Entanglement blossom in a simplex matryoshka

Exotic entanglement entropy scaling properties usually present interesting structures in real space and novel metrics of the spacetime lattice. One prominent example is rainbow chain where lattice sites which are symmetric about center form entangled Bell pairs due to an effective long-range coupling strong inhomogeneity regime. This manuscript generalizes a Hausdorff dimension one embedded higher dimensional enlarged local Hilbert keeping Hamiltonian frustration free. The from Schrieffer-Wolf transformation given by stacking layers k-simplices with 0-dimensional (all-to-all interacting) antiferromagnetic Hamiltonians, can be diagonalized analytically Young operators. original obtained introducing disinclination defects regular k-dimensional cubical lattice, introduces curvature at model interpolates between SYK free-fermionic XX spin chain, hence might potentially useful understanding black hole physics holography.