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 Sα(k = 0) < Sα(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.
