Finite-state automata for exact matrix product operators of tight-binding Hamiltonians: fractals, quasicrystals, trees and hyperbolic lattices

This arXiv paper introduces a systematic method for constructing exact matrix product operators (MPOs) for single-particle tight-binding Hamiltonians on recursively structured lattices. By encoding lattice geometry into finite-state automata and adapting Abelian-symmetric tensor network techniques, the method achieves exact and efficient representation for complex geometries including fractals, quasicrystals, trees, and hyperbolic lattices. The approach leverages the recursive structure inherent in these lattices to enable scalable quantum system simulations.