Simulating fermions in spin-dependent potentials with spin models on an energy lattice

2020/01/14 by Michael L. Wall
Physics and Astronomy · #Anharmonicity #Cold Atom Physics and Bose-Einstein Condensates #Degenerate energy levels #Fermion #Matrix multiplication #Matrix product state #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum many-body systems #Quantum mechanics #Spin (aerodynamics) #Statistical physics #cond-mat.quant-gas #quant-ph

paper · pdf · doi:10.1103/physreva.102.023329

published as Phys. Rev. A 102, 023329 (2020) · 16 pages, 13 figures

arxiv created 2020/01/14 · openalex publication_date 2020/08/26 · arxiv updated 2020/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study spin-1/2 fermions in spin-dependent potentials under the spin-model approximation, in which interatomic collisions that change the total occupation of single-particle modes are ignored. The spin-model approximation maps the interacting fermion problem to an ensemble of lattice spin models in energy space, where spin-spin interactions are long range and spin anisotropic. We consider a Ramsey-type sequence in which quantum degenerate, initially spin-polarized fermions are rotated to a spin superposition, and the differences in potential for the two spin states induce s-wave interactions. Applied to such a setup, we show that the spin-model approximation qualitatively captures the collective spin dynamics for weak interactions compared to the harmonic-oscillator frequency, and often captures quantitative features at timescales much longer than would be expected from perturbation theory. We explore corrections to the spin model, and the relative importance of corrections for both collective spin and fidelity metrics when realistic anharmonic potential corrections are taken into account, demonstrating that anharmonicity can significantly improve the fidelity of the spin-model approximation. Additionally, we present numerical techniques that are useful for analysis of spin models on an energy lattice, including enacting a change of single-particle basis on a many-body state as an effective time evolution, and fitting of spatially inhomogeneous long-range interactions with exponentials. This latter technique is useful for constructing matrix product operators for use in density-matrix renormalization group analyses, and may have broader applicability within the tensor network community.

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