Ground state of electron-doped t-t0-J model on cylinders: An investigation of finite size and boundary condition effects

doi:10.1088/1674-1056/add00b

中国物理B ›› 2025, Vol. 34 ›› Issue (8): 87105-087105.doi: 10.1088/1674-1056/add00b

Ground state of electron-doped t-t0-J model on cylinders: An investigation of finite size and boundary condition effects

Yang Shen(沈阳)¹, Xiangjian Qian(钱湘坚)¹, and Mingpu Qin(秦明普)^1,2,†

1 Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China;
2 Hefei National Laboratory, Hefei 230088, China

收稿日期:2025-02-20 修回日期:2025-04-22 接受日期:2025-04-24 出版日期:2025-07-17 发布日期:2025-07-21
通讯作者: Mingpu Qin E-mail:qinmingpu@sjtu.edu.cn
基金资助:
Project supported by the National Key Research and Development Program of China (Grant No. 2022YFA1405400), the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0301902), the National Natural Science Foundation of China (Grant No. 12274290), and the sponsorship from Yangyang Development Fund.

Ground state of electron-doped t-t0-J model on cylinders: An investigation of finite size and boundary condition effects

Yang Shen(沈阳)¹, Xiangjian Qian(钱湘坚)¹, and Mingpu Qin(秦明普)^1,2,†

1 Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China;
2 Hefei National Laboratory, Hefei 230088, China

Received:2025-02-20 Revised:2025-04-22 Accepted:2025-04-24 Online:2025-07-17 Published:2025-07-21
Contact: Mingpu Qin E-mail:qinmingpu@sjtu.edu.cn
Supported by:
Project supported by the National Key Research and Development Program of China (Grant No. 2022YFA1405400), the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0301902), the National Natural Science Foundation of China (Grant No. 12274290), and the sponsorship from Yangyang Development Fund.

摘要/Abstract

摘要： We perform a comprehensive study of the electron-doped $t$-$t'$-$J$ model on cylinders with density matrix renormalization group (DMRG). We conduct a systematic study on the finite-size and boundary condition effects on $t$-$t'$-$J$ model on cylinders. Periodic and anti-periodic boundary conditions are implemented along the circumference direction, with the system's width extending up to as large as 8 lattice units. We study doping levels of $1/6$, $1/8$, and $1/12$, which represent the most interesting region in the phase diagram of electron-doped cuprates. We find that for width-4 and width-6 systems, the ground state for fixed doping switches between anti-ferromagnetic Neel state and stripe state under different boundary conditions and system widths, indicating the presence of large finite size effect in the $t$-$t'$-$J$ model. We also have a careful analysis of the d-wave pairing correlations which also change quantitatively with boundary conditions and widths of the system. However, the pairing correlations are enhanced when the system becomes wider for all dopings, suggesting the existence of possible long-range superconducting order in the thermodynamic limit. The width-8 results are found to be dependent on the starting state in the DMRG calculation for the kept states we can reach. For the width-8 system, only Neel (stripe) state can be stabilized in DMRG calculation for $1/12$ ($1/6$) doping, while both stripe and Neel states are stable in the DMRG sweep for $1/8$ doping, regardless of the boundary conditions. These results indicate that $1/8$ doping is likely to lie on the boundary of a phase transition between the Neel phase with lower doping and the stripe phase with higher doping, consistent with the previous study. The sensitivity of the ground state on boundary conditions and size observed for narrow systems is similar to that found in the $t'$-Hubbard model, where the $t'$ term introduces frustration and makes the stripe state fragile. The study of different boundary conditions provides a useful tool to check the finite size effect in the future DMRG calculations.

关键词: $t$-$t'$-$J$ model, finite-size effect, boundary conditions, DMRG, superconductivity

Abstract: We perform a comprehensive study of the electron-doped $t$-$t'$-$J$ model on cylinders with density matrix renormalization group (DMRG). We conduct a systematic study on the finite-size and boundary condition effects on $t$-$t'$-$J$ model on cylinders. Periodic and anti-periodic boundary conditions are implemented along the circumference direction, with the system's width extending up to as large as 8 lattice units. We study doping levels of $1/6$, $1/8$, and $1/12$, which represent the most interesting region in the phase diagram of electron-doped cuprates. We find that for width-4 and width-6 systems, the ground state for fixed doping switches between anti-ferromagnetic Neel state and stripe state under different boundary conditions and system widths, indicating the presence of large finite size effect in the $t$-$t'$-$J$ model. We also have a careful analysis of the d-wave pairing correlations which also change quantitatively with boundary conditions and widths of the system. However, the pairing correlations are enhanced when the system becomes wider for all dopings, suggesting the existence of possible long-range superconducting order in the thermodynamic limit. The width-8 results are found to be dependent on the starting state in the DMRG calculation for the kept states we can reach. For the width-8 system, only Neel (stripe) state can be stabilized in DMRG calculation for $1/12$ ($1/6$) doping, while both stripe and Neel states are stable in the DMRG sweep for $1/8$ doping, regardless of the boundary conditions. These results indicate that $1/8$ doping is likely to lie on the boundary of a phase transition between the Neel phase with lower doping and the stripe phase with higher doping, consistent with the previous study. The sensitivity of the ground state on boundary conditions and size observed for narrow systems is similar to that found in the $t'$-Hubbard model, where the $t'$ term introduces frustration and makes the stripe state fragile. The study of different boundary conditions provides a useful tool to check the finite size effect in the future DMRG calculations.

Key words: $t$-$t'$-$J$ model, finite-size effect, boundary conditions, DMRG, superconductivity

中图分类号: (Lattice fermion models (Hubbard model, etc.))

71.10.Fd

74.72.-h (Cuprate superconductors) 64.60.an (Finite-size systems) 05.10.Cc (Renormalization group methods)

Yang Shen(沈阳), Xiangjian Qian(钱湘坚), and Mingpu Qin(秦明普). Ground state of electron-doped t-t0-J model on cylinders: An investigation of finite size and boundary condition effects[J]. 中国物理B, 2025, 34(8): 87105-087105.

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Ground state of electron-doped t-t0-J model on cylinders: An investigation of finite size and boundary condition effects

Ground state of electron-doped t-t0-J model on cylinders: An investigation of finite size and boundary condition effects

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