扭转双层石墨烯的哈特利－福克 coercivity
Hartree--Fock coercivity for twisted bilayer graphene
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中文总结 AI 辅助
该研究针对扭转双层石墨烯手性模型的哈特利－福克泛函，证明了二重平带半填充时存在两个极小值，并给出其 Hessian 严格 coercivity 的新结果。
中文摘要 AI 辅助
我们研究由Tarnopolsky、Kruchkov和Vishwanath提出的扭转双层石墨烯手性模型中平带的哈特利－福克泛函的极小值。我们的模型是Becker、Lin和Stubbs在之前工作中考虑的离散模型的连续版本，第一个结果是这些论文主要定理的直接类似物：在二重平带半填充时，恰好存在两个极小值，通过占据两个子带中的任意一个获得。（该结果的更一般版本，强调其拓扑起源，已在Tao-Zworski讲义的附录A.8中呈现。）新的贡献是哈特利－福克泛函在两个极小值处的 Hessian 的严格 coercivity，这是分量带的陈数之间差异的结果，可被乐观地视为“谱隙”的软版本。
英文摘要
We study the minimisers of the Hartree--Fock functional for flat bands in the chiral model of twisted bilayer graphene introduced by Tarnopolsky, Kruchkov, and Vishwanath. Our model is a continuous version of the discrete model considered by Becker, Lin and Stubbs in previous works and the first result is a direct analogue of main theorems of those papers: at half filling of the flat band of multiplicity two, there are exactly two minimisers, obtained by occupying either one of the two sub-bands. (A more general version of this result, stressing its topological origins, was presented in Appendix A.8 of the Lecture Notes by Tao-Zworski.) The new contribution is the strict coercivity of the Hessian of the Hartree--Fock functional at the two minimisers. It is a consequence of the difference between the Chern numbers of the component bands and can be optimistically considered as a soft version of a ``spectral gap''.
