Exact ground state properties of the t-j model with open boundary conditions

doi:10.1088/1674-1056/ae37fa

中国物理B ›› 2026, Vol. 35 ›› Issue (5): 57501-057501.doi: 10.1088/1674-1056/ae37fa

Exact ground state properties of the t-j model with open boundary conditions

Pei Sun(孙佩)^1,2, Yuanyuan Lei(雷瑗瑗)¹, Xiaotian Xu(许小甜)^2,3,4,†, Junpeng Cao(曹俊鹏)^4,5,6,‡, Tao Yang(杨涛)^2,3,4, and Wen-Li Yang(杨文力)^1,2,3,4

1 School of Physics, Northwest University, Xi'an 710127, China;
2 Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China;
3 Institute of Modern Physics, Northwest University, Xi'an 710127, China;
4 Peng Huanwu Center for Fundamental Theory, Xi'an 710127, China;
5 Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;
6 School of Physical Science, University of Chinese Academy of Sciences, Beijing 100049, China

收稿日期:2025-11-10 修回日期:2026-01-13 接受日期:2026-01-14 发布日期:2026-04-24
通讯作者: Xiaotian Xu, Junpeng Cao E-mail:xtxu@nwu.edu.cn;junpengcao@iphy.ac.cn
基金资助:
We acknowledge the financial supports from the National Key R&D Program of China (Grant No. 2021YFA1402104), the National Natural Science Foundation of China (Grant Nos. 12205235, 12105221, 12434006, 12247103, 12247179, 12175180, and 12547107), China Postdoctoral Science Foundation (Grant No. 2022M712580), Scientific Research Program Funded by Education Department of Shaanxi Provincial Government (Grant No. 22JK0577), Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant No. 23JS0008), the Major Basic Research Program of Natural Science of Shaanxi Province (Grant Nos. 2021JCW-19 and 2017ZDJC-32).

Exact ground state properties of the t-j model with open boundary conditions

Pei Sun(孙佩)^1,2, Yuanyuan Lei(雷瑗瑗)¹, Xiaotian Xu(许小甜)^2,3,4,†, Junpeng Cao(曹俊鹏)^4,5,6,‡, Tao Yang(杨涛)^2,3,4, and Wen-Li Yang(杨文力)^1,2,3,4

1 School of Physics, Northwest University, Xi'an 710127, China;
2 Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China;
3 Institute of Modern Physics, Northwest University, Xi'an 710127, China;
4 Peng Huanwu Center for Fundamental Theory, Xi'an 710127, China;
5 Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;
6 School of Physical Science, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2025-11-10 Revised:2026-01-13 Accepted:2026-01-14 Published:2026-04-24
Contact: Xiaotian Xu, Junpeng Cao E-mail:xtxu@nwu.edu.cn;junpengcao@iphy.ac.cn
Supported by:
We acknowledge the financial supports from the National Key R&D Program of China (Grant No. 2021YFA1402104), the National Natural Science Foundation of China (Grant Nos. 12205235, 12105221, 12434006, 12247103, 12247179, 12175180, and 12547107), China Postdoctoral Science Foundation (Grant No. 2022M712580), Scientific Research Program Funded by Education Department of Shaanxi Provincial Government (Grant No. 22JK0577), Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant No. 23JS0008), the Major Basic Research Program of Natural Science of Shaanxi Province (Grant Nos. 2021JCW-19 and 2017ZDJC-32).

摘要/Abstract

摘要： We develop a new method to study the ground state energy of the one-dimensional supersymmetric t-J model with open boundary conditions. The eigenvalues of the nested transfer matrix are characterized by the zero roots of corresponding polynomials instead of the T-Q relation and Bethe roots. The distribution of zero roots at the ground state is studied. We find that the zero roots form two-string pairs, finite pure real and pure imaginary boundary strings. Based on the distribution of zero roots, we obtain the ground state energy of the system in the thermodynamic limit.

关键词: quantum spin chains, zero roots, ground state energy

Abstract: We develop a new method to study the ground state energy of the one-dimensional supersymmetric t-J model with open boundary conditions. The eigenvalues of the nested transfer matrix are characterized by the zero roots of corresponding polynomials instead of the T-Q relation and Bethe roots. The distribution of zero roots at the ground state is studied. We find that the zero roots form two-string pairs, finite pure real and pure imaginary boundary strings. Based on the distribution of zero roots, we obtain the ground state energy of the system in the thermodynamic limit.

Key words: quantum spin chains, zero roots, ground state energy

中图分类号: (Spin chain models)

75.10.Pq

02.30.Ik (Integrable systems) 71.10.Pm (Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.))

Pei Sun(孙佩), Yuanyuan Lei(雷瑗瑗), Xiaotian Xu(许小甜), Junpeng Cao(曹俊鹏), Tao Yang(杨涛), and Wen-Li Yang(杨文力). Exact ground state properties of the t-j model with open boundary conditions[J]. 中国物理B, 2026, 35(5): 57501-057501.

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Exact ground state properties of the t-j model with open boundary conditions

Exact ground state properties of the t-j model with open boundary conditions

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