Entanglement-entropy study of phase transitions in six-state clock model

The Berezinskii-Kosterlitz-Thouless (BKT) transitions of the six-state clock model on the square lattice are investigated by means of the corner-transfer matrix renormalization group method. A classical analog of the entanglement entropy $S(L,T)$ is calculated for $L\times L$ square system up to $L = 129$,asafunctionoftemperature$T$\mathrm{.}Theentropyexhibitsapeakat$T = T^*_{~}( L )$,wherethetemperaturedependsonboth$L$ and the boundary conditions. Applying the finite-size scaling to $T_{}^{\ast }(L)$ and assuming presence of the BKT transitions, the two distinct phase-transition temperatures are estimated to be $T_1^{}=0.70$ and $T_2^{}=0.88$. The results are in agreement with earlier studies. It should be noted that no thermodynamic functions have been used in this study.