横场自旋模型中的量子相变：从统计物理到量子信息
Quantum phase transitions in transverse field spin models: from statistical physics to quantum information
摘要：
本文以自旋为1/2的横场伊辛模型和XY模型为例，综述了自旋系统在横场磁场中的量子相变。首先概述了量子相变，我们介绍了一些模型哈密顿量。我们提供了精确的解决方案，在一个空间维度连接他们的共形场理论研究。我们还讨论了Kitaev模型和其他一些精确可解的自旋系统。研究量子相变的存在下淬火的随机性和挫折的相互作用的详细介绍。我们讨论新的现象，如格里菲斯-麦考伊奇点。然后，我们转向最近的主题，如信息理论措施的量子相变在这些模型中，如并发，纠缠熵，量子不和谐和量子保真度。然后，我们专注于非平衡动力学的各种横向场系统的量子临界点和线。在提到快速淬火研究后，我们详细讨论了缓慢的动力学和讨论Kibble-Zurek缩放的缺陷密度淬火后，跨临界点和其修改淬火跨临界线，无间隙区域和多临界点。主题，如不同的淬火方案的作用，局部淬火，淬火模型与随机相互作用和淬火耦合到一个热浴的自旋链被触及。非平衡动力学和量子信息理论措施之间的联系，在一定程度上。我们表明Kibble-Zurek标度和绝热演化的状态之间的连接，以及绝热动力学作为量子优化技术称为量子退火的工具的应用。最后一节是致力于详细讨论最近的横向伊辛类系统的实验研究。
英文摘要：
We review quantum phase transitions of spin systems in transverse magnetic fields taking the examples of the spin-1/2 Ising and XY models in a transverse field. Beginning with an overview of quantum phase transitions, we introduce a number of model Hamiltonians. We provide exact solutions in one spatial dimension connecting them to conformal field theoretical studies. We also discuss Kitaev models and some other exactly solvable spin systems. Studies of quantum phase transitions in the presence of quenched randomness and with frustrating interactions are presented in detail. We discuss novel phenomena like Griffiths-McCoy singularities. We then turn to more recent topics like information theoretic measures of the quantum phase transitions in these models such as concurrence, entanglement entropy, quantum discord and quantum fidelity. We then focus on non-equilibrium dynamics of a variety of transverse field systems across quantum critical points and lines. After mentioning rapid quenching studies, we dwell on slow dynamics and discuss the Kibble-Zurek scaling for the defect density following a quench across critical points and its modifications for quenching across critical lines, gapless regions and multicritical points. Topics like the role of different quenching schemes, local quenching, quenching of models with random interactions and quenching of a spin chain coupled to a heat bath are touched upon. The connection between non-equilibrium dynamics and quantum information theoretic measures is presented at some length. We indicate the connection between Kibble-Zurek scaling and adiabatic evolution of a state as well as the application of adiabatic dynamics as a tool of a quantum optimization technique known as quantum annealing. The final section is dedicated to a detailed discussion on recent experimental studies of transverse Ising-like systems.
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