Universality in few-body systems with large scattering length

Braaten, Eric; Hammer, H.-W.

doi:10.1016/j.physrep.2006.03.001

Cited by 1,302 publications

(2,649 citation statements)

References 208 publications

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“…When the transformation can be used, (11) splits into a free boson field for b and a sine-Gordon model for a:…”

Section: B Field Transformationmentioning

confidence: 99%

“…We stress that the family of operators (38) is different from the "polaronic" operators introduced in Ref. [18]: The latter are constructed specifically for minimizing the decay exponents in the massless phase of (11). On the contrary, the family (38) arises naturally in the massive phase of Eq.…”

Section: The Single-mode Luttinger (1m-ll) Multimer Phasementioning

confidence: 99%

“…On the contrary, the family (38) arises naturally in the massive phase of Eq. (11) as a many-body consequence of a existence of (p + q)-body bound states in the microscopic counterpart of (11). The effective theory of this (p + q)-mer object is then governed by the gapless mode b.…”

Section: The Single-mode Luttinger (1m-ll) Multimer Phasementioning

confidence: 99%

“…The simplest, albeit nontrivial, way of breaking the symmetry is to assume species-dependent masses of the particles. Even if we consider the few-body problem, this is known to bring new physics like the Efimov phenomenon: While for an equal-mass Fermi liquid the only allowed bound state is a Cooper pair, three-body bound states (trimers) appear once the mass ratio exceeds a certain threshold [11]. The atom-dimer scattering is strongly affected by the mass asymmetry [12] and the ultimate fate of a Fermi liquid in presence of the Efimov effect is currently an open question being actively investigated [13].…”

Section: Introductionmentioning

confidence: 99%

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Multimer formation in one-dimensional two-component gases and trimer phase in the asymmetric attractive Hubbard model

2011

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We consider two-component one-dimensional quantum gases at special imbalanced commensurabilities which lead to the formation of multimer (multiparticle bound-states) as the dominant order parameter. Luttinger liquid theory supports a mode-locking mechanism in which mass (or velocity) asymmetry is identified as the key ingredient to stabilize such states. While the scenario is valid both in the continuum and on a lattice, the effects of umklapp terms relevant for densities commensurate with the lattice spacing are also mentioned. These ideas are illustrated and confronted with the physics of the asymmetric (mass-imbalanced) fermionic Hubbard model with attractive interactions and densities such that a trimer phase can be stabilized. Phase diagrams are computed using density-matrix renormalization group techniques, showing the important role of the total density in achieving the latter phase. The effective physics of the trimer gas is studied as well. Last, the effect of a parabolic confinement and the emergence of a crystal phase of trimers are briefly addressed. This model has connections with the physics of imbalanced two-component fermionic gases and Bose-Fermi mixtures as the latter gives a good phenomenological description of the numerics in the strong-coupling regime.

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“…When the transformation can be used, (11) splits into a free boson field for b and a sine-Gordon model for a:…”

Section: B Field Transformationmentioning

confidence: 99%

Section: The Single-mode Luttinger (1m-ll) Multimer Phasementioning

confidence: 99%

Section: The Single-mode Luttinger (1m-ll) Multimer Phasementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multimer formation in one-dimensional two-component gases and trimer phase in the asymmetric attractive Hubbard model

2011

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“…(27). At NLO in the complex mass scheme, the normalization constant Z X and the propagator ∆ X (E, 0) are given in Eqs.…”

Section: E Line Shape Of X In a Short-distance Decay Channelmentioning

confidence: 99%

Weakly-bound hadronic molecule near a 3-body threshold

2007

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The X(3872) seems to be a loosely-bound hadronic molecule whose constituents are two charm mesons. A novel feature of this molecule is that the mass difference of the constituents is close to the mass of a lighter meson that can be exchanged between them, namely the pion. We analyze this feature in a simple model with spin-0 mesons only. Various observables are calculated to next-to-leading order in the interaction strength of the exchanged meson. Renormalization requires summing a geometric series of next-to-leading order corrections. The dependence of observables on the ultraviolet cutoff can be removed by renormalizations of the mass of the heaviest meson, the coupling constant for the contact interaction between the heavy mesons, and short-distance coefficients in the operator product expansion. The next-to-leading order correction has an unphysical infrared divergence at the threshold of the two heavier mesons that can be eliminated by a further resummation that takes into account the nonzero width of the heaviest meson.

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Functional renormalization group approach to the BCS‐BEC crossover

Diehl¹,

et al. 2010

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The phase transition to superfluidity and the BCS-BEC crossover for an ultracold gas of fermionic atoms is discussed within a functional renormalization group approach. Non-perturbative flow equations, based on an exact renormalization group equation, describe the scale dependence of the flowing or average action. They interpolate continuously from the microphysics at atomic or molecular distance scales to the macroscopic physics at much larger length scales, as given by the interparticle distance, the correlation length, or the size of the experimental probe. We discuss the phase diagram as a function of the scattering length and the temperature and compute the gap, the correlation length and the scattering length for molecules. Close to the critical temperature, we find the expected universal behavior. Our approach allows for a description of the few-body physics (scattering and molecular binding) and the many-body physics within the same formalism.

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Universality in few-body systems with large scattering length

Cited by 1,302 publications

References 208 publications

Multimer formation in one-dimensional two-component gases and trimer phase in the asymmetric attractive Hubbard model

Multimer formation in one-dimensional two-component gases and trimer phase in the asymmetric attractive Hubbard model

Weakly-bound hadronic molecule near a 3-body threshold

Functional renormalization group approach to the BCS‐BEC crossover

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