Strong-coupling RPA theory of a Bose gas near the superfluid--Mott-insulator transition: universal thermodynamics and two-body contact Article Swipe

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N. Dupuis , N. Dupuis , Adam Rançon · YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2501.14887

We present a strong-coupling expansion of the Bose-Hubbard model based on a mean-field treatment of the hopping term, while onsite fluctuations are taken into account exactly. This random phase approximation (RPA) describes the universal features of the generic Mott-insulator--superfluid transition (induced by a density change) and the superfluid state near the phase transition. The critical quasi-particles at the quantum critical point have a quadratic dispersion with an effective mass $m^*$ and their mutual interaction is described by an effective $s$-wave scattering length $a^*$. The singular part of the pressure takes the same form as in a dilute Bose gas, provided we replace the boson mass $m$ and the scattering length in vacuum $a$ by $m^*$ and $a^*$, and the density $n$ by the excess density $|n-n_{\rm MI}|$ of particles (or holes) with respect to the Mott insulator. We define a ``universal'' two-body contact $C_{\rm univ}$ that controls the high-momentum tail $\sim 1/|{\bf k}|^4$ of the singular part $n^{\rm sing}_{\bf k}$ of the momentum distribution. We also apply the strong-coupling RPA to a lattice model of hard-core bosons and find that the high-momentum distribution is controlled by a universal contact, in complete agreement with the Bose-Hubbard model. Finally, we discuss a continuum model of bosons in an optical lattice and define two additional two-body contacts: a short-distance ``universal'' contact $C_{\rm univ}^{\rm sd}$ which controls the high-momentum tail of $n^{\rm sing}_{\bf k}$ at scales larger than the inverse lattice spacing, and a ``full'' contact $C$ which controls the high-momentum tail of the full momentum distribution $n_{\bf k}$.

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preprint

Language

en

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http://arxiv.org/abs/2501.14887

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https://arxiv.org/pdf/2501.14887

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green

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10

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https://openalex.org/W4406879686

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https://openalex.org/W4406879686

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DOI

https://doi.org/10.48550/arxiv.2501.14887

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Title

Strong-coupling RPA theory of a Bose gas near the superfluid--Mott-insulator transition: universal thermodynamics and two-body contact

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preprint

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en

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2025

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2025-01-24

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N. Dupuis, N. Dupuis, Adam Rançon

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https://arxiv.org/abs/2501.14887

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https://arxiv.org/pdf/2501.14887

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Yes

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green

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https://arxiv.org/pdf/2501.14887

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Concepts

Superfluidity, Bose gas, Physics, Condensed matter physics, Mott insulator, Coupling (piping), Bose–Einstein condensate, Materials science, Metallurgy

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0

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10

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