Universal order-parameter and quantum phase transition for two-dimensional q-state quantum Potts model

doi:10.1088/1674-1056/ac4bd1

中国物理B ›› 2022, Vol. 31 ›› Issue (7): 70502-070502.doi: 10.1088/1674-1056/ac4bd1

Universal order-parameter and quantum phase transition for two-dimensional q-state quantum Potts model

Yan-Wei Dai(代艳伟)^1,†, Sheng-Hao Li(李生好)^1,2, and Xi-Hao Chen(陈西浩)^1,3

1 Centre for Modern Physics and Department of Physics, Chongqing University, Chongqing 400044, China;
2 Chongqing Vocational Institute of Engineering, Chongqing 402260, China;
3 Research Institute for New Materials and Technology, Chongqing University of Arts and Sciences, Chongqing 400000, China

收稿日期:2021-10-07 修回日期:2021-12-02 接受日期:2022-01-17 出版日期:2022-06-09 发布日期:2022-06-09
通讯作者: Yan-Wei Dai E-mail:daiyanwei1027@126.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11805285), Natural Science Foundation of Chongqing of China (Grant No. cstc2020jcyjmsxmX0034), and the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJQN 201900703).

Universal order-parameter and quantum phase transition for two-dimensional q-state quantum Potts model

Yan-Wei Dai(代艳伟)^1,†, Sheng-Hao Li(李生好)^1,2, and Xi-Hao Chen(陈西浩)^1,3

1 Centre for Modern Physics and Department of Physics, Chongqing University, Chongqing 400044, China;
2 Chongqing Vocational Institute of Engineering, Chongqing 402260, China;
3 Research Institute for New Materials and Technology, Chongqing University of Arts and Sciences, Chongqing 400000, China

Received:2021-10-07 Revised:2021-12-02 Accepted:2022-01-17 Online:2022-06-09 Published:2022-06-09
Contact: Yan-Wei Dai E-mail:daiyanwei1027@126.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11805285), Natural Science Foundation of Chongqing of China (Grant No. cstc2020jcyjmsxmX0034), and the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJQN 201900703).

摘要/Abstract

摘要： We investigate quantum phase transitions for q-state quantum Potts models (q=2,3,4) on a square lattice and for the Ising model on a honeycomb lattice by using the infinite projected entangled-pair state algorithm with a simplified updating scheme. We extend the universal order parameter to a two-dimensional lattice system, which allows us to explore quantum phase transitions with symmetry-broken order for any translation-invariant quantum lattice system of the symmetry group G. The universal order parameter is zero in the symmetric phase, and it ranges from zero to unity in the symmetry-broken phase. The ground-state fidelity per lattice site is computed, and a pinch point is identified on the fidelity surface near the critical point. The results offer another example highlighting the connection between (i) critical points for a quantum many-body system undergoing a quantum phase-transition and (ii) pinch points on a fidelity surface. In addition, we discuss three quantum coherence measures: the quantum Jensen-Shannon divergence, the relative entropy of coherence, and the l₁ norm of coherence, which are singular at the critical point, thereby identifying quantum phase transitions.

关键词: quantum phase transitions, universal order parameter, fidelity

Abstract: We investigate quantum phase transitions for q-state quantum Potts models (q=2,3,4) on a square lattice and for the Ising model on a honeycomb lattice by using the infinite projected entangled-pair state algorithm with a simplified updating scheme. We extend the universal order parameter to a two-dimensional lattice system, which allows us to explore quantum phase transitions with symmetry-broken order for any translation-invariant quantum lattice system of the symmetry group G. The universal order parameter is zero in the symmetric phase, and it ranges from zero to unity in the symmetry-broken phase. The ground-state fidelity per lattice site is computed, and a pinch point is identified on the fidelity surface near the critical point. The results offer another example highlighting the connection between (i) critical points for a quantum many-body system undergoing a quantum phase-transition and (ii) pinch points on a fidelity surface. In addition, we discuss three quantum coherence measures: the quantum Jensen-Shannon divergence, the relative entropy of coherence, and the l₁ norm of coherence, which are singular at the critical point, thereby identifying quantum phase transitions.

Key words: quantum phase transitions, universal order parameter, fidelity

中图分类号: (Quantum phase transitions)

05.30.Rt

75.40.Cx (Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.)) 03.67.-a (Quantum information)

Yan-Wei Dai(代艳伟), Sheng-Hao Li(李生好), and Xi-Hao Chen(陈西浩). Universal order-parameter and quantum phase transition for two-dimensional q-state quantum Potts model[J]. 中国物理B, 2022, 31(7): 70502-070502.

Yan-Wei Dai(代艳伟), Sheng-Hao Li(李生好), and Xi-Hao Chen(陈西浩). Universal order-parameter and quantum phase transition for two-dimensional q-state quantum Potts model[J]. Chin. Phys. B, 2022, 31(7): 70502-070502.

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Universal order-parameter and quantum phase transition for two-dimensional q-state quantum Potts model

Universal order-parameter and quantum phase transition for two-dimensional q-state quantum Potts model

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