Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session G33: Quantum Simulation II
11:30 AM–2:18 PM,
Tuesday, March 15, 2022
Room: McCormick Place W-192C
Sponsoring
Unit:
DAMOP
Chair: Krutik Patel, University of Chicago
Abstract: G33.00009 : The Ground State Properties of a spin-3/2 Fermi gas*
1:06 PM–1:18 PM
Presenter:
Bei Xu
(Department of Physics, University of Science and Technology Beijing, Beijing 100083, China)
Authors:
Bei Xu
(Department of Physics, University of Science and Technology Beijing, Beijing 100083, China)
Qiang Gu
(Department of Physics, University of Science and Technology Beijing, Beijing 100083, China)
Collaboration:
Department of Physics, University of Science and Technology Beijing, Beijing 100083, China
In this paper, we study ground state properties of a generalized spin-3/2 Fermi model in which interactions are set to be spin-dependent and emphasize contributions of the spin-mixing interaction. The system with SU(N) or SP(N) symmetry is just the special case of the generalized model by supposing
some interaction parameters to be related. Our treatment is different from but complementary to the methods used previously for the SU(N) and SP(N) systems. We calculate the effective interaction via Galitskii's equation and integrate the self-energy with the tricky method that was originally used to treat the uniform electron gas by Onsager and Ziesche . The obtained results can be compared to previous studies.
After the calculation , we find that the ground state energy and effective mass always increase with the spin-dependent interaction strengths in the spin-3/2 Fermi system with lower symmetry which is consistent with the conclusion of SP(N) and SU(N) Fermi liquid. We derive the effective interaction iterately by using the Green's function and ladder diagrams. These techniques make it easier to get the higher-order approximation terms of each spin channel and avoid some redundant cross terms. We can get the contribution of spin-mixing term g_0 separately. The numerical integration results of spin-1/2 system is approximately equal to the result calculated by Galitskii in 1958 , but the scattering length is spin-dependent because of the contact interaction. Otherwise, there are more interaction parameters especially the spin-mixing term that always strengthens the ground state energy and effective mass in spin-3/2 Fermi gas. Taking the value of scattering length as ( g_1=g_2=g_3=g_4=1/2 g), we obtain the result of effective mass for spin-3/2 system, which can recover the SU(2) and SU(N) results but add a spin-mixing term.The chemical potential, ground state energy and effective mass are calculated after elaborately dealing with the effective interaction and the self-energy. Contributions of each interaction term are derived within the second-order perturbation. It is found that the spin-mixing term always strengthens the ground state energy and effective mass.
*This study was supported by the National Natural Science Foundation ofChina (Grant No. 11574028)
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