Entanglement spectrum and entropy of the 1D quantum q-state clock model via exact diagonalization and density matrix renormalization group

Abstract

This work studies the entanglement spectrum and Rényi entropy of the one-dimensional quantum q-state clock model for q = 2 to q = 6 using exact diagonalization (ED) and the density matrix renormalization group (DMRG), implemented with the conserved modular charge k for symmetry resolution. For all q values, the entanglement spectra display a mapping between sectors labeled by k and q−k, with the ground state of the entanglement Hamiltonian consistently located in the neutral-charge sector k = 0. Furthermore, the Rényi entropy follows an ordered structure S_α,k=0 < S_α,k=1,q−1 < ..., with the largest entropy contributions occurring at k = q/2 for even q and k = (q±1)/2 for odd q. These results suggest an effectively local entanglement Hamiltonian consistent with the Bisognano–Wichmann theorem and the area law, despite the global Z_q symmetry.