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Unconventional quasiparticles emerging in the fractional quantum Hall regime present the challenge of observing their exotic properties unambiguously. Although the fractional charge of quasiparticles has been demonstrated since nearly three decades, the first convincing evidence of their anyonic quantum statistics has only recently been obtained and, so far, the so-called scaling dimension that determines the quasiparticles propagation dynamics remains elusive. In particular, while the non-linearity of the tunneling quasiparticle current should reveal their scaling dimension, the measurements fail to match theory, arguably because this observable is not robust to non-universal complications. Here we expose the scaling dimension from the thermal noise to shot noise crossover, and observe an agreement with expectations. Measurements are fitted to the predicted finite temperature expression involving both the quasiparticles scaling dimension and their charge, in contrast to previous charge investigations focusing on the high bias shot noise regime. A systematic analysis, repeated on multiple constrictions and experimental conditions, consistently matches the theoretical scaling dimensions for the fractional quasiparticles emerging at filling factors 1/3, 2/5 and 2/3. This establishes a central property of fractional quantum Hall anyons, and demonstrates a powerful and complementary window into exotic quasiparticles.

Anyons are exotic low-dimensional quasiparticles whose unconventional quantum statistics extends the binary particle division into fermions and bosons. The fractional quantum Hall regime provides a natural host, with first convincing anyon signatures recently observed through interferometry and cross-correlations of colliding beams. However, the fractional regime is rife with experimental complications, such as an anomalous tunneling density of states, which impede the manipulation of anyons. Here we show experimentally that the canonical integer quantum Hall regime can provide a robust anyon platform. Exploiting the Coulomb interaction between two co-propagating quantum Hall channels, an electron injected into one channel splits into two fractional charges behaving as abelian anyons. Their unconventional statistics is revealed by negative cross-correlations between dilute quasiparticle beams. Similarly to fractional quantum Hall observations, we show that the negative signal stems from a time-domain braiding process, here involving the incident fractional quasiparticles and spontaneously generated electron-hole pairs. Beyond the dilute limit, a theoretical understanding is achieved via the edge magnetoplasmon description of interacting integer quantum Hall channels. Our findings establish that, counter-intuitively, the integer quantum Hall regime provides a platform of choice for exploring and manipulating quasiparticles with fractional quantum statistics., Comment: 6 pages, 4 figures, Methods, Supplemental Information