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.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.

arXiv:1405.2256Nature CommunicationsOct 27, 201429 citations

An Elementary Examination of Quantum Phase Transitions Involving Fermions⁎

Jurgen Michael Honig, Józef Spałek

Elsevier eBooksJan 1, 20180 citations

Universality in phase transitions for ultracold fermionic atoms

Sebastian Diehl, CHRISTOF WETTERICH

We describe the gas of ultracold fermionic atoms by a functional integral for atom and molecule fields. The crossover from Bose-Einstein condensation (BEC) to BCS-type superfluidity shows universal features in terms of a concentration parameter for the ratio between scattering length and average interatomic distance. We discuss the relevance of the Yukawa coupling between atoms and molecules, establish an exact narrow resonance limit, and show that renormalized quantities are independent of the Yukawa coupling for the broad resonance and BCS and BEC limits. Within our functional integral formalism we compute the atom scattering in vacuum and the molecular binding energy. This connects the universal concentration parameter to the magnetic field of a given experiment. Beyond mean-field theory we include the fluctuations of the molecule field and the renormalization effects for the atom-molecule coupling. We find excellent agreement with the observed fraction of bare molecules in $^{6}\mathrm{Li}$ and qualitative agreement with the condensate fraction in $^{6}\mathrm{Li}$ and $^{40}\mathrm{K}$ . In addition to the phase diagram and condensate fraction we compute the correlation length for molecules, the in-medium scattering length for molecules and atoms, and the sound velocity.We describe the gas of ultracold fermionic atoms by a functional integral for atom and molecule fields. The crossover from Bose-Einstein condensation (BEC) to BCS-type superfluidity shows universal features in terms of a concentration parameter for the ratio between scattering length and average interatomic distance. We discuss the relevance of the Yukawa coupling between atoms and molecules, establish an exact narrow resonance limit, and show that renormalized quantities are independent of the Yukawa coupling for the broad resonance and BCS and BEC limits. Within our functional integral formalism we compute the atom scattering in vacuum and the molecular binding energy. This connects the universal concentration parameter to the magnetic field of a given experiment. Beyond mean-field theory we include the fluctuations of the molecule field and the renormalization effects for the atom-molecule coupling. We find excellent agreement with the observed fraction of bare molecules in $^{6}\mathrm{Li}$ and qualitative agreement with the condensate fraction in $^{6}\mathrm{Li}$ and $^{40}\mathrm{K}$. In addition to the phase diagram and condensate fraction we compute the correlation length for molecules, the in-medium scattering length for molecules and atoms, and the sound velocity.

arXiv:cond-mat/0502534Physical Review AMar 17, 200651 citations

^{6}\mathrm{Li}

and qualitative agreement with the condensate fraction in

^{6}\mathrm{Li}

and

^{40}\mathrm{K}

. In addition to the phase diagram and condensate fraction we compute the correlation length for molecules, the in-medium scattering length for molecules and atoms, and the sound velocity.