arXiv:0707.4520 · Journal of Physics A Mathematical and Theoretical

Correlation functions of one-dimensional Lieb–Liniger anyons

Ovidiu I. Pâţu, V. E. Korepin, D. V. Averin

Published Nov 28, 2007• 83 citations

Abstract

We have investigated the properties of a model of 1D anyons interacting through a δ-function repulsive potential. The structure of the quasi-periodic boundary conditions for the anyonic field operators and the many-anyon wavefunctions is clarified. The spectrum of the low-lying excitations including the particle–hole excitations is calculated for periodic and twisted boundary conditions. Using the ideas of the conformal field theory we obtain the large-distance asymptotics of the density and field correlation function at the critical temperature T = 0 and at small finite temperatures. Our expression for the field correlation function extends the results in the literature obtained for harmonic quantum anyonic fluids.

DOI: 10.1088/1751-8113/40/50/004

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arXiv:0707.4520 · Journal of Physics A Mathematical and Theoretical

Correlation functions of one-dimensional Lieb–Liniger anyons

Ovidiu I. Pâţu, V. E. Korepin, D. V. Averin

Published Nov 28, 2007• 83 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/1751-8113/40/50/004

Related papers

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This work presents the derivation of the large time and distance asymptotic behavior of the field-field correlation functions of impenetrable one-dimensional anyons at finite temperature. In the appropriate limits of the statistics parameter, we recover the well-known results for impenetrable bosons and free fermions. In the low-temperature (usually expected to be the "conformal") limit, and for all values of the statistics parameter away from the bosonic point, the leading term in the correlator does not agree with the prediction of the conformal field theory, and is determined by the singularity of the density of the single-particle states at the bottom of the single-particle energy spectrum.This work presents the derivation of the large time and distance asymptotic behavior of the field-field correlation functions of impenetrable one-dimensional anyons at finite temperature. In the appropriate limits of the statistics parameter, we recover the well-known results for impenetrable bosons and free fermions. In the low-temperature (usually expected to be the "conformal") limit, and for all values of the statistics parameter away from the bosonic point, the leading term in the correlator does not agree with the prediction of the conformal field theory, and is determined by the singularity of the density of the single-particle states at the bottom of the single-particle energy spectrum.

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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 $({q}_{m},{\ensuremath{\omega}}_{m})$, which induces a peak in the momentum distribution function at ${q}_{m}$ and a power-law singularity in the local spectral function at ${\ensuremath{\omega}}_{m}$. 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.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 $({q}_{m},{\ensuremath{\omega}}_{m})$, which induces a peak in the momentum distribution function at ${q}_{m}$ and a power-law singularity in the local spectral function at ${\ensuremath{\omega}}_{m}$. 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.

arXiv:2202.06543Physical review. B./Physical review. BMay 31, 202210 citations

κ\to 1

and

κ\to 0

, of the statistics parameter

κ

, and coincide with the predictions of the conformal field theory at low temperatures.

{q}_{m}

and a power-law singularity in the local spectral function at ${\ensuremath{\omega}}_{m}$. 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.