Quantum criticality of a ${\mathbb{Z}}_3$ symmetric spin chain with long-range interactions

Abstract

Based on large-scale density matrix renormalization group techniques, we investigate the critical behaviors of quantum three-state Potts chains with long-range interactions. Using fidelity susceptibility as an indicator, we obtain a complete phase diagram of the system. The results show that as the long-range interaction power $\alpha$ increases, the critical points $f_c^{\ast }$ shift towards lower values. In addition, the critical threshold ${\alpha }_c(\approx 1.43$) of the long-range interaction power is obtained for the first time by a non-perturbative numerical method. This indicates that the critical behavior of the system can be naturally divided into two distinct universality classes, namely the long-range ($α\textless α_c$) and short-range ($α\textgreater α_c$) universality classes, qualitatively consistent with the classical ${\varphi }^3$ effective field theory. This work provides a useful reference for further research on phase transitions in quantum spin chains with long-range interaction.

5+7 pages. Any comments or suggestions are welcome !

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• Emergent self-duality in long range critical spin chain: from deconfined criticality to first order transition
• Dynamical phase transition and scaling in the chiral clock Potts chain
• Critical quantum geometric tensors of parametrically-driven nonlinear resonators