Static and dynamic properties of a few spin $1/2$ interacting fermions trapped in an harmonic potential

Abstract

We provide a detailed study of the properties of a few interacting spin $1/2$ fermions trapped in a one-dimensional harmonic oscillator potential. The interaction is assumed to be well represented by a contact delta potential. Numerical results obtained by means of direct diagonalization techniques are combined with analytical expressions for both the non-interacting and strongly interacting regime. The $N=2$ case is used to benchmark our numerical techniques with the known exact solution of the problem. After a detailed description of the numerical methods, in a tutorial-like manner, we present the static properties of the system for $N=2,3,4$ and 5 particles, e.g. low-energy spectrum, one-body density matrix, ground-state densities. Then, we consider dynamical properties of the system exploring first the excitation of the breathing mode, using the dynamical structure function and corresponding sum-rules, and then a sudden quench of the interaction strength.

arXiv commentCorrected typo in Eq. (35) and Eq. (41)

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• Enhanced strong interaction effect in synthetic spin-orbit coupling with mixed spin symmetry
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• Composite Bosons Superposition Ansatz Approach to One-Dimensional Trapped Few-Fermion Systems