Abelian Cayley High-Dimensional Expanders with Polylogarithmic Degree

We construct an explicit infinite family of simple two-dimensional Cayley complexes over $\mathbb{F}_2^n$ whose degree is polynomial in $n$ and whose nontrivial vertex-link eigenvalues lie in $[-λ,λ]$ for every fixed $λ>0$. For every fixed $d\ge2$, we also obtain an explicit infinite family of weigh