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It has long been known that particles with short-range repulsive interactionsin spatial dimension d=1 form universal quantum liquids in the low densitylimit: all properties can be related to those of the spinless free Fermi gas.Previous renormalization group (RG) analyses demonstrated that thisuniversality is described by an RG fixed point, infrared stable for d<2, of thezero density gas. We show that for d>2 the same fixed point describes theuniversal properties of particles with short-range attractive interactions neara Feshbach resonance; the fixed point is now infrared unstable, and therelevant perturbation is the detuning of the resonance. Some exponents aredetermined exactly, and the same expansion in powers of (d-2) applies forscaling functions for d<2 and d>2. A separate exact RG analysis of a fieldtheory of the particles coupled to `molecules' finds an alternative descriptionof the same fixed point, with identical exponents; this approach yields a (4-d)expansion which agrees with the recent results of Nishida and Son(cond-mat/0604500). The existence of the RG fixed point implies a universalphase diagram as a function of density, temperature, population imbalance, anddetuning; in particular, this applies to the BEC-BCS crossover of fermions withs-wave pairing. Our results open the way towards computation of these universalproperties using the standard field-theoretic techniques of critical phenomena,along with a systematic analysis of corrections to universality. We alsopropose a 1/N expansion (based upon models with Sp(2N) symmetry) of the fixedpoint and its vicinity, and use it to obtain results for the phase diagram.Comment: 15 pages, 8 figures; (v3) added refs and improved figure

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

Renormalization-group fixed points, universal phase diagram, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>∕</mml:mo><mml:mi>N</mml:mi></mml:mrow></mml:math>expansion for quantum liquids with interactions near the unitarity limit

Renormalization-group fixed points, universal phase diagram, and1∕Nexpansion for quantum liquids with interactions near the unitarity limit