Abstract
This review reports a series of theoretical and experimental progress on researches of the transverse field Ising chain (TFIC) and the quantum <i>E</i><sub>8</sub> integrable 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<sub>2</sub>V<sub>2</sub>O<sub>8</sub> and SrCo<sub>2</sub>V<sub>2</sub>O<sub>8</sub>. For the quantum <i>E</i><sub>8</sub> integrable 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 <i>E</i><sub>8</sub> integrable model in BaCo<sub>2</sub>V<sub>2</sub>O<sub>8</sub> for the first time. The experimental realization of the quantum <i>E</i><sub>8</sub> integrable 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 <i>E</i><sub>8</sub> integrable 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.
Highlights
The two tilted dotted lines illustrate the crossovers of different disorder phases in low temperature region, while the dotted line above shows a crossover from quantum critical region to classical region
图 4 (a) CoO6 八面体的结构 ; (b) CoO6 四周期螺旋链的单元结构及局域坐标系 ξψζ ; (c) 局域坐标系 ξψζ 与实验室坐标系 XYZ 的关系
Summary
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 BaCo2V2O8 中首次实现量子 E8 可积模型. 在量子临界点 (quantum critical point, QCP) 附近, 强烈的量子 涨落往往会涌现出奇异的量子临界行为 [2−7]. 一普适类的模型在 QCP 附近也会展示出非常一致 的物理, 如标度规律、关联行为及动力学激发等 [1]. 比如, QCP 处的 TFIC 模型在纵向磁场的微扰下 会涌现出量子 E8 可积模型 [23,24,27−31]. 近年来, 吴建达及其合作者在理论和实验的共 同努力下, 在强关联材料 BaCo2V2O8 (BCVO) 和 SrCo2V2O8 (SCVO) 中首次成功实现 TFIC 模型 的普适类 [22,32−35], 并在 BCVO 材料中首次实现量 子 E8 可积模型 [30,36,37].
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