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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 |
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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.
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Received: 20 February 2025
Revised: 22 April 2025
Accepted manuscript online: 24 April 2025
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PACS:
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71.10.Fd
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(Lattice fermion models (Hubbard model, etc.))
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74.72.-h
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(Cuprate superconductors)
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64.60.an
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(Finite-size systems)
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05.10.Cc
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(Renormalization group methods)
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| Fund: 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. |
Corresponding Authors:
Mingpu Qin
E-mail: qinmingpu@sjtu.edu.cn
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Cite this article:
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 2025 Chin. Phys. B 34 087105
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