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

Hao, Yajiang

doi:10.1103/physreva.93.063627

Cited by 21 publications

(19 citation statements)

References 61 publications

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“…There has been an extensive study of the properties of 1D hard-core spinless anyon gases [22][23][24][25][26][27][28][29][30][31][32][33][34][35] (and the references therein). In particular, their OBDM and momentum distributions have been calculated.…”

Section: One-body Density Matrixmentioning

confidence: 99%

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One-body density matrix and momentum distribution of strongly interacting one-dimensional spinor quantum gases

Yang

2017

Phys. Rev. A

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The one-body density matrix (OBDM) and the momentum distribution of quantum many-body systems are usually very difficult to calculate. Here we develop a technique to calculate the OBDM and the momentum distribution of a general one dimensional (1D) spinor quantum gas in the strong interaction regime. This technique relies on a remarkable connection between the OBDM of the spinor gas and that of a spinless 1D hard-core anyon gas, which allows us to efficiently calculate the OBDM of the spinor system with particle numbers much larger than what was previously possible. Given the OBDM, we can easily calculate the momentum distribution of the spinor system, which is also related to the momentum distribution of the hard-core anyon gas. Our study not only provides a practical method for the calculation of the OBDM, but also provides significant new insights into the properties of 1D strongly interacting spinor quantum gases.

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Section: One-body Density Matrixmentioning

confidence: 99%

“…The OBDM of a hamonically trapped hard-core spinless anyon gas ρ κ (x , x) = ρ κ,κ (x , x) have been investigated previously [32,33] (for hard-core spinless Bose gas, see Ref. [34,35]).…”

Section: A Harmonically Trapped Systemmentioning

confidence: 99%

One-body density matrix and momentum distribution of strongly interacting one-dimensional spinor quantum gases

Yang

2017

Phys. Rev. A

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“…Focusing mainly on ground-state and thermal physics, these investigations already provided quantitative predictions for several quantities, including correlation functions [16,[18][19][20][21][22] and the (particle) entanglement entropy [23,24]. As a distinguished qualitative feature, it was found that anyonic gases at equilibrium display a momentum distribution that is not symmetric, signaling the fact that the Hamiltonian breaks parity symmetry [25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Determinant formula for the field form factor in the anyonic Lieb-Liniger model

Piroli,

Scopa,

Calabrese

2020

Preprint

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We derive an exact formula for the field form factor in the anyonic Lieb-Liniger model, valid for arbitrary values of the interaction c, anyonic parameter κ, and number of particles N . Analogously to the bosonic case, the form factor is expressed in terms of the determinant of a N × N matrix, whose elements are rational functions of the Bethe quasimomenta but explicitly depend on κ. The formula is efficient to evaluate, and provide an essential ingredient for several numerical and analytical calculations. Its derivation consists of three steps. First, we show that the anyonic form factor is equal to the bosonic one between two special off-shell Bethe states, in the standard Lieb-Liniger model. Second, we characterize its analytic properties and provide a set of conditions that uniquely specify it. Finally, we show that our determinant formula satisfies these conditions.

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“…In Sec. II, we introduce the single-particle density matrix for 1D SU(κ) fermions in terms of separate spatial and spin parts of the density matrix with anyonic statistics [55][56][57]. In Sec.…”

Section: Introductionmentioning

confidence: 99%

Spin-incoherent Luttinger liquid of one-dimensional SU( κ ) fermions

Jen

Yip

2018

Phys. Rev. A

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We theoretically investigate one-dimensional (1D) SU(κ) fermions in the regime of spin-incoherent Luttinger liquid. We specifically focus on the Tonks-Girardeau gas limit where its density is sufficiently low that effective repulsions between atoms become infinite. In such case, spin exchange energy of 1D SU(κ) fermions vanishes and all spin configurations are degenerate, which automatically puts them into spin-incoherent regime. In this limit, we are able to express the single-particle density matrices in terms of those of anyons. This allows us to numerically simulate the number of particles up to N = 32. We numerically calculate single-particle density matrices in two cases: (1) equal populations for each spin components (balanced) and (2) all Sz manifolds included. In contrast to noninteracting multi-component fermions, the momentum distributions are broadened due to strong interactions. As κ increases, the momentum distributions are less broadened for fixed N , while they are more broadened for fixed number of particle per spin component. We then compare numerically calculated high momentum tails with analytical predictions which are proportional to 1/p 4 , in good agreement. Thus, our theoretical study provides a comparison with the experiments of repulsive multicomponent alkaline-earth fermions with a tunable SU(κ) spin-symmetry in the spin-incoherent regime.

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

Cited by 21 publications

References 61 publications

One-body density matrix and momentum distribution of strongly interacting one-dimensional spinor quantum gases

One-body density matrix and momentum distribution of strongly interacting one-dimensional spinor quantum gases

Determinant formula for the field form factor in the anyonic Lieb-Liniger model

Spin-incoherent Luttinger liquid of one-dimensional SU( κ ) fermions

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