title: Critical behaviours of contact near phase transitions.
abstract: A central quantity of importance for ultracold atoms is contact, which measures two-body correlations at short distances in dilute systems. It appears in universal relations among thermodynamic quantities, such as large momentum tails, energy and dynamic structure factors, through the renowned Tan relations. However, a conceptual question remains open as to whether or not contact can signify phase transitions that are insensitive to short-range physics. Here we show that, near a continuous classical or quantum phase transition, contact exhibits a variety of critical behaviours, including scaling laws and critical exponents that are uniquely determined by the universality class of the phase transition, and a constant contact per particle. We also use a prototypical exactly solvable model to demonstrate these critical behaviours in one-dimensional strongly interacting fermions. Our work establishes an intrinsic connection between the universality of dilute many-body systems and universal critical phenomena near a phase transition.
authors.affiliation: State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China.
authors.forename: Y-Y
authors.initials: YY
authors.lastname: Chen
authors.affiliation: State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China.
authors.forename: Y-Z
authors.initials: YZ
authors.lastname: Jiang
authors.affiliation: 1] State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China [2] Center for Cold Atom Physics, Chinese Academy of Sciences, Wuhan 430071, China [3] Department of Theoretical Physics, Research School of Physics and Engineering, Australian National University, Canberra, Australian Capital Territory 0200, Australia.
authors.forename: X-W
authors.initials: XW
authors.lastname: Guan
authors.affiliation: Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong.
authors.forename: Qi
authors.initials: Q
authors.lastname: Zhou