Heisenberg symmetry and collective modes of one dimensional unitary correlated fermions

Abstract The correlated fermionic many-particle system, near infinite scattering length, reveals an underlying Heisenberg symmetry in one dimension, as compared to an S O ( 2 , 1 ) symmetry in two dimensions. This facilitates an exact map from the interacting to the non-interacting system, both with and without a harmonic trap, and explains the short-distance scaling behavior of the wave-function. Taking advantage of the phenomenological Calogero–Sutherland-type interaction, motivated by the density functional approach, we connect the ground-state energy shift, to many-body correlation effect. For the excited states, modes at integral values of the harmonic frequency ω are predicted in one dimension, in contrast to the breathing modes with frequency 2 ω in two dimensions.