Accurate quantum critical points and nonlocal string order parameters in the spin tetrahedron chain

doi:10.1088/1674-1056/ae0c7c

中国物理B ›› 2025, Vol. 34 ›› Issue (11): 117502-117502.doi: 10.1088/1674-1056/ae0c7c

Accurate quantum critical points and nonlocal string order parameters in the spin tetrahedron chain

Zhi-Yong Wu(吴志勇), Kai-Ming Zhang(张凯铭), and Li-Xiang Cen(岑理相)†

Center of Theoretical Physics, College of Physics, Sichuan University, Chengdu 610065, China

收稿日期:2025-07-16 修回日期:2025-09-25 接受日期:2025-09-29 发布日期:2025-10-30
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 12471443).

Accurate quantum critical points and nonlocal string order parameters in the spin tetrahedron chain

Zhi-Yong Wu(吴志勇), Kai-Ming Zhang(张凯铭), and Li-Xiang Cen(岑理相)†

Center of Theoretical Physics, College of Physics, Sichuan University, Chengdu 610065, China

Received:2025-07-16 Revised:2025-09-25 Accepted:2025-09-29 Published:2025-10-30
Contact: Li-Xiang Cen E-mail:lixiangcen@scu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 12471443).

摘要/Abstract

摘要： The ground-state phase diagram and nonlocal order parameters of an infinite spin tetrahedron chain with inhomogeneous exchange couplings are investigated. It is shown that the phase boundaries of the three phases in the model can be determined precisely, in line with the precision of its ground-state energy. Numerical calculations using the regularized time-evolving block decimation (rTEBD) algorithm yield the locations of the two quantum critical points with an accuracy about 10 digits. Moreover, we explain how to calculate the parity-associated string order for the output wave function obtained through the rTEBD procedure, which not only reveals the presence of long-range correlations but also identifies the symmetry-protected topological order within the intermediate phase of the model.

关键词: quantum phase transition, time-evolving block decimation algorithm, string order

Abstract: The ground-state phase diagram and nonlocal order parameters of an infinite spin tetrahedron chain with inhomogeneous exchange couplings are investigated. It is shown that the phase boundaries of the three phases in the model can be determined precisely, in line with the precision of its ground-state energy. Numerical calculations using the regularized time-evolving block decimation (rTEBD) algorithm yield the locations of the two quantum critical points with an accuracy about 10 digits. Moreover, we explain how to calculate the parity-associated string order for the output wave function obtained through the rTEBD procedure, which not only reveals the presence of long-range correlations but also identifies the symmetry-protected topological order within the intermediate phase of the model.

Key words: quantum phase transition, time-evolving block decimation algorithm, string order

中图分类号: (Quantized spin models, including quantum spin frustration)

75.10.Jm

75.10.Pq (Spin chain models) 64.70.Tg (Quantum phase transitions)

Zhi-Yong Wu(吴志勇), Kai-Ming Zhang(张凯铭), and Li-Xiang Cen(岑理相). Accurate quantum critical points and nonlocal string order parameters in the spin tetrahedron chain[J]. 中国物理B, 2025, 34(11): 117502-117502.

Zhi-Yong Wu(吴志勇), Kai-Ming Zhang(张凯铭), and Li-Xiang Cen(岑理相). Accurate quantum critical points and nonlocal string order parameters in the spin tetrahedron chain[J]. Chin. Phys. B, 2025, 34(11): 117502-117502.

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Accurate quantum critical points and nonlocal string order parameters in the spin tetrahedron chain

Accurate quantum critical points and nonlocal string order parameters in the spin tetrahedron chain

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