Harvard Condensed Matter Theory Seminars

Yusuke Nishida , University of Washington

Fermions at unitarity as a nonrelativistic conformal field theory

We prove an operator-state correspondence in nonrelativistic conformal field theories (NCFT); a primary operator in NCFT corresponds to an energy eigenstate of a few-particle system in a harmonic potential. The scaling dimension of the operator coincides with the energy of the corresponding eigenstate, divided by the oscillator frequency. As a concrete example, we consider spin-1/2 fermions with point-like interaction fine-tuned to the infinite scattering length (fermions at unitarity). Using the correspondence, we compute analytically the ground state energy of a few-fermions at unitarity in a harmonic potential by the systematic expansion in terms of d-2 or 4-d where d is the dimensionality of space.

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