@inproceedings {738, title = {Entanglement spectrum and entropy of the 1D quantum q-state clock model via exact diagonalization and density matrix renormalization group}, booktitle = {Proceedings of the 44th Samahang Pisika ng Pilipinas Physics Conference}, year = {2026}, month = {17-20 Jun 2026}, pages = {SPP-2026-PC-02}, address = {Los Ba{\~n}os}, abstract = {This work studies the entanglement spectrum and R{\'e}nyi 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 R{\'e}nyi 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 {\textpm} 1)/2 for odd q. These results suggest an effectively local entanglement Hamiltonian consistent with the Bisognano{\textendash}Wichmann theorem and the area law, despite the global Zq symmetry.}, url = {https://proceedings.spp-online.org/article/view/SPP-2026-PC-02}, author = {Winonna Kylie C. Chua and Noel M. Lamsen} } @inproceedings {714, title = {Density matrix renormalization group and exact diagonalization analysis of the one-dimensional quantum q-state clock model}, booktitle = {Proceedings of the 43rd Samahang Pisika ng Pilipinas Physics Conference}, year = {2025}, month = {25{\textendash}28 Jun 2025}, pages = {SPP-2025-PA-18}, address = {Quezon City}, abstract = {This study investigates the one-dimensional quantum q-state clock model using exact diagonalization (ED) and the density matrix renormalization group (DMRG). At zero temperature, this model maps onto the two-dimensional classical vector Potts model via the transfer matrix formalism. ED was used to solve the ground state energy density and energy gap per site for q = 5 and q = 6 at small system sizes. DMRG was implemented to examine the same observables for larger system sizes. The results show general agreement between ED and DMRG, with minor deviations for q = 6. These findings provide insights into the low-energy properties of the 1D quantum q-state clock model and its relation to topological phase transitions.}, url = {https://proceedings.spp-online.org/article/view/SPP-2025-PA-18}, author = {Winonna Kylie C. Chua and Noel M. Lamsen} }