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.
Highlights
A central quantity of importance for ultracold atoms is contact, which measures two-body correlations at short distances in dilute systems
Whereas the Tan relations have revealed how contact controls various thermodynamic quantities, it is in general difficult to make quantitative predictions as to how contact depends on the many-body physics of the system
Our results have shown that in the critical region near a phase transition point, contact and its derivatives are uniquely determined by the universality class of the phase transition
Summary
A central quantity of importance for ultracold atoms is contact, which measures two-body correlations at short distances in dilute systems. Our approach is to derive exact results on the behaviour of contact near a classical or quantum phase transition based on a fundamental thermodynamic relation that is free from any approximations. These results unambiguously show that contact must display critical behaviours near the transitions, and that the corresponding critical behaviours are uniquely determined by the universality class of the phase transition. We use a one-dimensional (1D) exactly solvable model of strongly interacting fermions exhibiting exotic quantum phase transitions to demonstrate these critical phenomena. Whereas our general results apply to all dimensions, this 1D example sheds light on the universal features of contact near a phase transition
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