Strongly correlated one-dimensional Bose–Fermi quantum mixtures: symmetry and correlations

Decamp, Jean; Jünemann, Johannes; Albert, Mathias; Rizzi, Matteo; Minguzzi, Anna; Vignolo, Patrizia

doi:10.1088/1367-2630/aa94ef

Cited by 26 publications

(25 citation statements)

References 59 publications

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“…Generally, such a system is no longer integrable when subjected to an external potential but a notable exception is the limit of infinitely strong repulsive interactions, known as the Tonks-Girardeau limit, where fermionization occurs. In that case, the system remains exactly solvable, for any number of bosons and fermions [4][5][6][7][8][9][10][11][12]. At finite interactions, the harmonically-trapped system can be exactly solved for 2 particles [13] and is approximately solved in the large-N limit by a local density approximation (LDA) on the Lieb-Liniger solution [14].…”

Section: Introductionmentioning

confidence: 99%

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Scaling behavior of Tan's contact for trapped Lieb-Liniger bosons: From two to many

et al. 2018

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We show that the contact parameter of N harmonically-trapped interacting 1D bosons at zero temperature can be analytically and accurately obtained by a simple rescaling of the exact two-boson solution, and that N -body effects can be almost factorized. The small deviations observed between our analytical results and DMRG calculations are more pronounced when the interaction energy is maximal (i.e. at intermediate interaction strengths) but they remain bounded by the large-N local-density approximation obtained from the Lieb-Liniger equation of state stemming from the Bethe Ansatz. The rescaled two-body solution is so close to the exact ones, that is possible, within a simple expression interpolating the rescaled two-boson result to the local-density, to obtain Nboson contact and ground state energy functions in very good agreement with DMRG calculations. Our results suggest a change of paradigm in the study of interacting quantum systems, giving to the contact parameter a more fundamental role than energy. PACS numbers:arXiv:1805.02463v2 [cond-mat.quant-gas]

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Section: Introductionmentioning

confidence: 99%

“…The contact embeds information on the interaction energy and the density-density correlation function [22][23][24]. It is a univocal measure of the wavefunction symmetry of fermionic and/or bosonic mixtures [11,12]. The contact parameter is also determined by the probability density of finding 2 particles at a vanishing distance [14].…”

Section: Introductionmentioning

confidence: 99%

Scaling behavior of Tan's contact for trapped Lieb-Liniger bosons: From two to many

et al. 2018

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“…Therefore, in the FF limit, the ground state has a large degeneracy, equal to N !/(N B N F ). A complete classification of these states from the immanent symmetries of the system is given in [333] while in [334] it is discussed how the degeneracy of the ground manifold is lifted when the interactions are large but finite. As discussed above, the system is controlled by two independent dimensionless quantities η = |g BF |/g BB and the sign of g BF .…”

Section: Bose-fermi Mixturesmentioning

confidence: 99%

One-dimensional mixtures of several ultracold atoms: a review

Sowiński¹,

2019

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Recent theoretical and experimental progress on studying one-dimensional systems of bosonic, fermionic, and Bose-Fermi mixtures of a few ultracold atoms confined in traps is reviewed in the broad context of mesoscopic quantum physics. We pay special attention to limiting cases of very strong or very weak interactions and transitions between them. For bosonic mixtures, we describe the developments in systems of three and four atoms as well as different extensions to larger numbers of particles. We also briefly review progress in the case of spinor Bose gases of a few atoms. For fermionic mixtures, we discuss a special role of spin and present a detailed discussion of the two-and three-atom cases. We discuss the advantages and disadvantages of different computation methods applied to systems with intermediate interactions. In the case of very strong repulsion, close to the infinite limit, we discuss approaches based on effective spin chain descriptions. We also report on recent studies on higherspin mixtures and inter-component attractive forces. For both statistics, we pay particular attention to impurity problems and mass imbalance cases. Finally, we describe the recent advances on trapped Bose-Fermi mixtures, which allow for a theoretical combination of previous concepts, well illustrating the importance of quantum statistics and inter-particle interactions. Lastly, we report on fundamental questions related to the subject which we believe will inspire further theoretical developments and experimental verification. :1903.12189v3 [cond-mat.quant-gas] CONTENTS arXiv

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“…In recent years there have also been an increasing number of studies on few-body mixtures, which are, in general, focused on the strong coupling regime. Various methods are employed such as: the multi-component generalization of the Bose-Fermi mapping [42][43][44][45][46][47][48][49][50][51], approximation by spin-chains [52][53][54], energy-functional techniques [55][56][57][58] and trial wave functions [59][60][61].…”

Section: Introductionmentioning

confidence: 99%

Momentum reconstruction and contact of the one-dimensional Bose-Fermi mixture

Pâţu

Klümper

2019

Phys. Rev. A

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We investigate the one-dimensional mixture of scalar bosons and spin polarized fermions interacting through a δ-function potential. Using a thermodynamic description derived by employing a lattice embedding of the continuum model and the quantum transfer matrix method we perform a detailed analysis of the contact and quantum critical behaviour. We show that the compressibility Wilson ratio presents anomalous enhancement at the quantum critical points and that the boundaries of the quantum critical regions can be well mapped by the maxima of the specific heat. As a function of the coupling strength and temperature the contact presents nonmonotonic behavior. In the strong coupling regime the local minimum exhibited by the contact as a function of temperature is accompanied by a significant momentum reconstruction at both low and high momenta. This momentum reconstruction occurs as the system crosses the boundary between the Tomonaga-Luttinger liquid phase to the spin-incoherent regime and provides an experimental signature of the transition. arXiv:1811.08692v2 [cond-mat.quant-gas]

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Strongly correlated one-dimensional Bose–Fermi quantum mixtures: symmetry and correlations

Cited by 26 publications

References 59 publications

Scaling behavior of Tan's contact for trapped Lieb-Liniger bosons: From two to many

Scaling behavior of Tan's contact for trapped Lieb-Liniger bosons: From two to many

One-dimensional mixtures of several ultracold atoms: a review

Momentum reconstruction and contact of the one-dimensional Bose-Fermi mixture

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