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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 |
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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)].
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Received: 26 July 2024
Revised: 28 September 2024
Accepted manuscript online: 09 October 2024
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PACS:
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75.10.Jm
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(Quantized spin models, including quantum spin frustration)
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02.70.Ss
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(Quantum Monte Carlo methods)
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05.10.Cc
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(Renormalization group methods)
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| Fund: 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). |
Corresponding Authors:
Rong-Qiang He, Yibin Guo, Zhong-Yi Lu
E-mail: rqhe@ruc.edu.cn;yibin.guo@desy.de;zlu@ruc.edu.cn
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Cite this article:
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 2024 Chin. Phys. B 33 117504
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