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本文综述了近年来关于横场伊辛链模型及量子
$E_{8}$ 可积模型研究工作的一系列理论及实验进展. 在针对横场伊辛链的研究工作中, 理论上发现格林艾森比率 (热或磁胀系数与比热之比) 在此模型中独特的奇异量子临界行为, 并实质性地扩展了能涌现横场伊辛链普适类的微观模型. 这些理论进展成功地推进了一系列合作实验在准一维反铁磁材料BaCo 2V 2O 8及SrCo 2V 2O 8中首次实现横场伊辛链普适类. 在针对量子$E_{8}$ 可积模型的研究工作中, 理论上严格计算了该系统的低温局域动力学行为及在零转移动量之时的动力学结构因子, 并在动力学结构因子的连续谱区域得到了级联幂次发散的奇性谱边激发. 这些理论进展在结合详细的量子临界标度行为分析及大规模iTEBD数值计算之后, 成功促成了包括太赫兹谱学测量、非弹性中子散射、核磁共振等系列实验, 在BaCo 2V 2O 8中首次实现量子$E_8$ 可积模型. 量子$E_8$ 可积模型的物理实现为在真实材料中研究量子可积系统的物理开拓了新的边界. 这一系列关于横场伊辛链及量子$E_8$ 可积模型的研究进展为量子不可积系统的研究带来了新的契机, 并将启发凝聚态系统、冷原子系统、统计场论和共形场论等相关方向的研究.This review reports a series of theoretical and experimental progress on researches of the transverse field Ising chain (TFIC) and the quantum E 8integrable model. For the TFIC, on one hand, a unique exotic quantum critical behavior of Grüneisen ratio (a ratio from magnetic or thermal expansion coefficient to specific heat) is theoretically established; on the other hand microscopic models can accommodate the TFIC universality class are substantially expanded. These progresses successfully promote a series of experiments collaborations to first-time realize the TFIC universality class in quasi one-dimensional anti-ferromagnetic material BaCo 2V 2O 8and SrCo 2V 2O 8. For the quantum E 8integrable model, the low temperature local dynamics and the dynamical structure factor with zero transfer momentum of this system are analytically determined, where a cascade of edge singularities with power-law divergences are obtained in the continuum region of the dynamical structure factor. After combining with detailed quantum critical scaling behaviors analysis and large scale iTEBD calculation, it successfully facilitates a series of experiments, including THz spectrum measurements, inelastic neutron scattering and NMR experiments, to realize the quantum E 8integrable model in BaCo 2V 2O 8for the first time. The experimental realization of the quantum E 8integrable model substantially extends the frontiers of studying quantum integrable models in real materials. The series of progress and developments on the TFIC and the quantum E 8integrable model lay down a concrete ground to go beyond quantum integrability, and can inspire studies in condensed matter systems, cold atom systems, statistical field theory and conformal field theory.[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] -
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