We study the thermodynamic properties of the anyon gas in the presence of a contact interaction. In particular, we use dimensional and analytical regularizations to calculate the second virial coefficient for free and contact-interacting anyons. The Bethe-Uhlenbeck formula is discussed and it is shown that the same result is regained using the \ensuremath{\zeta} regularization. Finally, the second virial coefficients for contact-interacting particles in two and three spatial dimensions are obtained as special cases. \textcopyright{} 1996 The American Physical Society.We study the thermodynamic properties of the anyon gas in the presence of a contact interaction. In particular, we use dimensional and analytical regularizations to calculate the second virial coefficient for free and contact-interacting anyons. The Bethe-Uhlenbeck formula is discussed and it is shown that the same result is regained using the \ensuremath{\zeta} regularization. Finally, the second virial coefficients for contact-interacting particles in two and three spatial dimensions are obtained as special cases. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matterApr 15, 199614 citations

Anyon with Coulomb interaction

J.Y. Kim, Yun Soo Myung, S.H. Yi

Physics Letters BJul 1, 19941 citation

Robust protocols to reveal anyonic time-exchange phase

Inès Safi A

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 $δ>1/2$ .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 $δ>1/2$.

arXiv:2510.10525Oct 12, 20250 citations

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