Universal Tan relations for quantum gases in one dimension

Abstract

We investigate universal properties of one-dimensional multi-component systems comprised of fermions, bosons, or an arbitrary mixture, with contact interactions and subjected to an external potential. The masses and the coupling strengths between different types of particles are allowed to be different and we also take into account the presence of an arbitrary magnetic field. We show that the momentum distribution of these systems exhibits a universal $n_{\sigma }(k)\sim C_{\sigma }/k^4$ decay with $C_{\sigma }$ the contact of species $\sigma$ which can be computed from the derivatives of an appropriate thermodynamic potential with respect to the scattering lengths. In the case of integrable fermionic systems we argue that at fixed density and repulsive interactions the total contact reaches its maximum in the balanced system and monotonically decreases to zero as we increase the magnetic field. The converse effect is present in integrable bosonic systems: the contact is largest in the fully polarized state and reaches its minimum when all states are equally populated. We obtain short distance expansions for the Green's function and pair distribution function and show that the coefficients of these expansions can be expressed in terms of the density, kinetic energy and contact. In addition we derive universal thermodynamic identities relating the total energy of the system, pressure, trapping energy and contact. Our results are valid at zero and finite temperature, for homogeneous or trapped systems and for few-body or many-body states.

arXiv comment12 pages, RevTeX 4.1

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Cited by in corpus (23)

• Tan's Contact for Trapped Lieb-Liniger Bosons at Finite Temperature
• Thermal instability, evaporation and thermodynamics of one-dimensional liquids in weakly-interacting Bose-Bose mixtures
• Few-body correlations in two-dimensional Bose and Fermi ultracold mixtures
• Correlation functions of one-dimensional strongly interacting two-component gases
• Analytic thermodynamic properties of the Lieb-Liniger gas
• Correlation properties of a one-dimensional repulsive Bose gas at finite temperature
• Dynamical fermionization in a one-dimensional Bose-Fermi mixture
• High-momentum tail and universal relations of a Fermi gas near a Raman-dressed Feshbach resonance
• Quantum critical behavior and thermodynamics of the repulsive one-dimensional Hubbard model in a magnetic field
• Universality and quantum criticality of the one-dimensional spinor Bose gas
• P-wave contacts of quantum gases in quasi-one-dimensional and quasi-two-dimensional traps
• Universal relations for hybridized $s$- and $p$-wave interactions from spin-orbital coupling
• Symmetry oscillations in strongly interacting one-dimensional mixtures
• Thermal fading of the $1/k^4$-tail of the momentum distribution induced by the hole anomaly
• High-momentum oscillating tails of strongly interacting 1D gases in a box
• Universal relations and normal-state properties of a Fermi gas with laser-dressed mixed-partial-wave interactions
• Critical behavior of Tan's contact for bosonic systems with a fixed chemical potential
• Momentum reconstruction and contact of the one-dimensional Bose-Fermi mixture
• Large-momentun tail of one-dimensional Fermi gases with spin-orbit coupling
• Momentum distribution and non-local high order correlation functions of 1D strongly interacting Bose gas
• Dynamical probing of high-order spin coherence in one-dimensional mixtures
• Numerical methods and analytic results for one-dimensional strongly interacting spinor gases
• Universal properties and dynamical bosonization of strongly interacting one-dimensional anyons