Two interacting fermions in a one-dimensional harmonic trap: Matching the Bethe ansatz and variational approaches

Rubeni, D.; Foerster, Angela; Roditi, I.

doi:10.1103/physreva.86.043619

Cited by 21 publications

(30 citation statements)

References 26 publications

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“…In this way, we propose a geometrical variational wave function in the sense that where the contact interaction is dominant, this wave function is the exact one for a non-diffractive regime, while in the region where the harmonic trap is dominant, the quantum system is described by a smoothly decreasing function. This idea is a sharp advance with respect to a one used for just two fermions that already provided interesting results [22] (see also [23]). For the ground state of particles in a harmonic trap, an exact analytical solution only exists for the two-body case [24] (see also [25]).…”

Section: Introductionmentioning

confidence: 99%

A geometric wave function for a few interacting bosons in a harmonic trap

et al. 2014

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We establish a new geometric wave function that combined with a variational principle efficiently describes a system of bosons interacting in a onedimensional trap. By means of a a combination of the exact wave function solution for contact interactions and the asymptotic behaviour of the harmonic potential solution we obtain the ground state energy, probability density and profiles of a few boson system in a harmonic trap. We are able to access all regimes, ranging from the strongly attractive to the strongly repulsive one with an original and simple formulation.

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Section: Introductionmentioning

confidence: 99%

A geometric wave function for a few interacting bosons in a harmonic trap

et al. 2014

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“…The experimental progress has generated great interest for few-body problems in one-dimensional geometries for both bosonic [21][22][23][24][25][26][27][28], fermionic [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46], and mixed systems [47][48][49][50][51][52][53][54][55][56][57][58][59][60][61]. Recently, it has been shown that for strong short-range repulsive interactions a 1D two-component Fermi system in a harmonic trap exhibits strong magnetic correlations already at the three-body level [37,40].…”

Section: Introductionmentioning

confidence: 99%

A variational approach to repulsively interacting three-fermion systems in a one-dimensional harmonic trap

et al. 2015

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We study a three-body system with zero-range interactions in a one-dimensional harmonic trap. The system consists of two spin-polarized fermions and a third particle which is distinct from two others (2+1 system). First we assume that the particles have equal masses. For this case the system in the strongly and weakly interacting limits can be accurately described using wave function factorized in hypercylindrical coordinates. Inspired by this result we propose an interpolation ansatz for the wave function for arbitrary repulsive zero-range interactions. By comparison to numerical calculations, we show that this interpolation scheme yields an extremely good approximation to the numerically exact solution both in terms of the energies and also in the spin-resolved densities. As an outlook, we discuss the case of mass imbalanced systems in the strongly interacting limit. Here we find spectra that demonstrate that the triply degenerate spectrum at infinite coupling strength of the equal mass case is in some sense a singular case as this degeneracy will be broken down to a doubly degenerate or non-degenerate ground state by any small mass imbalance.

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“…From a theoretical standpoint, the problem of few particles interacting in a harmonic trap has been addressed through different approaches, both exact and approximative [14][15][16][17][18][19][20]. The case of strongly interacting atoms, in particular, has been shown to be analogous to an effective 1D spin chain [21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Dynamical realization of magnetic states in a strongly interacting Bose mixture

2017

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We describe the dynamical preparation of magnetic states in a strongly interacting two-component Bose gas in a harmonic trap. By mapping this system to an effective spin chain model, we obtain the dynamical spin densities and the fidelities for a few-body system. We show that the spatial profiles transit between ferromagnetic and antiferromagnetic states as the intraspecies interaction parameter is slowly increased. PACS numbers: 67.85.-d, 03.75.Mn, 75.10.Pq * rafael.barfknecht@ufrgs.br † angela@if.ufrgs.br ‡ zinner@phys.au.dk II. HAMILTONIAN AND MAPPING TO AN EFFECTIVE SPIN CHAINWe consider a trapped 1D Bose gas with contact interactions and two different bosonic species (↑, ↓). The total number of particles is N = N ↑ +N ↓ where N ↑ and N ↓ are arXiv:1612.01570v4 [cond-mat.quant-gas]

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Two interacting fermions in a one-dimensional harmonic trap: Matching the Bethe ansatz and variational approaches

Cited by 21 publications

References 26 publications

A geometric wave function for a few interacting bosons in a harmonic trap

A geometric wave function for a few interacting bosons in a harmonic trap

A variational approach to repulsively interacting three-fermion systems in a one-dimensional harmonic trap

Dynamical realization of magnetic states in a strongly interacting Bose mixture

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