From Středa’s formula to Luttinger’s theorem: Topological signatures unveiled through density probes

Appears in collection : 2024 - T1 - WS1 - Quantum simulators

Identifying experimentally accessible probes that are able to reveal truly distinctive properties of topological phases of matter has remained as an ever-relevant mission. In this talk, I will start reviewing recent advances that were made possible thanks to a remarkable thermodynamic relation known as the Widom-Středa formula, which relates the quantized Hall conductivity of an insulator to its density response under an external probe magnetic field.

I will discuss how this response can be interpreted as a genuine local topological marker and briefly show how we adapted this well-known formula to explore the emergence of quantized valley Hall signals in strained honeycomb lattices [1]. Then, 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 winding numbers built from single-particle Green’s functions [2].