Exact dynamical correlations of hard-core anyons in one-dimensional lattices

The dynamical correlations of a strongly correlated system are an essential ingredient to describe its nonequilibrium properties. We present a general method to calculate exactly the dynamical correlations of hard-core anyons in one-dimensional lattices, valid for any type of confining potential and any temperature. We obtain exact explicit expressions of the Green's function, the spectral function, and the out-of-time-ordered correlators (OTOCs). We find that the anyonic spectral function displays three main singularity lines which can be explained as a double spectrum in analogy to the Lieb-Liniger gas. The dispersion relations of these lines can be given explicitly and they cross at a hot point (q(m), omega(m)), which induces a peak in the momentum distribution function at q(m) and a power-law singularity in the local spectral function at omega(m). We also find that the anyonic statistics can induce spatial asymmetry in the Green's function, its spectrum, and the OTOC. Moreover, the information spreading characterized by the OTOCs shows light-cone dynamics, asymmetric for general statistics and low temperatures, but symmetric at infinite temperature. Our results pave the way toward studying the nonequilibrium dynamics of hard-core anyons and experimentally probing anyonic statistics through spectral functions.

Automated summary

The dynamical correlations of hard-core anyons in one-dimensional lattices are studied in this paper. Exact expressions for the Green's function, the spectral function, and the out-of-time-ordered correlators are obtained. Three main singularity lines are observed in the anyonic spectral function, which correspond to a peak in the momentum distribution function and a power-law singularity in the local spectral function. The anyonic statistics also induce spatial asymmetry in the correlations. Light-cone dynamics are observed in the information spreading characterized by the out-of-time-ordered correlators.