DMRG study of the Berezinskii–Kosterlitz–Thouless transitions of the 2D five-state clock model

Abstract

The two Berezinskii–Kosterlitz–Thouless phase transitions of the two-dimensional 5-state clock model are studied on infinite strips using the DMRG algorithm. Because of the open boundary conditions, the helicity modulus ϒ2 is computed by imposing twisted magnetic fields at the two boundaries. Its scaling behavior is in good agreement with the existence of essential singularities with σ = 1/2 at the two transitions. The predicted universal values of ϒ2 are shown to be reached in the thermodynamic limit. The fourth-order helicity modulus is observed to display a dip at the high-temperature BKT transition, like the XY model, and shown to take a new universal value at the low-temperature BKT transition. Finally, the scaling behavior of magnetization at the low-temperature transition is compatible with η = 1/4.