Quantum criticality of a Z3-symmetric spin chain with long-range interactions

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 fc* shift towards lower values. In addition, the critical threshold alpha c(approximate to 1.43) of the long-range interaction power is obtained for the first time by a nonperturbative numerical method. This indicates that the critical behavior of the system can be naturally divided into two distinct universality classes, namely the long-range (alpha < alpha c) and short-range (alpha > alpha c) universality classes, qualitatively consistent with the classical 03 effective field theory. This work provides a useful reference for further research on phase transitions in quantum spin chains with long-range interaction.

Automated summary

Based on large-scale density matrix renormalization group techniques, this study investigates the critical behaviors of quantum three-state Potts chains with long-range interactions. Using fidelity susceptibility as an indicator, a complete phase diagram of the system is obtained. The results reveal that as the long-range interaction power increases, the critical points shift towards lower values, and a critical threshold for the long-range interaction power is determined for the first time. This work provides important insights into phase transitions in quantum spin chains with long-range interactions.