Density matrix renormalization group and exact diagonalization analysis of the one-dimensional quantum q-state clock model

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.