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Multipartite nonlocality and topological quantum phase transitions in a spin-1/2 XXZ model on a zigzag lattice

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Abstract

Multipartite nonlocality is a measure of multipartite quantum correlations. In this paper, we investigate multipartite nonlocality in a spin-\(\frac{1}{2}\) XXZ model on a one-dimensional (1D) infinite-size zigzag lattice. In the ground states, the model can undergo topological-type quantum phase transitions (QPTs) between a singlet dimer (SD) phase and an even-parity dimer (ED) phase. Two nonlocality measures \({\mathcal {S}}_o\) (defined on the odd-bond subchains) and \({\mathcal {S}}_e\) (defined on the even-bond subchains) are used to characterize these topological-type QPTs. Both measures show some kinds of singularity (i.e., a discontinuity of the measure or the divergence of its derivative) in the QPTs. Furthermore, in the SD phase and in the vicinity of critical regions, \({\mathcal {S}}_o\) is relatively large, and in most regions of the ED phase, \({\mathcal {S}}_o\) is nearly zero. Thus, similar to order parameters in traditional phase transitions, \({\mathcal {S}}_o\) is an effective physical quantity to characterize these topological-type QPTs. Scaling behavior of the nonlocality measure is also discussed.

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Data Availability Statement

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Notes

  1. According to Eq. (7), if \(\text {Tr}( {\hat{\rho }}_n{\hat{S}}_{n} )\) achieves its maximum value for some \(\underline{{\varvec{a}}}\), the same maximum value can be achieved by \(\text {Tr}( {\hat{\rho }}_n{\hat{S}}'_{n} )\) for \(\underline{{\varvec{a}}}'\). Generally speaking, we shall have \(\underline{{\varvec{a}}}\ne \underline{{\varvec{a}}}'\), and thus, \(\text {Tr}( {\hat{\rho }}_n{\hat{S}}_{n} )\) and \(\text {Tr}( {\hat{\rho }}_n{\hat{S}}'_{n} )\) could not achieve this maximum at the same time.

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Acknowledgements

We would like to thank Professor Ian McCulloch for his great software Matrix-Product Toolkit. The research was supported by the National Natural Science Foundation of China (Grant Nos. 11675124 and 12105210).

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  1. School of Electrical and Electronic Engineering, Wuhan Polytechnic University, Wuhan, 430000, China

    Hui-Xin Wen, Zhao-Yu Sun, Hong-Guang Cheng, Duo Zhang & Yu-Ying Wu

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Correspondence to Zhao-Yu Sun.

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Wen, HX., Sun, ZY., Cheng, HG. et al. Multipartite nonlocality and topological quantum phase transitions in a spin-1/2 XXZ model on a zigzag lattice. Eur. Phys. J. B 95, 148 (2022). https://doi.org/10.1140/epjb/s10051-022-00416-8

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