One-particle density matrix and momentum distribution function of one-dimensional anyon gases

Santachiara, Raoul; Calabrese, Pasquale

doi:10.1088/1742-5468/2008/06/p06005

Cited by 48 publications

(97 citation statements)

References 69 publications

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“…Thus, when κ = 1 the model is the well-known fermionic TL model, while the bosonic limit κ → 0 is not well defined in this formalism as will be clearer in the following. We stress that this anyonic model is different from the gases discussed elsewhere 42,43,46,49,56 , that also have a Luttinger liquid description. As in the fermionic case, the model is naturally solved exactly through bosonization 27 .…”

Section: Introductionmentioning

confidence: 72%

“…The reason for this generalization is twofold. On one hand the study of 1D anyonic model is attracting a renewed interest [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59] , mainly motivated by possible experiments with cold atoms 60 . On the other hand, the transport of wires joined with a quantum Hall island is driven by anyonic excitations 12 .…”

Section: Introductionmentioning

confidence: 99%

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Junctions of anyonic Luttinger wires

2009

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We present an extended study of anyonic Luttinger liquids wires jointing at a single point. The model on the full line is solved with bosonization and the junction of an arbitrary number of wires is treated imposing boundary conditions that preserve exact solvability in the bosonic language. This allows us to reach, in the low momentum regime, some of the critical fixed points found with the electronic boundary conditions. The stability of all the fixed points is discussed.

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Section: Introductionmentioning

confidence: 72%

Section: Introductionmentioning

confidence: 99%

Junctions of anyonic Luttinger wires

2009

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“…Kundu proved that a 1D Bose gas interacting through δ-function potential combined with double δ-function potential and derivative δ-function potential is equivalent to the anyon gas interacting via δ-function potential [21]. This stimulated many research interests on δ-anyon gas [22][23][24][25][26][27][28][29][30][31][32]. It turns out that the ground state density distribution of δ-anyon gas displays similar behavior as that of Bose gas with the increasing interaction.…”

Section: Introductionmentioning

confidence: 99%

“…The momentum distribution of anyon differs from fermion's oscillations and boson's single peak structure, which are symmetric about the zero momentum. The momentum distribution of anyons is asymmetric when the statistical parameters deviate from the Bose and Fermi limit [27][28][29][30][31]. This special behavior originates from that the reduced one body density matrix is a complex Hermitian one rather than a real one for Boson and Fermion.…”

Section: Introductionmentioning

confidence: 99%

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

Hao

Chen

2012

Phys. Rev. A

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We investigate the dynamical properties of anyons confined in one-dimensional optical lattice combined with a weak harmonic trap using the exact numerical method based on a generalized Jordan-Wigner transformation. The density profiles, momentum distribution, occupation distribution and occupations of the lowest natural orbital are obtained for different statistical parameters. The density profiles of anyons display the same behaviors irrespective of statistical parameter in the full evolving period. While the behaviors dependent on statistical property are shown in the momentum distributions and occupations of natural orbitals.

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“…Ultracold atoms with two hyperfine levels in non-Abelian potentials could yield ground states with non-Abelian anyonic excitations [16], while bosons in Floquet-driven optical lattices may effectively exhibit fermionic statistics [17]. The one-dimensional (1D) version of anyons [18][19][20][21][22][23][24][25][26] has also aroused interest, especially in 1D optical lattices [23][24][25][26]. Such particles were proposed to emerge from occupation dependent hopping amplitudes, which could be realized with laser-assisted tunneling [23,25], or Floquet modulations [26].…”

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confidence: 99%

Quasimomentum distribution and expansion of an anyonic gas

et al. 2018

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We point out that the momentum distribution is not a proper observable for a system of anyons in two-dimensions. In view of anyons as Wilczek's composite charged flux-tubes, this is a consequence of the fact that the orthogonal components of the kinetic momentum operator do not commute at the position of a flux tube, and thus cannot be diagonalized in the same basis. As a substitute for the momentum distribution of an anyonic (spatially localized) state, we propose to use the asymptotic single-particle density after expansion of anyons in free space from the state. This definition is identical with the standard one when the statistical parameter approaches that for bosons or fermions. Exact examples of expansion dynamics, which underpin our proposal, and observables that can be used to measure anyonic statistics, are shown.PACS numbers: 05.30. Pr, Anyons are quantum particles residing in two dimensions (2D), obeying fractional statistics interpolating between bosons and fermions [1,2]. The only physical realization of anyons so far is found in the fractional quantum Hall effect (FQHE) [3,4], where localized quasiparticle excitations have a fractional elementary charge [4] and statistics [5,6]. While fundamental motivation for exploring anyons is self-evident, the so-called non-Abelian anyonic excitations hold potential for technological advances, as they could be used for robust topological quantum computation [7] (for review see Ref.[8]).Some of the intriguing quantum mechanical implications of fractional statistics were pointed out decades ago [1,2]. Experiments with ultracold atomic gases seem to be a perfect playground for exploring anyonic physics, because of the quality in preparation, manipulation, and detection of numerous intriguing quantum states [9], and because of the possibility to explore 2D systems [10], with synthetic magnetic fields [11], which could be used to tinker with statistics. In an early paper, Paredes et al., inspired by the FQHE, proposed the realization of a 1/2-Laughlin state in a bulk rotating gas [12]. Different schemes were later proposed with atoms in optical lattices [13][14][15]. Ultracold atoms with two hyperfine levels in non-Abelian potentials could yield ground states with non-Abelian anyonic excitations [16], while bosons in Floquet-driven optical lattices may effectively exhibit fermionic statistics [17]. The one-dimensional (1D) version of anyons [18][19][20][21][22][23][24][25][26] has also aroused interest, especially in 1D optical lattices [23][24][25][26]. Such particles were proposed to emerge from occupation dependent hopping amplitudes, which could be realized with laser-assisted tunneling [23,25], or Floquet modulations [26]. Other proposals include lattices of polar molecules [27], photonics lattices [28] and circuit-QED systems [29]. An undoubtedly important ingredient that needs to be investigated in this context is the detection of the anyonic quantum state. The studied detection schemes rely on braiding [12,14,30,31], the pair-correlation function [15], and...

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One-particle density matrix and momentum distribution function of one-dimensional anyon gases

Cited by 48 publications

References 69 publications

Junctions of anyonic Luttinger wires

Junctions of anyonic Luttinger wires

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

Quasimomentum distribution and expansion of an anyonic gas

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