Effective spin-chain model for strongly interacting one-dimensional atomic gases with an arbitrary spin

Yang, Lijun; Cui, Xiaoling

doi:10.1103/physreva.93.013617

Cited by 67 publications

(35 citation statements)

References 50 publications

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“…a  g 1 1, recent research also unveiled the existence of a mapping to an effective spin-chain model by employing perturbation theory with respect to the 'snippet' basis. Various intriguing ground-state configurations have been revealed depending on the ratio and the sign of the interaction parameters: Heisenberg antiferromagnet (AFM)/ferromagnet (FM), Ising AFM/FM and XY phase [64][65][66][67][68]. Such a mapping is applicable not only for Bose-Bose mixtures, but also Bose-Fermi and Fermi-Fermi mixtures may be treated with this approach.…”

Section: Energy Spectramentioning

confidence: 99%

Spectral properties and breathing dynamics of a few-body Bose–Bose mixture in a 1D harmonic trap

et al. 2018

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-Beyond mean-field dynamics of ultra-cold bosonic atoms in higher dimensions: facing the challenges with a multiconfigurational approach V J Bolsinger, S Krönke and P Schmelcher - Recent citationsCorrelation effects in the quench-induced phase separation dynamics of a two species ultracold quantum gas S I Mistakidis et al AbstractWe investigate a few-body mixture of two bosonic components, each consisting of two particles confined in a quasi one-dimensional harmonic trap. By means of exact diagonalization with a correlated basis approach we obtain the low-energy spectrum and eigenstates for the whole range of repulsive intra-and inter-component interaction strengths. We analyse the eigenvalues as a function of the inter-component coupling, covering hereby all the limiting regimes, and characterize the behaviour in-between these regimes by exploiting the symmetries of the Hamiltonian. Provided with this knowledge we study the breathing dynamics in the linear-response regime by slightly quenching the trap frequency symmetrically for both components. Depending on the choice of interactions strengths, we identify 1 to 3 monopole modes besides the breathing mode of the centre of mass coordinate. For the uncoupled mixture each monopole mode corresponds to the breathing oscillation of a specific relative coordinate. Increasing the inter-component coupling first leads to multi-mode oscillations in each relative coordinate, which turn into single-mode oscillations of the same frequency in the composite-fermionization regime.

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Section: Energy Spectramentioning

confidence: 99%

Spectral properties and breathing dynamics of a few-body Bose–Bose mixture in a 1D harmonic trap

et al. 2018

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“…Such behaviour mimics the Fermi statistics in identical fermions. The Bose-Fermi mapping has tremendous applications in the study of strongly interacting quantum gases of ultracold atoms [10][11][12][13][14][15][16][17] 8 . In this paper we present a new application of Girardeau's Bose-Fermi mapping to the study of higher-order local and non-local correlation functions.…”

Section: Introductionmentioning

confidence: 99%

Higher-order local and non-local correlations for 1D strongly interacting Bose gas

et al. 2016

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The correlation function is an important quantity in the physics of ultracold quantum gases because it provides information about the quantum many-body wave function beyond the simple density profile. In this paper we first study the M-body local correlation functions, g M , of the one-dimensional (1D) strongly repulsive Bose gas within the Lieb-Liniger model using the analytical method proposed by Gangardt and Shlyapnikov (2003 Phys. Rev. Lett. 90 010401; 2003 New J. Phys. 5 79). In the strong repulsion regime the 1D Bose gas at low temperatures is equivalent to a gas of ideal particles obeying the non-mutual generalized exclusion statistics with a statistical parameter a g = -1 2 , i.e. the quasimomenta of N strongly interacting bosons map to the momenta of N free fermions via a » k kHere γ is the dimensionless interaction strength within the Lieb-Liniger model. We rigorously prove that such a statistical parameter α solely determines the sub-leading order contribution to the M-body local correlation function of the gas at strong but finite interaction strengths. We explicitly calculate the correlation functions g M in terms of γ and α at zero, low, and intermediate temperatures. For M = 2 and 3 our results reproduce the known expressions for g 2 and g 3 with sub-leading terms (see for instance (Vadim et al 2006 Phys. Rev. A 73 051604(R); Kormos et al 2009 Phys. Rev. Lett. 103 210404; Wang et al 2013 Phys. Rev. A 87 043634). We also express the leading order of the short distance non-local correlation functions1 of the strongly repulsive Bose gas in terms of the wave function of M bosons at zero collision energy and zero total momentum. Here ( ) Y x is the boson annihilation operator. These general formulas of the higherorder local and non-local correlation functions of the 1D Bose gas provide new insights into the manybody physics.

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“…One-dimensional (1D) systems are among the most widely studied problems in physics, especially due to their invaluable pedagogical properties and their more friendly manipulation of mathematical expressions both analytically and numerically, which often guide us through the understanding of interesting physical systems [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]. Furthermore, 1D structures such as nanotubes and nanowires, among others, may be highly relevant in technological applications [23].…”

Section: Introductionmentioning

confidence: 99%

Comparing numerical and analytical approaches to strongly interacting two-component mixtures in one dimensional traps

2017

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Abstract. Abstract is missing.e investigate one-dimensional harmonically trapped twocomponent systems for repulsive interaction strengths ranging from the non-interacting to the strongly interacting regime for Fermi-Fermi mixtures. A new and powerful mapping between the interaction strength parameters from a continuous Hamiltonian and a discrete lattice Hamiltonian is derived. As an example, we show that this mapping does not depend neither on the state of the system nor on the number of particles. Energies, density profiles and correlation functions are obtained both numerically (DMRG and Exact diagonalization) and analytically. Since DMRG results do not converge as the interaction strength is increased, analytical solutions are used as a benchmark to identify the point where these calculations become unstable. We use the proposed mapping to set a quantitative limit on the interaction parameter of a discrete lattice Hamiltonian above which DMRG gives unrealistic results.

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Effective spin-chain model for strongly interacting one-dimensional atomic gases with an arbitrary spin

Cited by 67 publications

References 50 publications

Spectral properties and breathing dynamics of a few-body Bose–Bose mixture in a 1D harmonic trap

Spectral properties and breathing dynamics of a few-body Bose–Bose mixture in a 1D harmonic trap

Higher-order local and non-local correlations for 1D strongly interacting Bose gas

Comparing numerical and analytical approaches to strongly interacting two-component mixtures in one dimensional traps

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