Off-diagonal approach to the exact solution of quantum integrable systems
Yi Qiao(乔艺)1, Junpeng Cao(曹俊鹏)2,3,4,5,†, Wen-Li Yang(杨文力)1,5,6,‡, Kangjie Shi(石康杰)1, and Yupeng Wang(王玉鹏)2,5
1 Institute of Modern Physics, Northwest University, Xi'an 710127, China; 2 Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China; 3 School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China; 4 Songshan Lake Materials Laboratory, Dongguan 523808, China; 5 Peng Huanwu Center for Fundamental Theory, Xi'an 710127, China; 6 Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China
Abstract We investigate the t-W scheme for the anti-ferromagnetic XXX 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 operator (see Eqs. (10) and (70)) in the thermodynamic limit. We find that the ratio of the quantum determinant with the eigenvalue of 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.
Fund: Project supported by the National Key R&D Program of China (Grant No. 2021YFA1402104), the National Natural Science Foundation of China (Grant Nos. 12247103, 12305005, 12074410, 11934015, and 11975183), Major Basic Research Program of Natural Science of Shaanxi Province (Grant Nos. 2021JCW-19 and 2017ZDJC-32), Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB33000000), Young Talent Fund of Xi’an Association for Science and Technology (Grant No. 959202313086), and Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant No. 22JSZ005).
Corresponding Authors:
Junpeng Cao, Wen-Li Yang
E-mail: junpengcao@iphy.ac.cn;wlyang@nwu.edu.cn
Cite this article:
Yi Qiao(乔艺), Junpeng Cao(曹俊鹏), Wen-Li Yang(杨文力), Kangjie Shi(石康杰), and Yupeng Wang(王玉鹏) Off-diagonal approach to the exact solution of quantum integrable systems 2023 Chin. Phys. B 32 117504
[1] Yang C N 1967 Phys. Rev. Lett.19 1312 [2] Baxter R J 1982 Exactly Solved Models in Statistical Mechanics (London:Academic Press) [3] Lax P D 1968 Commun. Pure Appl. Math.21 467 [4] Onsager L 1944 Phys. Rev.65 117 [5] Faddeev L D and Takhtajan L A 1981 Phys. Lett. A85 375 [6] Lieb E H and Liniger W 1963 Phys. Rev.130 1605 [7] Lieb E H 1963 Phys. Rev.130 1616 [8] Lieb E H and Wu F Y 1968 Phys. Rev. Lett.20 1445 [9] Gaudin M 1967 Phys. Lett. A24 55 [10] Guan X W, Batchelor M T and Lee C 2013 Rev. Mod. Phys.85 1633 [11] Beisert N, Ahn C, et al. 2012 Lett. Math. Phys.99 3 [12] Chen B, Wang X J and Wu Y S 2004 Journal of High Energy Physics2004 029 [13] Bethe H 1931 Zeitschrift für Physik 71 205 [14] Baxter R J 1971 Phys. Rev. Lett.26 832 [15] Baxter R J 1971 Phys. Rev. Lett.26 834 [16] Takhtadzhan L A and Faddeev L D 1979 Rush. Math. Surv.34 11 [17] Sklyanin E K, Takhtajan L A and Faddeev L D 1980 Theor. Math. Phys.40 688 [18] Faddeev L D 1980 Sov. Sci. Rev. Math. C1 107 [19] Sklyanin E K 1982 J. Sov. Math.19 1546 [20] Takhtadzhan L A 1985 Lect. Notes Phys.242 175 [21] Cao J, Lin H Q, Shi K J and Wang Y 2003 Nucl. Phys. B663 487 [22] Yung C M and Batchelor M T 1995 Nucl. Phys. B446 461 [23] Nepomechie R I 2002 Nucl. Phys. B662 615 [24] Baseilhac P 2006 Nucl. Phys. B754 309 [25] Baseilhac P and Koizumi K 2007 J. Stat. Mech. 2007 P09006 [26] Niekamp S, Wirth T and Frahm H 2009 J. Phys. A:Math. Gen.42 195008 [27] Niccoli G 2013 Nucl. Phys. B870 397 [28] Belliard S 2015 Nucl. Phys. B892 1 [29] Belliard S and Pimenta R A 2015 Nucl. Phys. B894 527 [30] Cao J, Yang W L, Shi K and Wang Y 2013 Phys. Rev. Lett.111 137201 [31] Wang Y, Yang W L, Cao J and Shi K 2015 Off-Diagonal Bethe Ansatz for Exactly Solvable Models (Berlin:Springer) [32] Yang C N and Yang C P 1969 J. Math. Phys.10 1115 [33] Gaudin M 1971 Phys. Rev. Lett.26 1301 [34] Takahashi M 1971 Progress Theoret. Phys.46 401 [35] Takahashi M 1972 Progress Theoret. Phys.47 69 [36] Takahashi M 1974 Progress Theoret. Phys.52 103 [37] Qiao Y, Sun P, Cao J, Yang W L, Shi K and Wang Y 2020 Phys. Rev. B102 085115 [38] Qiao Y, Cao J, Yang W L, Shi K and Wang Y 2021 Phys. Rev. B 103 L220401 [39] Le X, Qiao Y, Cao J, Yang W L, Shi K and Wang Y 2021 Journal of High Energy Physics2021 044 [40] Lu P, Qiao Y, Cao J, Yang W L, Shi K and Wang Y 2021 Journal of High Energy Physics2021 133 [41] Yi Y, Wang J, Qiao Y, Cao J and Yang W L 2021 Results Phys.29 104721 [42] Yi Y, Qiao Y, Cao J and Yang W L 2022 Nucl. Phys. B977 115732 [43] Wang W, Qiao Y, Cao J, Liu W M and Liu R H 2022 Nucl. Phys. B975 115663 [44] Wang W, Qiao Y, Liu R H, Liu W M and Cao J 2023 Phys. Rev. D107 056005 [45] Sun P, Yang J, Qiao Y, Cao J and Yang W L 2022 Nucl. Phys. B974 115626 [46] Li G L, Qiao Y, Cao J, Yang W L, Shi K and Wang Y 2022 Nucl. Phys. B984 115946 [47] Stroganov Y G 1979 Phys. Lett. A74 116 [48] Shankar R 1981 Phys. Rev. Lett.47 1177 [49] Kulish P P, Reshetikhin N Yu and Sklyanin E K 1981 Lett. Math. Phys.5 393 [50] Kirillov A N and Reshetikhin N Yu 1986 J. Sov. Math.35 2627 [51] Cao J, Yang W L, Shi K J and Wang Y 2014 Nucl. Phys. B886 185 [52] Hao K, Cao J, Li G L, Yang W L, Shi K and Wang Y 2014 Journal of High Energy Physics2014 128
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