Critical behaviours of contact near phase transitions

TL;DR

This paper investigates how the contact parameter, related to two-body correlations, exhibits universal critical behaviors and scaling laws near phase transitions in ultracold atomic systems, linking many-body physics and critical phenomena.

Contribution

It demonstrates that contact shows universal critical behaviors near phase transitions, connecting dilute many-body systems with critical phenomena through scaling laws and exponents.

Findings

Contact exhibits critical scaling laws near phase transitions.

Universal critical exponents are determined by the universality class.

Exactly solvable models confirm the critical behaviors of contact.

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 behaviors, 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 behaviors 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.