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.
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.
Quantum point contacts (QPCs) are essential tools for transport experiments in solid-state systems, enabling the detection of fractional charges and anyonic braiding statistics. Realizing analogous transport setups in isolated quantum-simulation platforms, such as ultracold atoms, remains challenging, since it typically requires coupling to external reservoirs. Here we show that the scattering properties of chiral edge states at a QPC can instead be extracted directly from the stationary edge currents of an isolated, reservoir-free lattice system. Exploiting the sensitivity of this scattering to Aharonov-Bohm-type phases, we propose an equilibrium protocol to detect local magnetic fluxes from ground-state edge currents. We further introduce a dynamical scheme, robust against finite temperature and particle-number fluctuations, based on the post-quench evolution following a sudden potential-bias removal. Since anyonic excitations are themselves associated with a local, quantized magnetic flux, our approach should extend to probing anyonic statistical phases in quantum-engineered platforms.
Two-dimensional topological insulators, characterized by symmetry-protected anomalous boundary modes, have been generalized to the strongly correlated regime for both bosonic and fermionic systems. As correlated topological insulators (TI) approach experimental realization in quantum simulators, conventional probes, such as transport measurements, are not easily applicable to these synthetic platforms. In this study, we focus on two examples of correlated TI: a bosonic TI protected by Z2×U(1) symmetry and the fermionic quantum spin Hall insulator protected by time-reversal symmetry. We propose a unified, readily implementable protocol based on measuring the disorder parameter ⟨exp(iθQ^A)⟩ for a large subregion A, with Q^A the total charge operator within A. Our key finding is that this quantity exhibits non-analytical dependence on θ for correlated TI, a signature robust against decoherence. We establish this diagnostic through both numerical simulations and analytical derivations. This protocol is well-suited for implementation on near-term quantum simulation platforms, providing a direct route to experimentally confirm correlated TI.
Characterizing carrier type in strongly correlated quantum systems conventionally relies on the Hall effect. In cold-atom quantum simulators, implementing Hall transport measurements typically requires synthetic gauge fields, which introduces significant heating. Here, we present nonlinear spectroscopic and fluctuation-based protocols that establish an alternative route to identifying the sign of quasiparticle charge. We demonstrate that second-order density and current responses to finite-momentum quenches and drives-as well as equilibrium third-order density cumulants-distinguish electron- from hole-like quasiparticles. For a Fermi-Hubbard multi-leg ladder on a square lattice, numerical simulations reveal a crossover from hole- to electron-like carriers upon hole-doping away from half-filling, matching the sign change in the Hall coefficient. To demonstrate the applicability of our protocols beyond fermionic systems, we show that the nonlinear density response to a finite-momentum, finite-frequency drive reveals the sign of charge carriers in a hard-core boson ladder, and that the nonlinear signal can be significantly enhanced when driving near resonance with a nonlinear collective mode. Our results establish nonlinear density and current response and equilibrium non-Gaussian fluctuations as complementary probes, offering quantum simulators a direct route to characterize the carrier sign, without the experimental hurdles of conventional transport setups.
Luttinger's theorem constrains the particle density of interacting fermions through global properties of the single-particle Green's function, and its violation signals a breakdown of the identification between the quantized Hall response and the Green-function-based Ishikawa-Matsuyama invariant. This phenomenon becomes especially compelling in strongly correlated topological phases, such as fractional Chern insulators, where fractionalized quasiparticles lack an adiabatic connection to electrons, raising the question of how Green's-function-based topological invariants manifest in such phases. Using exact diagonalization of the fermionic Harper-Hofstadter-Hubbard model, we compute bulk single-particle Green's functions deep inside a fractional Chern insulating phase and directly evaluate the Luttinger count, its possible correction (the Luttinger integral), and the Ishikawa-Matsuyama invariant N3[G]. We demonstrate a clear violation of Luttinger's theorem and show that the fractional nature of the many-body Chern number is encoded in the Středa response of the Luttinger integral, while the integer invariant N3[G] arises from the Středa response of the Luttinger count. We also analytically prove that N3[G] is fully determined by the Luttinger count together with the Chern number of the occupied Bloch band, upon neglecting Bloch-band mixing. Finally, we propose an experimental protocol to extract all Green-function-based topological invariants from local density-of-states measurements, experimentally accessible in fractional quantum Hall systems.
Transport measurements are fundamental for understanding condensed matter phenomena, from superconductivity to the fractional quantum Hall effect. Analogously, they can be powerful tools for probing synthetic quantum matter in quantum simulators. Here we demonstrate the measurement of in situ particle current in a superconducting circuit lattice and apply it to study transport in both coherent and bath-coupled lattices. Our method utilizes controlled tunneling in a double-well potential to map current to on-site density, revealing site-resolved current and current statistics. We prepare a strongly interacting Bose-Hubbard lattice at different lattice fillings, and observe the change in current statistics as the many-body states transition from superfluid to Mott insulator. Furthermore, we explore nonequilibrium current dynamics by coupling the lattice to engineered driven-dissipative baths that serve as tunable particle source and drain. We observe steady-state current in discrete conduction channels and interaction-assisted transport. These results establish a versatile platform to investigate microscopic quantum transport in superconducting circuits.
Realizing strongly-correlated topological phases of ultracold gases is a central goal for ongoing experiments. And while fractional quantum Hall states could soon be implemented in small atomic ensembles, detecting their signatures in few-particle settings remains a fundamental challenge. In this work, we numerically analyze the center-of-mass Hall drift of a small ensemble of hardcore bosons, initially prepared in the ground state of the Harper-Hofstadter-Hubbard model. By extracting the Hall conductivity in a wide range of the magnetic flux, we identify an emergent Hall plateau compatible with a fractional Chern insulator state: the width of the plateau agrees with the spectral and topological properties of the prepared ground state, while the Hall conductivity approaches a fractional value determined by the many-body Chern number. A comparison with a direct application of Streda's formula is also discussed. Our calculations suggest that fractional Chern insulators can be detected in cold-atom experiments, using available detection methods.