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arXiv · 2005.10886

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

Abel Rojo-Francàs·Artur Polls·Bruno Juliá-Díaz
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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.

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Abel Rojo-Francàs, Artur Polls, Bruno Juliá-Díaz. 2020-05-21. Static and dynamic properties of a few spin $1/2$ interacting fermions trapped in an harmonic potential. https://doi.org/10.3390/math8071196

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