Extracting transport coefficients from local ground-state currents

Abstract

Transport properties are central to characterizing quantum matter, yet their extraction typically requires external forcing and time-resolved measurements. In this work, we propose a scheme to access transport coefficients directly from measurements of local static ground-state currents -- quantities readily accessible in quantum-engineered platforms. By exploiting the exponential decay of correlations in gapped systems and the finite velocity of correlation spreading, we demonstrate that the local Hall response of correlated insulators can be reconstructed from a small set of quasi-local current observables. We derive explicit relations connecting these static observables to a practical local Chern marker, and introduce a scalable digital protocol for measuring the required generalized currents in quantum simulators. We demonstrate the applicability of our approach through numerical studies of emblematic Chern-insulator systems, both in the non-interacting and strongly-correlated (fractional) regime. Our method extends naturally to a broad class of correlated systems, even at finite temperature, offering a broadly applicable route to probing transport in engineered quantum matter.