论文标题
用自旋模型在能量晶格上模拟自旋依赖性电势中的费米子
Simulating fermions in spin-dependent potentials with spin models on an energy lattice
论文作者
论文摘要
我们研究\ emph {自旋模型近似}下自旋依赖势的自旋1/2费物，其中改变了单粒子模式的总职业的原子间碰撞被忽略。旋转模型近似将相互作用的费用问题映射到能量空间中的晶格自旋模型的集合，其中自旋旋转相互作用是长期且自旋 - 抗疾病的。我们表明，与谐波振荡器频率相比，自旋模型近似对于弱相互作用是准确的，并且捕获了对时间表的集体旋转动力学比扰动理论所预期的要长得多。我们探讨了对旋转模型的校正，并考虑了校正的相对重要性。此外，我们提出的数值技术可用于在能量晶格上分析自旋模型，包括在多体态上制定单粒子基础的变化，作为有效的时间演化，以及在空间上与指数不均匀的长距离相互作用的拟合。后一种技术可用于构建用于DMRG分析的矩阵产品运营商，并且在张量网络社区中可能具有更广泛的适用性。
We study spin-1/2 fermions in spin dependent potentials under the \emph{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-ranged and spin-anisotropic. We show that the spin model approximation is accurate for weak interactions compared to the harmonic oscillator frequency, and captures the collective spin dynamics to timescales much longer than would be expected from perturbation theory. We explore corrections to the spin model, and the relative importance of corrections when realistic anharmonic potential corrections are taken into account. 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 DMRG analyses, and may have broader applicability within the tensor network community.
