A hybrid method integrating Green's function Monte Carlo and projected entangled pair states

doi:10.1088/1674-1056/ad84c9

中国物理B ›› 2024, Vol. 33 ›› Issue (11): 117504-117504.doi: 10.1088/1674-1056/ad84c9

A hybrid method integrating Green's function Monte Carlo and projected entangled pair states

He-Yu Lin(林赫羽)^1,2, Rong-Qiang He(贺荣强)^1,2,†, Yibin Guo (郭奕斌)^3,‡, and Zhong-Yi Lu(卢仲毅)^1,2,4,§

1 Department of Physics, Renmin University of China, Beijing 100872, China;
2 Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China, Beijing 100872, China;
3 CQTA, Deutsches Elektronen-Synchrotron DESY, Platanenallee 6, 15738 Zeuthen, Germany;
4 Hefei National Laboratory, Hefei 230088, China

收稿日期:2024-07-26 修回日期:2024-09-28 接受日期:2024-10-09 出版日期:2024-11-15 发布日期:2024-11-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11934020) and the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0302402).

A hybrid method integrating Green's function Monte Carlo and projected entangled pair states

He-Yu Lin(林赫羽)^1,2, Rong-Qiang He(贺荣强)^1,2,†, Yibin Guo (郭奕斌)^3,‡, and Zhong-Yi Lu(卢仲毅)^1,2,4,§

1 Department of Physics, Renmin University of China, Beijing 100872, China;
2 Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China, Beijing 100872, China;
3 CQTA, Deutsches Elektronen-Synchrotron DESY, Platanenallee 6, 15738 Zeuthen, Germany;
4 Hefei National Laboratory, Hefei 230088, China

Received:2024-07-26 Revised:2024-09-28 Accepted:2024-10-09 Online:2024-11-15 Published:2024-11-15
Contact: Rong-Qiang He, Yibin Guo, Zhong-Yi Lu E-mail:rqhe@ruc.edu.cn;yibin.guo@desy.de;zlu@ruc.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11934020) and the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0302402).

摘要/Abstract

摘要： This paper introduces a hybrid approach combining Green's function Monte Carlo (GFMC) method with projected entangled pair state (PEPS) ansatz. This hybrid method regards PEPS as a trial state and a guiding wave function in GFMC. By leveraging PEPS's proficiency in capturing quantum state entanglement and GFMC's efficient parallel architecture, the hybrid method is well-suited for the accurate and efficient treatment of frustrated quantum spin systems. As a benchmark, we applied this approach to study the frustrated $J_1$-$J_2$ Heisenberg model on a square lattice with periodic boundary conditions (PBCs). Compared with other numerical methods, our approach integrating PEPS and GFMC shows competitive accuracy in the performance of ground-state energy. This paper provides systematic and comprehensive discussion of the approach of our previous work [Phys. Rev. B 109 235133 (2024)].

关键词: projected entangled pair states, Green's function Monte Carlo, frustrated $J_1$-$J_2$ Heisenberg model

Abstract: This paper introduces a hybrid approach combining Green's function Monte Carlo (GFMC) method with projected entangled pair state (PEPS) ansatz. This hybrid method regards PEPS as a trial state and a guiding wave function in GFMC. By leveraging PEPS's proficiency in capturing quantum state entanglement and GFMC's efficient parallel architecture, the hybrid method is well-suited for the accurate and efficient treatment of frustrated quantum spin systems. As a benchmark, we applied this approach to study the frustrated $J_1$-$J_2$ Heisenberg model on a square lattice with periodic boundary conditions (PBCs). Compared with other numerical methods, our approach integrating PEPS and GFMC shows competitive accuracy in the performance of ground-state energy. This paper provides systematic and comprehensive discussion of the approach of our previous work [Phys. Rev. B 109 235133 (2024)].

Key words: projected entangled pair states, Green's function Monte Carlo, frustrated $J_1$-$J_2$ Heisenberg model

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

75.10.Jm

02.70.Ss (Quantum Monte Carlo methods) 05.10.Cc (Renormalization group methods)

He-Yu Lin(林赫羽), Rong-Qiang He(贺荣强), Yibin Guo (郭奕斌), and Zhong-Yi Lu(卢仲毅). A hybrid method integrating Green's function Monte Carlo and projected entangled pair states[J]. 中国物理B, 2024, 33(11): 117504-117504.

He-Yu Lin(林赫羽), Rong-Qiang He(贺荣强), Yibin Guo (郭奕斌), and Zhong-Yi Lu(卢仲毅). A hybrid method integrating Green's function Monte Carlo and projected entangled pair states[J]. Chin. Phys. B, 2024, 33(11): 117504-117504.

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A hybrid method integrating Green's function Monte Carlo and projected entangled pair states

A hybrid method integrating Green's function Monte Carlo and projected entangled pair states

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