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arXiv:2510.10525

Robust protocols to reveal anyonic time-exchange phase

Inès Safi A

Published Oct 12, 2025• 0 citations
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Abstract

We consider hierarchical quantum Hall edge states with $N$ modes and a spatially local quantum point contact (QPC). In general, the field of an injected anyon does not directly acquire the universal statistical phase $θ$. Short-range inter-edge interactions split the universal anyon charge and phase into $N$ fractionalized charges associated with nonuniversal phases $πδ_m$. In contrast, their sum $δ=\sum_{m=1}^Nδ_m$, which defines the local scaling dimension at the QPC, remains protected and is tied to the statistical angle through $πδ=θ$. If the injected anyon is of the same species as the one dominating backscattering at the QPC, time-domain braiding with phase $θ$ is recovered either in the absence of inter-edge interactions with equal mode velocities, or by performing a spatially local anyon injection at the QPC. We then exploit a more robust \emph{local} anyonic time-exchange (ATE) link between anyons and quasiholes at the QPC, which is also a necessary ingredient for realizing such braiding. This allows us to propose minimal single-QPC protocols that do not rely on diluted anyon sources and that disentangle the role of $θ$ as a genuine statistical phase from that as a scaling dimension. From the ATE link we derive two novel nonequilibrium fluctuation--dissipation relations (FDRs) that isolate $θ$. They relate the DC backscattering noise either to an integral over the DC current or to the phase shift of the AC current with respect to an applied AC voltage (i.e., the phase of the admittance), accessible down to low frequencies. For thermalized edges, we show that in the quantum regime this admittance phase directly yields $θ$ whenever $δ>1/2$.

DOI
10.48550/arxiv.2510.10525

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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\barθθˉ, 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 δδδ determined by θˉ=πδ(modπ)\barθ=πδ\pmodπθˉ=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 δδδ and statistical phase θθθ, identical to θˉ\barθθˉ 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 θθθ and δδδ 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−δδ\mapsto1-δδ↦1−δ at fixed θθθ. For independent statistical phase and scaling dimension, the thermal crossover can reverse the sign of output cross-correlations.
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-particle interferometry is an important tool for extracting the exchange statistics of quantum particles. We theoretically investigate the prospects of such interferometry to probe the statistics of pointlike anyonic excitations injected in a Hong-Ou-Mandel (HOM) setup based on a quantum point contact device in the fractional quantum Hall regime. We compute the standard HOM ratio, i.e., the ratio of tunneling noises for two- and one-particle injections, and find that for pointlike anyons it only depends on the temperature and the anyon scaling dimension. Importantly, the latter is not necessarily related to the exchange phase. In fact, we establish that the HOM ratio does not reveal the exchange phase of the injected anyons: For injection-time delays that are small compared to the thermal timescale, we find that the exchange phase accumulated due to time-domain braiding between injected and thermally activated anyons is erased due to two mutually canceling subprocesses. In contrast, for time delays large compared to the thermal time, only a single subprocess contributes to the braiding, but the accumulated phase is canceled in the HOM ratio. These findings suggest caution when interpreting HOM interferometry experiments with anyons, and approaches beyond the standard HOM ratio are thus necessary to extract anyonic statistics with two-particle interferometry experiments.
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.
Observation of Time-Domain Braiding of Non-Abelian Anyons at ν=5/2ν= 5/2ν=5/2 State
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The low-energy dynamics of two-dimensional topological matter hinges on its one-dimensional edge modes. Tunneling between fractional quantum Hall edge modes facilitates the study of anyonic statistics: it induces time-domain braiding that dominates signals from diluted anyon beams. We develop a framework for characterizing one-dimensional out-of-equilibrium anyonic states and define their effective potential and temperature, both arising from anyonic braiding, as well as the landscape of their excitations. Unlike fermions, the effective anyon potential depends on the type of the tunneling quasiparticles; nonequilibrium anyonic states are underlain by power-law energy distributions. This allows "hot" anyons to tunnel above the chemical potential of the source, which we capture by a measurable universal witness function. Our analysis raises the prospect of generalizing the kinetic approach to compressible anyonic matter in higher dimensions.