Fractional quantum Hall quasiparticles are generally characterized by two quantum numbers: electric charge
Q and scaling dimension $\mathrm{\ensuremath{\Delta}}$. For the simplest states (such as the Laughlin series), the scaling dimension determines the anyonic statistics of the quasiparticle (the statistical phase $\ensuremath{\theta}=2\ensuremath{\pi}\mathrm{\ensuremath{\Delta}}$). For more complicated states (featuring counterpropagating modes or non-Abelian statistics), knowing the scaling dimension is not enough to extract the quasiparticle statistics. Nevertheless, even in those cases, knowing the scaling dimension facilitates distinguishing different candidate theories for describing the quantum Hall state at a particular filling (such as PH-Pfaffian and anti-Pfaffian at $\ensuremath{\nu}=\frac{5}{2}$). Here, we propose a scheme for extracting the scaling dimension of quantum Hall quasiparticles from thermal tunneling noise produced at a quantum point contact. Our scheme makes only minimal assumptions about the edge structure and features the level of robustness, simplicity, and model independence comparable with extracting the quasiparticle charge from tunneling shot noise.
We propose a method to extract the mutual exchange statistics of the anyonic excitations of a general Abelian fractional quantum Hall state, by comparing the tunneling characteristics of a quantum point contact in two different experimental conditions. In the first, the tunneling current between two edges at different chemical potentials is measured. In the second, one of these edges is strongly diluted by an earlier point contact. We describe the case of the dilute beam in terms of a time-domain interferometer between the anyons flowing along the edge and quasiparticle-quasihole excitations created at the tunneling quantum point contact. In both cases, temperature is kept large, such that the measured current is given to linear response. Remarkably, our proposal does not require the measurement of current correlations, and allows us to carefully separate effects of the fractional charge and statistics from effects of intra- and interedge interactions.
We study delta-T noise -- excess charge noise at zero voltage but finite temperature bias -- for weak tunneling in 1D interacting systems. We show that the sign of the delta-T noise is generically determined by the nature of the dominating tunneling process (more specifically, its scaling dimension). We clarify the relation between the sign of delta-T noise and the quantum exchange statistics of tunneling quasiparticles. We find that, for infinite systems hosting chiral channels with local interactions (e.g., quantum Hall or quantum spin Hall edges), when the delta-T noise is negative, the tunneling particles are boson-like, revealing their tendency towards bunching. However, the opposite is not true: Boson-like particles do not necessarily produce negative delta-T noise. Importantly, the bosonic nature of particles generating the negative delta-T is not necessarily intrinsic, but can be induced by the interactions. This particularly implies that negative delta-T noise for tunneling between the edge states cannot serve as a smoking gun for detecting "intrinsic anyons". We also establish a connection between the delta-T noise and the temperature derivative of the thermal noise in interacting systems, both governed by the same scaling dimensions. As a demonstration of the above statements, we study tunneling between two interacting quantum spin Hall edges. With bosonization and renormalization-group techniques, we find that many-body interactions can generate negative delta-T noise for both direct tunneling through a point contact and in Kondo exchange tunneling via a localized spin. In both setups, we show that the noise can become negative at sufficiently low temperatures, when interactions renormalize the tunneling to favor boson-like pair-tunneling of electrons. Our findings show that delta-T noise can probe the nature of collective excitations in interacting 1D systems.
We address hierarchical fractional quantum Hall edges coupled by a spatially local quantum point contact within the Unified Nonequilibrium Perturbative (UNEP) framework. Without assuming a Tomonaga-Luttinger liquid (TLL) tunneling correlator, we impose a local anyonic time-exchange (ATE) constraint with phase
θˉ, yielding a nonequilibrium fluctuation-dissipation integral equation relating DC tunneling current and noise. For thermal initial states, detailed balance closes this equation for the current. Using the Wiener-Hopf method, we find a unique physical solution of local TLL form, with scaling dimension
δ determined by
θˉ=πδ(modπ), emerging from the solution rather than being imposed via a TLL correlator. By contrast, ATE and inversion symmetry alone fix the exchange monodromy but not the full transport dynamics. We then study the "anyon collider" beyond Laughlin states at finite temperatures. Detailed balance is broken and noise becomes super-Poissonian, but the relation between nonequilibrium and equilibrium correlators determines current and noise. The output cross-correlation and balanced generalized Fano factor depend on both
δ and statistical phase
θ, identical to
θˉ for co-propagating modes with short-range interactions. A temperature-dependent current scale separates the zero-temperature asymptotic regime from the low-current regime, where the balanced Fano factor saturates to a function of
θ and
δ distinct from its zero-temperature value. This latter regime is particularly relevant to ``anyon collider'' experiments. These complementary regimes constrain the statistical phase and scaling dimension, subject to the symmetry
δ↦1−δ at fixed
θ. For independent statistical phase and scaling dimension, the thermal crossover can reverse the sign of output cross-correlations.
We have recently calculated exact nonequilibrium quantum transport properties through a point contact in a Luttinger liquid. Using a particular quasiparticle basis of the Hilbert space dictated by integrability, we here compute explicitly the exact I(V) characteristic and conductance out of equilibrium as a function of driving voltage V and temperature T. These are described by universal scaling functions of two variables, the scaled point-contact interaction strength, and V/T. The differential-conductance curve as a function of the interaction strength broadens significantly as V/T is increased, and develops a pronounced maximum at a (universal) critical value (eV/
kBT)=7.188 68. . .. In addition, we derive an exact duality between strong and weak backscattering. The theory presented here has recently been realized experimentally in resonant tunneling-transport experiments between edge states in fractional quantum Hall effect devices. In this context the exact duality is between electron tunneling and Laughlin-quasiparticle tunneling.
An upstream neutral mode can influence quasiparticle tunneling even when electric charge propagates only downstream. We propose a three-path fractional quantum Hall interferometer that probes this directional structure through the flux dependence of average terminal currents. Interference between direct and two-step tunneling first contributes at cubic order in the tunneling amplitudes of three weak quantum point contacts. In the local theory, equal drain voltages separate the downstream and upstream responses: for a purely downstream tunneling excitation, the cubic fundamental Aharonov-Bohm harmonic vanishes at one drain, while the other remains bright. Averaging measurements with exchanged unequal drain voltages extends this separation to a configuration in which all contacts are biased. It requires independent calibration of the electrostatic phase shift and fixed or known tunneling magnitudes. For a selected Abelian excitation with two-point correlation exponent
0<Δℓ<1, the common low-temperature bias power and directional amplitude ratio determine its scaling dimension and principal exchange angle. We also show that a weak static density interaction spanning two tunneling points can activate the dark harmonic without adding an upstream mode. In the high-bias static limit, the first-order Laughlin activated amplitude scales as
E2ν−1, where
E is the source-drain bias energy and
ν is the filling factor. In the weak localized single-mode infrared regime, the bright harmonic retains its leading scaling and can serve as a reference in the same device. The calculation assumes one coherent tunneling species and common-temperature edge correlations with unresolved propagation times.