Entanglement blossom in a simplex matryoshka

Abstract

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