probe magnetic field.

I will explain how this non-perturbative relation allowed us to derive a fundamental connection between the failure of Luttinger’s theorem and the classification of correlated quantum Hall phases with topological invariants built from single-particle Green’s functions [1].

I will also present our more recent findings on the generalization of the Streda formula to out-of-equilibrium Floquet systems, in which effective topological properties are generated by means of a time-periodic external field [2]. Building on elementary notions of spectral flow, which lie at the backbone of the Streda relation, we are able to derive the abstract winding numbers used to classify Floquet topological phases from physical principles and to connect them to tractable response functions.

[1] Lucila Peralta Gavensky, Subir Sachdev, and Nathan Goldman, “Connecting the Many-Body Chern Number to Luttinger’s Theorem through Streda’s Formula,” Phys. Rev. Lett. 131, 236601 (2023).

[2] Lucila Peralta Gavensky, Gonzalo Usaj, and Nathan Goldman, “The Streda Formula for Floquet Systems: Topological Invariants and Quantized Anomalies from Ces`aro Summation,” (2024), arXiv:2408.13576.