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Exact surface energy and elementary excitations of the XXX spin-1/2 chain with arbitrary non-diagonal boundary fields

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Chinese Physics B 2023年第1期32卷 483-492页

作者：董家生路鹏程孙佩乔艺曹俊鹏郝昆杨文力 Institute of Modern Physics Northwest UniversityXi'an 710127China Beijing National Laboratory for Condensed Matter Physics Institute of PhysicsChinese Academy of SciencesBeijing 100190China School of Physics Northwest UniversityXi'an 710127China Peng Huanwu Center for Fundamental Theory Xi'an 710127China Shaanxi Key Laboratory for Theoretical Physics Frontiers Xi'an 710127China School of Physical Sciences University of Chinese Academy of SciencesBeijing 100049China Songshan Lake Materials Laboratory Dongguan 523808China

We study the physical properties of the XXX spin-1/2 chain with arbitrary non-diagonal boundary fields. By using a combination of numerical analysis and analytical method, we obtain the surface energy and elementary excitations of the model. It shows that the contributions of the two boundary fields to the surface energy are additive. We also find that there exists a kind of excitations related to the boundary string.

关键词： quantum spin chain integrable systems Bethe ansatz

Off-diagonal approach to the exact solution of quantum integrable systems

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Chinese Physics B 2023年第11期32卷 105-115页

作者：乔艺曹俊鹏杨文力石康杰王玉鹏 Institute of Modern Physics Northwest UniversityXi'an 710127China Beijing National Laboratory for Condensed Matter Physics Institute of PhysicsChinese Academy of SciencesBeijing 100190China School of Physical Sciences University of Chinese Academy of SciencesBeijing 100049China Songshan Lake Materials Laboratory Dongguan 523808China Peng Huanwu Center for Fundamental Theory Xi'an 710127China Shaanxi Key Laboratory for Theoretical Physics Frontiers Xi'an 710127China

We investigate the t–W scheme for the anti-ferromagnetic X X X spin chain under both periodic and open boundary conditions. We propose a new parametrization of the eigenvalues of the transfer matrix. Based on it, we obtain the exact solution of the system. By analyzing the distribution of zero roots at the ground state, we obtain the explicit expressions of the eigenfunctions of the transfer matrix and the associated W operator(see Eqs.(10) and(70)) in the thermodynamic limit. We find that the ratio of the quantum determinant with the eigenvalue of W operator for the ground state exhibits exponential decay behavior. Thus this fact ensures that the so-called inversion relation(the t–W relation without the W-term) can be used to study the ground state properties of quantum integrable systems with/without U(1)-symmetry in the thermodynamic limit.

关键词： quantum spin chain bethe ansatz Yang-Baxter equation

Exact solution of an anisotropic J_(1)–J_(2)model with the Dzyloshinsky–Moriya interactions at boundaries

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Communications in Theoretical Physics 2021年第7期73卷 1-6页

作者： Yusong Cao Jian Wang Yi Qiao Junpeng Cao Wen-Li Yang Beijing National Laboratory for Condensed Matter Physics Institute of PhysicsChinese Academy of SciencesBeijing 100190China School of Physical Sciences University of Chinese Academy of SciencesBeijingChina Songshan Lake Materials Laboratory DongguanGuangdong 523808China Peng Huanwu Center for Fundamental Theory Xian 710127China Institute of Modern Physics Northwest UniversityXian 710127China Shaanxi Key Laboratory for Theoretical Physics Frontiers Xian 710127China School of Physics Northwest UniversityXian 710127China

We propose a method to construct new quantum integrable *** an example,we construct an integrable anisotropic quantum spin chain which includes the nearest-neighbor,next-nearestneighbor and chiral three-spin *** is shown that the boundary fields can enhance the anisotropy of the first and last bonds,and can induce the Dzyloshinsky–Moriya interactions along the z-direction at the *** using the algebraic Bethe ansatz,we obtain the exact solution of the *** energy spectrum of the system and the associated Bethe ansatz equations are given *** method provided in this paper is universal and can be applied to constructing other exactly solvable models with certain interesting interactions.

关键词： quantum spin chain Bethe ansatz Yang–Baxter equation reflection equation

Lax pair formulation for the open boundary Osp(1|2)spin chain

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Communications in Theoretical Physics 2022年第11期74卷 65-76页

作者： Xiaoyu Zhang Kun Hao Institute of Modern Physics Northwest UniversityXi'an 710127China Peng Huanwu Center for Fundamental Theory Xi'an 710127China

Based on the Lax pair formulation,we study the integrable conditions of the Osp(1|2)spin chain with open *** consider both the non-graded and graded versions of the Osp(1|2)*** Lax pair operators M_(±)for the boundaries can be induced by the Lax operator M_(j)for the bulk of the *** correspond to the reflection equations(RE)and the Yang-Baxter equation,*** further calculate the boundary K-matrices for both the non-graded and graded versions of the model with open *** double row monodromy matrix and transfer matrix of the spin chain have also been *** K-matrices obtained from the Lax pair formulation are consistent with those from Sklyanin’s *** construction is another way to prove the quantum integrability of the Osp(1|2)*** find that the Lax pair formulation has advantages in dealing with the boundary terms of the supersymmetric model.

关键词： Bethe Ansatz lattice integrable models quantum spin chain supersymmetry algebra