Dynamical properties of hard-core anyons in one-dimensional optical lattices

Hao, Yajiang; Chen, Shu

doi:10.1103/physreva.86.043631

Cited by 43 publications

(57 citation statements)

References 63 publications

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“…Another promising line of research concerns the study of the non-equilibrium properties of anyon gases. There are already a few manuscripts in this direction [37,38,39]. For example, Ref.…”

Section: Discussionmentioning

confidence: 99%

One-body reduced density matrix of trapped impenetrable anyons in one dimension

Marmorini

Calabrese

2016

J. Stat. Mech.

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Abstract. We study the one-body reduced density matrix of a system of N one-dimensional impenetrable anyons trapped by a harmonic potential. To this purpose we extend two methods developed to tackle related problems, namely the determinant approach and the replica method. While the former is the basis for exact numerical computations at finite N , the latter has the advantage of providing an analytic asymptotic expansion for large N . We show that the first few terms of such expansion are sufficient to reproduce the numerical results to an excellent accuracy even for relatively small N , thus demonstrating the effectiveness of the replica method.

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“…Another promising line of research concerns the study of the non-equilibrium properties of anyon gases. There are already a few manuscripts in this direction [37,38,39]. For example, Ref.…”

Section: Discussionmentioning

confidence: 99%

One-body reduced density matrix of trapped impenetrable anyons in one dimension

Marmorini

Calabrese

2016

J. Stat. Mech.

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“…4, we find that the statistical parameter χ breaks the symmetry in both the correlation fluctuation and the particle density for finite U or V . The statistics parameter plays an essential role in the symmetry of the density distribution, in contrast with the case of hard-core anyons [10] where the statistical factor makes no difference. The asymmetry here again arises from the statistics-dependent hopping term in Hamiltonian (5).…”

Section: Correlation Of Two Interacting Anyonsmentioning

confidence: 99%

“…Here we introduce another parame- ter κ to describe the statistical property of this newly defined anyon. The anyonic operators now satisfy CRs [9,10,28,30] …”

Section: Correlation Of Two Hard-core Anyonsmentioning

confidence: 99%

“…By far, most of the theoretical works [7][8][9][10] on anyon gases in one-dimensional focus on the ground state properties, like energy, density profiles, momentum distribution, occupation distribution and occupations of the lowest natural orbital for different statistical parameters. Little attention has been paid to * Electronic address: ybzhang@sxu.edu.cn anyon properties in other aspects.…”

Section: Introductionmentioning

confidence: 99%

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

Wang

Zhang

2014

Phys. Rev. A

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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 (χ = 0 ) and Fermi limit ( χ = 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 χ 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 anti-bunching to co-walking 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.

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“…Particularly the δ-anyon gas attracted many research interests in the exact solution [26][27][28], the low-energy properties [29], correlation function [30][31][32], entanglement properties [33,34], momentum distribution and the reduced one-body density matrix (ROBDM) [33,[35][36][37], the relaxation dynamics [38], quantum walks [39] and the fermionization [40,41]. It turns out that the properties dependent on the modulus of wavefunction are not related with the statistical properties, while those properties dependent on the wave function exhibit distinct behaviors with the change of the statical parameters.…”

Section: Introductionmentioning

confidence: 99%

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

Hao

2016

Phys. Rev. A

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Using 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 are obtained. Basing on the 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 parameter exhibit the similar properties to the hard-core Bosons although anyon system satisfy specific fractional statistics.

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Dynamical properties of hard-core anyons in one-dimensional optical lattices

Cited by 43 publications

References 63 publications

One-body reduced density matrix of trapped impenetrable anyons in one dimension

One-body reduced density matrix of trapped impenetrable anyons in one dimension

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

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

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