Nikolić, PredragSachdev, Subir2019-09-272007Nikolić, Predrag, and Subir Sachdev. 2007. “Renormalization-Group Fixed Points, Universal Phase Diagram, and1∕Nexpansion for Quantum Liquids with Interactions near the Unitarity Limit.” Physical Review A 75 (3). https://doi.org/10.1103/physreva.75.033608.1050-29471094-1622http://nrs.harvard.edu/urn-3:HUL.InstRepos:41417419It has long been known that particles with short-range repulsive interactions in spatial dimension d=1 form universal quantum liquids in the low density limit: all properties can be related to those of the spinless free Fermi gas. Previous renormalization-group (RG) analyses demonstrated that this universality is described by a RG fixed point, infrared stable for d < 2, of the zero density gas. We show that for d>2 the same fixed point describes the universal properties of particles with short-range attractive interactions near a Feshbach resonance; the fixed point is now infrared unstable, and the relevant perturbation is the detuning of the resonance. Some exponents are determined exactly, and the same expansion in powers of (d-2) applies for scaling functions for d < 2 and d>2. A separate exact RG analysis of a field theory of the particles coupled to "molecules" finds an alternative description of the same fixed point, with identical exponents; this approach yields a (4-d) expansion which agrees with the recent results of Nishida and Son [Phys. Rev. Lett. 97, 050403 (2006)]. The existence of the RG fixed point implies a universal phase diagram as a function of density, temperature, population imbalance, and detuning; in particular, this applies to the crossover between the Bose-Einstein condensate (BEC) and Bardeen-Cooper-Schrieffer (BCS) superfluid of s-wave paired fermions. Our results open the way towards computation of these universal properties using the standard field-theoretic techniques of critical phenomena, along with a systematic analysis of corrections to universality. We also propose a 1/N expansion [based upon models with Sp(2N) symmetry] of the fixed point and its vicinity, and use it to obtain results for the phase diagram.en-USJournal Article2019-09-2710.1103/PhysRevA.75.033608