[论文解读] Transverse field spin models: From Statistical Physics to Quantum Information

Amit Dutta, Uma Divakaran+4 more|arXiv (Cornell University)|Dec 3, 2010

Opinion Dynamics and Social Influence被引用 7

一句话总结

本文全面综述了横向场自旋模型中的量子相变，包括自旋-1/2伊辛模型和XY模型，涵盖一维情况下的精确解、与共形场论的联系，以及无序和几何阻挫的影响。文章强调了格里菲斯-麦考伊奇异性等关键现象，并将非平衡动力学（尤其是淬火过程中的基布尔-祖雷克标度）与量子信息度量及量子退火联系起来。

ABSTRACT

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.

研究动机与目标

• 系统性地回顾横向场自旋系统中的量子相变，重点关注伊辛和XY链等可积模型。
• 将量子临界现象与共形场论相联系，并探讨淬火无序与阻挫的作用。
• 研究跨量子临界点和临界线的非平衡动力学，特别关注基布尔-祖雷克标度。
• 建立量子相变与量子信息度量（如纠缠熵、 concurrence 和量子保真度）之间的联系。
• 探讨在量子退火及最近实现的横向伊辛类系统中的应用。

提出的方法

• 采用精确对角化和共形场论技术求解具有横向场的一维自旋模型。
• 分析基塔耶夫模型及其他精确可解系统，以理解拓扑序与量子临界性。
• 利用强无序重整化群方法研究无序系统中的格里菲斯-麦克莱南奇异性。
• 计算量子信息度量（如纠缠熵、concurrence 和量子失谐）以表征量子临界点。
• 通过淬火协议（包括快速与慢速淬火）模拟非平衡动力学，重点关注缺陷密度的标度行为。
• 推导并扩展基布尔-祖雷克标度至临界线、无能隙区域及多临界点，将其与绝热演化及量子退火联系起来。

实验结果

研究问题

• RQ1 量子相变在横向场伊辛和XY模型中如何表现，其与共形场论有何关联？
• RQ2 淬火无序与几何阻挫对自旋系统中量子临界性有何影响？
• RQ3 如纠缠熵与量子失谐等量子信息度量在量子临界点附近的行为如何？
• RQ4 基布尔-祖雷克标度在跨量子临界点和临界线淬火过程中缺陷形成中的作用是什么？
• RQ5 如何通过绝热演化与淬火协议将非平衡动力学与量子退火联系起来？

主要发现

• 一维情况下的精确解揭示了在量子临界点附近的普遍标度行为，与共形场论预测一致。
• 在无序系统中出现格里菲斯-麦考伊奇异性，导致即使在临界点之外，热力学量也表现出非解析行为。
• 纠缠熵在量子临界点处表现出对数发散，证实其作为临界性探测器的作用。
• 量子保真度与量子失谐在量子相变点处表现出尖锐特征，可实现临界点的检测。
• 基布尔-祖雷克标度预测缺陷密度与淬火速率呈幂律依赖关系，临界线与无能隙区域存在修正。
• 基布尔-祖雷克标度与绝热演化之间的联系为量子退火作为量子优化方法提供了理论基础。