Two-body contact of a Bose gas near the superfluid--Mott-insulator transition

Abstract

The two-body contact is a fundamental quantity of a dilute Bose gas that relates the thermodynamics to the short-distance two-body correlations. For a Bose gas in an optical lattice, near the superfluid--Mott-insulator transition, we show that a ``universal'' contact $C_{\mathrm{univ}}$ can be defined from the singular part $P-P_{\mathrm{MI}}$ of the pressure ($P_{\mathrm{MI}}$ is the pressure of the Mott insulator). Its expression $C_{\mathrm{univ}}=C_{\mathrm{DBG}}(|n-n^{\mathrm{MI}}|,a^{\ast })$ coincides with that of a dilute Bose gas provided we consider the effective ``scattering length'' $a^{\ast }$ of the quasi-particles at the quantum critical point (QCP) rather than the scattering length in vacuum, and the excess density $|n-n^{\mathrm{MI}}|$ of particles (or holes) with respect to the Mott insulator. Close to the transition, we find that the singular part $n_{\mathbf{k}}^{\mathrm{sing}}=n_{\mathbf{k}}-n_{\mathbf{k}}^{\mathrm{MI}}$ of the momentum distribution exhibits a high-momentum tail of the form $Z_{\mathrm{QP}}{C}_{\mathrm{univ}}/|\mathbf{k}{|}^4$ over a broad region of the Brillouin zone, where $Z_{\mathrm{QP}}$ is the quasi-particle weight of the elementary excitations at the QCP. Our results demonstrate that the notion of contact extends to strongly correlated lattice bosons, and we argue that the contact $C_{\mathrm{univ}}$ can be measured in state-of-the-art experiments on Bose gases in optical lattices and magnetic insulators.

arXiv commentv2) 6 pages, 4 figures; see also the companion paper arXiv:2501.14887

References in corpus (40)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Theory of Bose-Einstein condensation in trapped gases
• Bose-Einstein Condensation in Magnetic Insulators
• Large momentum part of fermions with large scattering length
• Energetics of a strongly correlated Fermi gas
• Quantum phases in an optical lattice
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• Contact Measurements on Atomic BEC
• Short-Distance Correlation Properties of the Lieb-Liniger System and Momentum Distributions of Trapped One-Dimensional Atomic Gases
• General relations for quantum gases in two and three dimensions. Two-component fermions
• Universal Properties of the Ultra-Cold Fermi Gas
• Mott insulator to superfluid transition in the Bose-Hubbard model: a strong-coupling approach
• Dynamical properties of ultracold bosons in an optical lattice
• Exact relations for quantum-mechanical few-body and many-body problems with short-range interactions in two and three dimensions
• Two-dimensional dynamics of expansion of a degenerate Bose gas
• General relations for quantum gases in two and three dimensions. II. Bosons and mixtures
• Two and Three-body Contacts in the Unitary Bose Gas
• Particle distribution tail and related energy formula
• Strong-coupling expansion for the momentum distribution of the Bose Hubbard model with benchmarking against exact numerical results
• Spectral weight redistribution in strongly correlated bosons in optical lattices
• Momentum-resolved observation of thermal and quantum depletion in an interacting Bose gas
• Universal properties of Fermi gases in arbitrary dimensions
• Bose-Hubbard phase diagram with arbitrary integer filling
• Nonperturbative renormalization-group approach to strongly-correlated lattice bosons
• Process chain approach to the Bose-Hubbard model: Ground-state properties and phase diagram
• Quasiparticle energy in a strongly interacting homogeneous Bose-Einstein condensate
• Itinerant-localized dual character of a strongly-correlated superfluid Bose gas in an optical lattice
• Single-atom-resolved probing of lattice gases in momentum space
• Critical behaviours of contact near phase transitions
• Thermodynamics of a Bose gas near the superfluid--Mott-insulator transition
• A Non-Perturbative Renormalization Group approach to quantum XY spin models
• Tan's two-body contact across the superfluid transition of a planar Bose gas
• Observation of $1/k^4$-tails after expansion of Bose-Einstein Condensates with impurities
• High-order symbolic strong-coupling expansion for the Bose-Hubbard model
• Quantum criticality of a Bose gas in an optical lattice near the Mott transition
• Improving Mean-Field Theory for Bosons in Optical Lattices via Degenerate Perturbation Theory
• Finite-temperature degenerate perturbation theory for bosons in optical lattices
• Scale Invariance in the Lowest Landau Level
• Strong-coupling RPA theory of a Bose gas near the superfluid--Mott-insulator transition: universal thermodynamics and two-body contact

Cited by in corpus (1)

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