Numerical study of the critical phases of the frustrated Z(5) model

TL;DR

This study uses numerical methods to explore the phase diagram of the frustrated Z(5) spin model, revealing a previously unobserved critical phase consistent with theoretical predictions and characterized by a central charge of 1.

Contribution

It identifies a new critical phase in the Z(5) model using DMRG, aligning with earlier theoretical predictions for similar models.

Findings

Discovery of a critical phase not seen in earlier simulations

Critical phases have central charge c=1

Magnetization scaling dimension varies across phases

Abstract

The phase diagram of the $\mathbb{Z}(5)$ spin model is studied numerically on the square lattice by means of the {\sl Density Matrix Renormalization Group}. In the regime where the two nearest-neighbor couplings have opposite signs, a critical phase, not observed in earlier Monte Carlo simulations, is identified. The new phase diagram is in agreement with predictions made by M. den Nijs [{\sl Phys. Rev. B} {\bf 31}, 266 (1985)] but for the $\mathbb{Z}(7)$ model rather than the $\mathbb{Z}(5)$ one. All critical phases are shown to be compatible with a central charge $c=1$. The magnetization scaling dimension displays however a different behavior in the different critical phases.