Paper detail

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

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 $Υ_2$ 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 $Υ_2$ 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 one. Finally, the scaling behavior of magnetization at the low-temperature transition is compatible with $η=1/4$.