Exact solution of a 1D quantum many-body system with momentum-dependent interactions

Grosse, Harald; Langmann, Edwin; Paufler, Cornelius

doi:10.1088/0305-4470/37/16/008

Cited by 26 publications

(53 citation statements)

References 23 publications

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“…Comparison with eigenenergies determined numerically for shapedependent 1D atom-atom potentials illustrates the applicability of our 1D pseudo-potential. Our results confirm the FermiBose duality [25,26,27,28,29] in 1D for two atoms under harmonic confinement.…”

Section: Introductionsupporting

confidence: 85%

Nondivergent pseudopotential treatment of spin-polarized fermions under one- and three-dimensional harmonic confinement

Kanjilal

Blume

2004

Phys. Rev. A

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Atom-atom scattering of bosonic one-dimensional (1D) atoms has been modeled successfully using a zerorange delta-function potential, while that of bosonic 3D atoms has been modeled successfully using FermiHuang's regularized s-wave pseudo-potential. Here, we derive the eigenenergies of two spin-polarized 1D fermions under external harmonic confinement interacting through a zero-range potential, which only acts on odd-parity wave functions, analytically. We also present a divergent-free zero-range potential treatment of two spin-polarized 3D fermions under harmonic confinement. Our pseudo-potential treatments are verified through numerical calculations for short-range model potentials.

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Section: Introductionsupporting

confidence: 85%

Nondivergent pseudopotential treatment of spin-polarized fermions under one- and three-dimensional harmonic confinement

Kanjilal

Blume

2004

Phys. Rev. A

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“…(4). From this expression, the non-relativistic limit of the tree-level Feynman diagrams is immediately recovered.…”

Section: B Non Relativistic Limit From the Large N Expansionmentioning

confidence: 89%

“…An analogue operation must be done for the fermionic fields, thus we consider the following mode splitting [4] …”

Section: The Super Sinh Gordon and Its Non Relativistic Limitmentioning

confidence: 99%

“…Interestingly, the duality between the Thirring model and the purely bosonic Sine Gordon model [27] is reflected also in their NR limits [4,26,28], being the NR limit of the Sine Gordon the attractive Lieb Liniger model [4,29]. The purpose of the present investigation is to enlarge the landscape of the known NR limits, in particular we consider the supersymmetric Sinh-Gordon model (SShG) [30,31], the O(N ) Gross-Neveu model (GN) [21,32,33] and 1 In Ref.…”

Section: Introductionmentioning

confidence: 99%

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Non relativistic limit of integrable QFT with fermionic excitations

Bastianello

Luca

Mussardo

2017

J. Phys. A: Math. Theor.

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The aim of this paper is to investigate the non-relativistic limit of integrable quantum field theories with fermionic fields, such as the O(N ) Gross-Neveu model, the supersymmetric Sinh-Gordon and non-linear sigma models. The non-relativistic limit of these theories is implemented by a double scaling limit which consists of sending the speed of light c to infinity and rescaling at the same time the relevant coupling constant of the model in such a way to have finite energy excitations. For the general purpose of mapping the space of continuous non-relativistic integrable models, this paper completes and integrates the analysis done in Ref.[1] on the non-relativistic limit of purely bosonic theories.Pacs numbers:

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“…And in some cases, for example, for a spin-polarized fermionic gas, the pwave interaction plays a dominant role as the s-wave scattering is forbidden due to the Pauli exclusion principle. For a 1D polarized fermionic gas with p-wave interactions, some theoretical works have unveiled the existence of a Bose-Fermi duality between the 1D spinless p-wave fermionic system and a bosonic system with the reversed role of strong and weak couplings [39][40][41][42][43][44][45]. Such studies inspire us to realize that the weak p-wave interaction may also play important role in 1D strongly interacting Bose-Fermi and Fermi-Fermi mixtures when the strength of p-wave interaction is comparable with the inverse of the strength of s-wave interaction.…”

Section: Introductionmentioning

confidence: 99%

Strongly interacting one-dimensional quantum gas mixtures with weakp-wave interactions

Pan

Chen

2016

Phys. Rev. A

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We study one-dimensional strongly interacting quantum gas mixtures, including both the BoseFermi and spin-1/2 Fermi-Fermi mixtures, with weak p-wave interactions between intra-component fermions, and demonstrate that the weak p-wave interaction can not be omitted in the strongly interacting regime where the strength of p-wave interactions is comparable with the inverse of the strength of strongly repulsive s-wave interactions. While the total density distribution is not sensitive to the weak p-wave interaction, we find that the p-wave interaction plays an important role in determining the species-dependent (or spin-dependent) density distributions and produces significant physical effects on the low-energy spin dynamics. We also derive effective spin-exchange models for strongly interacting quantum gas mixtures with weak p-wave interactions, which indicate that a quantum phase transition from anti-ferromagnetic state to ferromagnetic state can be induced by tuning the relative strengths of intra-component and inter-component interactions.

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Exact solution of a 1D quantum many-body system with momentum-dependent interactions

Cited by 26 publications

References 23 publications

Nondivergent pseudopotential treatment of spin-polarized fermions under one- and three-dimensional harmonic confinement

Nondivergent pseudopotential treatment of spin-polarized fermions under one- and three-dimensional harmonic confinement

Non relativistic limit of integrable QFT with fermionic excitations

Strongly interacting one-dimensional quantum gas mixtures with weakp-wave interactions

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