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Résumé |
Topological quantum matter is characterized by invariants, abstract quantities that remain unchanged
under perturbations. A paradigmatic example is the many-body Chern number, which quantizes the Hall
conductivity of quantum Hall states [1]. However, these many-body invariants are intrinsically complex,
motivating the search for simplified theoretical descriptions and experimentally accessible probes.
In this talk, I present two complementary approaches to this challenge. First, I show that the many-body
Chern number can be extracted from local, purely static ground-state current measurements [2]. This
leads to explicit relations between measurable observables and a local many-body Chern marker,
providing a practical route to detecting topological order at the level of individual lattice sites. These
results are directly relevant to current and emerging quantum simulation platforms. Then, I investigate
invariants formulated in terms of single-particle Green’s functions, addressing a fundamental tension in
strongly-correlated quantum matter [3]. Indeed, while single-particle Green’s functions provide a rigorous
framework for defining topological invariants, the low-energy physics of correlated topological phases is
governed by collective excitations rather than single-particle degrees of freedom. I clarify the extent to
which single-particle quantities encode the topological properties of fractional quantum Hall states [4].
[1] N. Goldman and T. Ozawa, Comptes Rendus. Physique, 25 289 (2024)
[2] F. Palm, A. Impertro, M. Aidelsburger and N. Goldman, arXiv:2510.19742
[3] L. Peralta Gavensky, S. Sachdev and N. Goldman, Phys. Rev. Lett. 131, 236601 (2023)
[4] A. Markov, A. Nikishin, N. Cooper, N. Goldman and L. Peralta Gavensky, arXiv:2603.17006 |
