Work

Equality of Magnetization and Edge Current for Interacting Lattice Fermions at Positive Temperature

Year: 2024

Type: article

Abstract: We prove that the magnetization is equal to the edge current in the thermodynamic limit for a large class of models of lattice fermions with finite-range interactions satisfying local indistinguishability of the Gibbs state, a condition known to hold for sufficiently high temperatures. Our result implies that edge currents in such systems are determined by bulk properties and are therefore stable against large perturbations near the boundaries. Moreover, the equality persists also after taking the derivative with respect to the chemical potential. We show that this form of bulk-edge correspondence is essentially a consequence of homogeneity in the bulk and locality of the Gibbs state. An important intermediate result is a new version of Bloch’s theorem for two-dimensional systems, stating that persistent currents vanish in the bulk.

Source: Mathematical Physics Analysis and Geometry

DOI: 10.1007/s11040-024-09495-8

Authors: Jonas Lampart, Massimo Moscolari, Stefan Teufel, Tom Wessel

Institutions: Centre National de la Recherche Scientifique, Université de Bourgogne, Laboratoire Interdisciplinaire Carnot de Bourgogne, Politecnico di Milano, University of Tübingen

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,890