Heisenberg Symmetry and Collective Modes of One Dimensional Unitary Correlated Fermions

Kumar Abhinav; Chandrasekhar Bhamidipati; Vivek M Vyas; Prasanta K. Panigrahi

doi:10.1016/j.physleta.2016.12.018

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arXiv · 0905.1911

Heisenberg Symmetry and Collective Modes of One Dimensional Unitary Correlated Fermions

Kumar Abhinav·Chandrasekhar Bhamidipati·Vivek M Vyas·Prasanta K. Panigrahi

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Abstract

The correlated fermionic many-particle system, near infinite scattering length, reveals an underlying Heisenberg symmetry in one dimension, as compared to an $SO(2,1)$ 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 $2ω$ in two dimensions.

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Kumar Abhinav, Chandrasekhar Bhamidipati, Vivek M Vyas, Prasanta K. Panigrahi. 2015-11-09. Heisenberg Symmetry and Collective Modes of One Dimensional Unitary Correlated Fermions. https://doi.org/10.1016/j.physleta.2016.12.018

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