Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1509.01888 · New Journal of Physics

Ground-state properties of anyons in a one-dimensional lattice

Guixin Tang, Sebastian Eggert, Axel Pelster

Published Dec 14, 2015• 47 citations
arXivHTMLPDF

Abstract

Using the Anyon–Hubbard Hamiltonian, we analyze the ground-state properties of anyons in a one-dimensional lattice. To this end we map the hopping dynamics of correlated anyons to an occupation-dependent hopping Bose–Hubbard model using the fractional Jordan–Wigner transformation. In particular, we calculate the quasi-momentum distribution of anyons, which interpolates between Bose–Einstein and Fermi–Dirac statistics. Analytically, we apply a modified Gutzwiller mean-field approach, which goes beyond a classical one by including the influence of the fractional phase of anyons within the many-body wavefunction. Numerically, we use the density-matrix renormalization group by relying on the ansatz of matrix product states. As a result it turns out that the anyonic quasi-momentum distribution reveals both a peak-shift and an asymmetry which mainly originates from the nonlocal string property. In addition, we determine the corresponding quasi-momentum distribution of the Jordan–Wigner transformed bosons, where, in contrast to the hard-core case, we also observe an asymmetry for the soft-core case, which strongly depends on the particle number density.

DOI
10.1088/1367-2630/17/12/123016

Related papers

Ground-state properties of hard-core anyons in one-dimensional optical lattices

Yajiang Hao, Yunbo Zhang, Shu Chen

We investigate the ground-state properties of anyons confined in one-dimensional optical lattices with a weak harmonic trap using the exact numerical method based on Jordan-Wigner transformation. It is shown that in the Bose limit $(\ensuremath{\chi}=1)$ and Fermi limit $(\ensuremath{\chi}=0)$ the momentum distributions are symmetric but in between they are asymmetric. It turns out that the origin of asymmetry comes from the fractional statistics that anyons obey. The occupation distribution and the modulus of natural orbitals show crossover behaviors from the Bose limit to the Fermi limit.

arXiv:0901.1224•Physical Review A•Apr 30, 2009•59 citations

Quantum walks of two interacting anyons in one-dimensional optical lattices

Limin Wang, Li Wang, Yunbo Zhang

We investigate continuous-time quantum walks of two indistinguishable anyons in one-dimensional lattices with both on-site and nearest-neighbor interactions based on the fractional Jordan-Wigner transformation. It is shown that the two-body correlations in position space are symmetric about the initial sites of two quantum walkers in the Bose limit ($\ensuremath{\chi}=0$) and Fermi limit ($\ensuremath{\chi}=1$), while in momentum space this happens only in the Bose limit. An interesting asymmetry arises in the correlation for most cases with the statistical parameter $\ensuremath{\chi}$ varying in between. It turns out that the origin of this asymmetry comes from the fractional statistics that anyons obey. On the other hand, the two-body correlations of hard-core anyons in position space show uniform behaviors from antibunching to cowalking regardless of the statistical parameter. The momentum correlations in the case of strong interaction undergo a smooth process of two stripes smoothly merging into a single one, i.e. the evolution of fermions into hard-core bosons.

arXiv:1411.5600•Physical Review A•Dec 9, 2014•44 citations

Ground-state properties of hard-core anyons in a harmonic potential

Yajiang Hao

Using an anyon-fermion mapping method, we investigate the ground-state properties of hard-core anyons confined in a one-dimensional harmonic trap. The concise analytical formula of the reduced one-body density matrix is obtained. Based on this formula, we evaluated the momentum distribution, the natural orbitals, and their occupation distributions for different statistical parameters. The occupation and occupation fraction of the lowest natural orbital versus anyon number are also displayed. It is shown that the ground-state properties of anyons interplay between bosons and fermions continuously. We can expect that the hard-core anyons of larger statistical parameters exhibit similar properties to the hard-core bosons although anyon systems satisfy specific fractional statistics.

arXiv:1604.00458•Physical Review A•Jun 21, 2016•21 citations

Quantum Dynamics and Correlations of Indistinguishable Anyons in One-Dimensional Lattices

Wang Li, Jia Lifang, Yunbo Zhang

Anyons, namely particles obeying fractional quantum statistics that interpolate between bosons and fermions, possess a lot of new and exotic physical properties related to the particle exchange statistics. In this work, we explore the few-body quantum dynamics and quantum correlations of indistinguishable anyons with on-site interactions in onedimensional lattices within the scheme of three-body continuous-time quantum walks. By employing a time-evolving block decimation (TEBD) algorithm, we numerically calculate the dynamical evolution process of the local density distribution of anyons among the whole lattice. Numerical simulations shown in the main text mainly focus on a threebody initial state as ψ|(t=0)＞=â†-1â†0â†1|0＞, in which three particles are located on neighbouring sites at lattice centre. This choice of initial state features that the three particles influence one another most strongly, while we have also implemented numerical simulations on other choices of three-body initial states as are discussed in appendix. It is shown that the local density distribution of anyons is dramatically altered by fractional particle statistics with new dynamical structure showing up during the time evolution. For free anyons, an inner cone emerges as the statistical parameter increases, while the outer cone remains robust all along. When the on-site interaction joins in, the structure of the inner cone is further modified with new features. Specifically, for interaction of finite strength, an exotic dynamical asymmetry in real space, is clearly demonstrated during the time evolution of the local density distribution for particles within the fractional statistics regime. However, for boson limit and pseudofermion limit, the time evolution of the local density distribution keeps symmetric as the three-body initial state. And remarkably, the dynamical asymmetry is interactiondependent manifested as the local density distribution of anyons favors opposite side of the lattice for repulsive and attractive interaction, respectively. Moreover, when the on-site interaction is further increased to hard-core limit, the dynamical asymmetry will then be largely suppressed. We also calculate the density-density correlations for anyons before they reach the lattice boundary to reveal the interesting effect of fractional statistics on quantum correlations. It is shown that the inner cone corresponds to co-walking of anyons, while the outer cone is related to individual walking and is immune to the variation of statistical parameter. Furthermore, the exotic real-space asymmetry originated from the interplay of fractional statistics and finite interaction is also shown up in the density-density correlations.

Acta Physica Sinica•Jan 1, 2022•0 citations

Ground-state properties of one-dimensional anyon gases

Yajiang Hao, Yunbo Zhang, Shu Chen

We investigate the ground state of the one-dimensional interacting anyonic system based on the exact Bethe ansatz solution for arbitrary coupling constant $(0\ensuremath{\leqslant}c\ensuremath{\leqslant}\ensuremath{\infty})$ and statistics parameter $(0\ensuremath{\leqslant}\ensuremath{\kappa}\ensuremath{\leqslant}\ensuremath{\pi})$. It is shown that the density of state in quasimomentum $k$ space and the ground-state energy are determined by the renormalized coupling constant ${c}^{\ensuremath{'}}$. The effect induced by the statistics parameter $\ensuremath{\kappa}$ exhibits in the momentum distribution in two aspects: Besides the effect of renormalized coupling, the anyonic statistics results in the nonsymmetric momentum distribution when the statistics parameter $\ensuremath{\kappa}$ deviates from 0 (Bose statistics) and $\ensuremath{\pi}$ (Fermi statistics) for any coupling constant $c$. The momentum distribution evolves from a Bose distribution to a Fermi one as $\ensuremath{\kappa}$ varies from 0 to $\ensuremath{\pi}$. The asymmetric momentum distribution comes from the contribution of the imaginary part of the nondiagonal element of reduced density matrix, which is an odd function of $\ensuremath{\kappa}$. The peak at positive momentum will shift to negative momentum if $\ensuremath{\kappa}$ is negative.

arXiv:0805.1988•Physical Review A•Aug 26, 2008•62 citations

Interaction-induced asymmetry in infinite-temperature dynamical correlations of hard-core anyons

Doru Sticlet, Ovidiu I. Pâţu, Balázs Dóra +1 more

We study dynamical correlations of interacting hard-core anyons on a one-dimensional lattice at infinite temperature. This is a setting in which the many-body spectrum is independent of the statistical phase θ , while dynamical correlators remain sensitive to θ through nonlocal Jordan-Wigner strings. We compute single-particle Green's functions, spectral functions, and density-density correlators, thereby separating the effects of fractional statistics on one-body coherence from those on density transport in a maximally mixed ensemble. In the noninteracting case V = 0 , high-temperature averaging leads to inversion-symmetric Green's functions for all θ despite the presence of anyonic strings. Finite nearest-neighbor interactions V generate, however, a pronounced left-right asymmetry in the Green's functions for 0 < θ < π , with the strongest chirality appearing at intermediate couplings V ∼ J where interactions and hopping compete most effectively. In this regime, the Green's function decays exponentially in time with a statistical-angle-dependent decay rate. At strong coupling, the dynamics crosses over to an atomic-limit regime in which the dependence on θ is reduced. Here, the Green's function decays universally as t − 1 and the corresponding spectral function displays a three-band structure. In contrast, density-density correlations are insensitive to statistics and recover the known infinite-temperature transport regimes of the XXZ chain, including ballistic, superdiffusive, and diffusive behaviors. These results identify dynamical correlation functions as direct probes of fractional statistics in high-entropy quantum systems.

arXiv:2604.20697•Physical Review Research•Jul 28, 2026•0 citations
Using the Anyon–Hubbard Hamiltonian, we analyze the ground-state properties of anyons in a one-dimensional lattice. To this end we map the hopping dynamics of correlated anyons to an occupation-dependent hopping Bose–Hubbard model using the fractional Jordan–Wigner transformation. In particular, we calculate the quasi-momentum distribution of anyons, which interpolates between Bose–Einstein and Fermi–Dirac statistics. Analytically, we apply a modified Gutzwiller mean-field approach, which goes beyond a classical one by including the influence of the fractional phase of anyons within the many-body wavefunction. Numerically, we use the density-matrix renormalization group by relying on the ansatz of matrix product states. As a result it turns out that the anyonic quasi-momentum distribution reveals both a peak-shift and an asymmetry which mainly originates from the nonlocal string property. In addition, we determine the corresponding quasi-momentum distribution of the Jordan–Wigner transformed bosons, where, in contrast to the hard-core case, we also observe an asymmetry for the soft-core case, which strongly depends on the particle number density.
We investigate the ground-state properties of anyons confined in one-dimensional optical lattices with a weak harmonic trap using the exact numerical method based on Jordan-Wigner transformation. It is shown that in the Bose limit $(\ensuremath{\chi}=1)$ and Fermi limit $(\ensuremath{\chi}=0)$ the momentum distributions are symmetric but in between they are asymmetric. It turns out that the origin of asymmetry comes from the fractional statistics that anyons obey. The occupation distribution and the modulus of natural orbitals show crossover behaviors from the Bose limit to the Fermi limit.
We investigate continuous-time quantum walks of two indistinguishable anyons in one-dimensional lattices with both on-site and nearest-neighbor interactions based on the fractional Jordan-Wigner transformation. It is shown that the two-body correlations in position space are symmetric about the initial sites of two quantum walkers in the Bose limit ($\ensuremath{\chi}=0$) and Fermi limit ($\ensuremath{\chi}=1$), while in momentum space this happens only in the Bose limit. An interesting asymmetry arises in the correlation for most cases with the statistical parameter $\ensuremath{\chi}$ varying in between. It turns out that the origin of this asymmetry comes from the fractional statistics that anyons obey. On the other hand, the two-body correlations of hard-core anyons in position space show uniform behaviors from antibunching to cowalking regardless of the statistical parameter. The momentum correlations in the case of strong interaction undergo a smooth process of two stripes smoothly merging into a single one, i.e. the evolution of fermions into hard-core bosons.
Using an anyon-fermion mapping method, we investigate the ground-state properties of hard-core anyons confined in a one-dimensional harmonic trap. The concise analytical formula of the reduced one-body density matrix is obtained. Based on this formula, we evaluated the momentum distribution, the natural orbitals, and their occupation distributions for different statistical parameters. The occupation and occupation fraction of the lowest natural orbital versus anyon number are also displayed. It is shown that the ground-state properties of anyons interplay between bosons and fermions continuously. We can expect that the hard-core anyons of larger statistical parameters exhibit similar properties to the hard-core bosons although anyon systems satisfy specific fractional statistics.
Anyons, namely particles obeying fractional quantum statistics that interpolate between bosons and fermions, possess a lot of new and exotic physical properties related to the particle exchange statistics. In this work, we explore the few-body quantum dynamics and quantum correlations of indistinguishable anyons with on-site interactions in onedimensional lattices within the scheme of three-body continuous-time quantum walks. By employing a time-evolving block decimation (TEBD) algorithm, we numerically calculate the dynamical evolution process of the local density distribution of anyons among the whole lattice. Numerical simulations shown in the main text mainly focus on a threebody initial state as ψ|(t=0)＞=â†-1â†0â†1|0＞, in which three particles are located on neighbouring sites at lattice centre. This choice of initial state features that the three particles influence one another most strongly, while we have also implemented numerical simulations on other choices of three-body initial states as are discussed in appendix. It is shown that the local density distribution of anyons is dramatically altered by fractional particle statistics with new dynamical structure showing up during the time evolution. For free anyons, an inner cone emerges as the statistical parameter increases, while the outer cone remains robust all along. When the on-site interaction joins in, the structure of the inner cone is further modified with new features. Specifically, for interaction of finite strength, an exotic dynamical asymmetry in real space, is clearly demonstrated during the time evolution of the local density distribution for particles within the fractional statistics regime. However, for boson limit and pseudofermion limit, the time evolution of the local density distribution keeps symmetric as the three-body initial state. And remarkably, the dynamical asymmetry is interactiondependent manifested as the local density distribution of anyons favors opposite side of the lattice for repulsive and attractive interaction, respectively. Moreover, when the on-site interaction is further increased to hard-core limit, the dynamical asymmetry will then be largely suppressed. We also calculate the density-density correlations for anyons before they reach the lattice boundary to reveal the interesting effect of fractional statistics on quantum correlations. It is shown that the inner cone corresponds to co-walking of anyons, while the outer cone is related to individual walking and is immune to the variation of statistical parameter. Furthermore, the exotic real-space asymmetry originated from the interplay of fractional statistics and finite interaction is also shown up in the density-density correlations.
We investigate the ground state of the one-dimensional interacting anyonic system based on the exact Bethe ansatz solution for arbitrary coupling constant $(0\ensuremath{\leqslant}c\ensuremath{\leqslant}\ensuremath{\infty})$ and statistics parameter $(0\ensuremath{\leqslant}\ensuremath{\kappa}\ensuremath{\leqslant}\ensuremath{\pi})$. It is shown that the density of state in quasimomentum kkk space and the ground-state energy are determined by the renormalized coupling constant ${c}^{\ensuremath{'}}$. The effect induced by the statistics parameter $\ensuremath{\kappa}$ exhibits in the momentum distribution in two aspects: Besides the effect of renormalized coupling, the anyonic statistics results in the nonsymmetric momentum distribution when the statistics parameter $\ensuremath{\kappa}$ deviates from 0 (Bose statistics) and $\ensuremath{\pi}$ (Fermi statistics) for any coupling constant ccc. The momentum distribution evolves from a Bose distribution to a Fermi one as $\ensuremath{\kappa}$ varies from 0 to $\ensuremath{\pi}$. The asymmetric momentum distribution comes from the contribution of the imaginary part of the nondiagonal element of reduced density matrix, which is an odd function of $\ensuremath{\kappa}$. The peak at positive momentum will shift to negative momentum if $\ensuremath{\kappa}$ is negative.
We study dynamical correlations of interacting hard-core anyons on a one-dimensional lattice at infinite temperature. This is a setting in which the many-body spectrum is independent of the statistical phase θ , while dynamical correlators remain sensitive to θ through nonlocal Jordan-Wigner strings. We compute single-particle Green's functions, spectral functions, and density-density correlators, thereby separating the effects of fractional statistics on one-body coherence from those on density transport in a maximally mixed ensemble. In the noninteracting case V = 0 , high-temperature averaging leads to inversion-symmetric Green's functions for all θ despite the presence of anyonic strings. Finite nearest-neighbor interactions V generate, however, a pronounced left-right asymmetry in the Green's functions for 0 < θ < π , with the strongest chirality appearing at intermediate couplings V ∼ J where interactions and hopping compete most effectively. In this regime, the Green's function decays exponentially in time with a statistical-angle-dependent decay rate. At strong coupling, the dynamics crosses over to an atomic-limit regime in which the dependence on θ is reduced. Here, the Green's function decays universally as t − 1 and the corresponding spectral function displays a three-band structure. In contrast, density-density correlations are insensitive to statistics and recover the known infinite-temperature transport regimes of the XXZ chain, including ballistic, superdiffusive, and diffusive behaviors. These results identify dynamical correlation functions as direct probes of fractional statistics in high-entropy quantum systems.