Entanglement entropy and massless phase in the antiferromagnetic three-state quantum chiral clock model

Abstract

The von Neumann entanglement entropy is used to estimate the critical point $h_c/J\simeq 0.143(3)$ of the mixed ferro-antiferromagnetic three-state quantum Potts model $H={\sum }_i[J(X_i{X}_{i+1}^2+X_i^2{X}_{i+1})-h{R}_i]$, where $X_i$ and $R_i$ are standard three-state Potts spin operators and $J>0$ is the antiferromagnetic coupling parameter. This critical point value gives improved estimates for two Kosterlitz-Thouless transition points in the antiferromagnetic ($\beta <0$) region of the $\Delta$--$\beta$ phase diagram of the three-state quantum chiral clock model, where $\Delta$ and $\beta$ are, respectively, the chirality and coupling parameters in the clock model. These are the transition points ${\beta }_c\simeq -0.143(3)$ at $\Delta =\frac{1}{2}$ between incommensurate and commensurate phases and ${\beta }_c\simeq -7.0(1)$ at $\Delta =0$ between disordered and incommensurate phases. The von Neumann entropy is also used to calculate the central charge $c$ of the underlying conformal field theory in the massless phase $h\le h_c$. The estimate $c\simeq 1$ in this phase is consistent with the known exact value at the particular point $h/J=-1$ corresponding to the purely antiferromagnetic three-state quantum Potts model. The algebraic decay of the Potts spin-spin correlation in the massless phase is used to estimate the continuously varying critical exponent $\eta$.

arXiv comment9 pages, 8 figures, revised version

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• Quantum coherence and spin nematic to nematic quantum phase transitions in biquadratic spin-1 and -2 XY chains with rhombic single-ion anisotropy
• Dynamical phase transition and scaling in the chiral clock Potts chain
• Thermalization at Low Temperatures via Weakly-Damped Multi-Site Baths
• Temperature dependence of energy transport in the ${\mathbb{Z}}_3$ chiral clock model