Tan’s contact of a harmonically trapped one-dimensional Bose gas: Strong-coupling expansion and conjectural approach at arbitrary interactions

Lang, Guillaume; Vignolo, Patrizia; Minguzzi, Anna

doi:10.1140/epjst/e2016-60343-6

Cited by 22 publications

(28 citation statements)

References 38 publications

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“…In the perspective of taking an harmonic trapping into account, it also allows to discuss the validity of the Local Density Approximation [18] by comparison with exact numerics [31]. To this aim, the equation of state from the 1/γ expansion is accurate in the strongly-interacting regime, while the conjecture thereby deduced is also accurate at intermediate γ [32]. The attractive regime of the super-Tonks-Girardeau gas may also provide new insights [33,34].…”

Section: Discussionmentioning

confidence: 99%

Connection between nonlocal one-body and local three-body correlations of the Lieb-Liniger model

et al. 2017

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We derive a connection between the fourth coefficient of the short-distance Taylor expansion of the one-body correlation function, and the local three-body correlation function of the LiebLiniger model of δ-interacting spinless bosons in one dimension. This connection, valid at arbitrary interaction strength, involves the fourth moment of the density of quasi-momenta. Generalizing recent conjectures, we propose approximate analytical expressions for the fourth coefficient covering the whole range of repulsive interactions, validated by comparison with accurate numerics. In particular, we find that the fourth coefficient changes sign at interaction strength γc 3.816, while the first three coefficients of the Taylor expansion of the one-body correlation function retain the same sign throughout the whole range of interaction strengths.

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Section: Discussionmentioning

confidence: 99%

Connection between nonlocal one-body and local three-body correlations of the Lieb-Liniger model

et al. 2017

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“…where C 2 is the exact Tan's contact coefficient for the two-atom system under study [14] (for a recent study of this coefficient see [26,27]) recovering the 1/ p 4 dependence originated from the short-range character of the interaction.…”

Section: Highp Behavior Of the Momentum Distribution And Tan's Coefficientmentioning

confidence: 99%

The momentum distribution of two bosons in one dimension with infinite contact repulsion in harmonic trap gets analytical

2021

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For a harmonically trapped system consisting of two bosons in one spatial dimension with infinite contact repulsion (hard core bosons), we derive an expression for the one-body density matrix $$\rho _\mathrm{B}$$ ρ B in terms of center of mass and relative coordinates of the particles. The deviation from $$\rho _\mathrm{F}$$ ρ F , the density matrix for the two fermions case, can be clearly identified. Moreover, the obtained $$\rho _\mathrm{B}$$ ρ B allows us to derive a closed form expression of the corresponding momentum distribution $$n_\mathrm{B}(p)$$ n B ( p ) . We show how the result deviates from the noninteracting fermionic case, the deviation being associated with the short-range character of the interaction. Mathematically, our analytical momentum distribution is expressed in terms of one and two variables confluent hypergeometric functions. Our formula satisfies the correct normalization and possesses the expected behavior at zero momentum. It also exhibits the high momentum $$1/p^4 $$ 1 / p 4 tail with the appropriate Tan’s coefficient. Numerical results support our findings.

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“…They are connected by a single coefficient C, referred to as the integrated contact intensity or 'contact'. Further, Tan's ideas were developed [4,5] and extended to Bose systems also [6][7][8][9]. It has been established that Tan's contact measures the density of pairs at short distances and determines the exact large-momentum or high frequency behavior of various physical observables.…”

Section: Introductionmentioning

confidence: 99%

Critical behavior of Tan’s contact for bosonic systems with a fixed chemical potential

Rakhimov¹,

Abdurakhmonov²,

Tanatar³

2021

J. Phys.: Condens. Matter

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The temperature dependence of Tan's contact parameter C and its derivatives for spin gapped quantum magnets are investigated. We use the paradigm of Bose-Einstein condensation (BEC) to describe the low temperature properties of quasiparticles in the system known as triplons. Since the number of particles and the condensate fraction are not fixed we use the μVT ensemble to calculate the thermodynamic quantities. The interactions are treated at the Hartree-Fock-Bogoliubov approximation level. We obtained the temperature dependence of C and its derivative with respect to temperature and applied magnetic field both above and below T c of the phase transition from the normal phase to BEC. We have shown that C is regular, while its derivatives are discontinuous at T c in accordance with Ehrenfest's classification of phase transitions. Moreover, we have found a sign change in ∂C/∂T close to the critical temperature. As to the quantum critical point, C and its derivatives are regular as a function of the control parameter r, which induces the quantum phase transition. At very low temperatures, one may evaluate C simply from the expression C = m 2 μ 2 /ā 4 , where the only parameter effective mass of quasiparticles should be estimated. We propose a method for measuring of Tan's contact for spin gapped dimerized magnets.

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Tan’s contact of a harmonically trapped one-dimensional Bose gas: Strong-coupling expansion and conjectural approach at arbitrary interactions

Cited by 22 publications

References 38 publications

Connection between nonlocal one-body and local three-body correlations of the Lieb-Liniger model

Connection between nonlocal one-body and local three-body correlations of the Lieb-Liniger model

The momentum distribution of two bosons in one dimension with infinite contact repulsion in harmonic trap gets analytical

Critical behavior of Tan’s contact for bosonic systems with a fixed chemical potential

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