Information Geometry of Quantum Phase Transitions

技术概述：该奖项支持理论和计算研究，以及旨在开发关键现象的量子信息几何方法的教育，并将其应用于高物理相关性的相关多体系统。具体而言，pi将结合分析，例如量子可分辨性措施的发展，精确可解模型的应用，以及量子蒙特卡罗和强无序重整化群等计算技术，研究量子自旋系统中拓扑有序的出现，分析无序对量子相变的影响，并研究环境诱导的退相干对量子临界性的影响。与传统方法相比，所提出的相变信息几何分析不是基于顺序参数的先验识别，因此不需要对称破缺模式的知识。取而代之的是，系统分析使用保真度度量，量化具有不同参数集的两个系统状态的接近度。因此，pi希望这种策略能够使他们对传统难题，即顺序参数未知、隐藏或未定义的系统，获得物理洞察力。这种度量方法将传统的重点从哈密顿量转移到量子态本身的分析上，或者换句话说，从研究有序参数转移到量子物质组织成不同相的普遍几何结构上。该奖项支持一项扩展工作，包括与洛杉矶地区贫困的市中心高中的当地物理教师合作。这项活动通过年度研讨会、培训课程和频繁的校园访问，为参与的教师提供了一个网络。非技术总结：该奖项支持理论和计算研究以及教育，旨在开发一种不同的方法来理解物质的一种状态如何转化为另一种状态。原子的组织方式可以区分物质的不同状态，例如，晶体固体中的原子按规则排列，而液体中的原子则按随机排列。最近的研究表明，这个概念是不完整的，物质的状态之间存在着更微妙的区别。本研究结合了量子信息理论新兴领域的思想和用于研究复杂材料中磁性和其他物质状态的计算机模拟方法，以研究可能从电子之间的强相互作用中出现的新物质状态，这些电子之间可能具有在标准相变理论中未区分的更微妙的差异。这项研究是基础性的，但涉及到量子信息科学与凝聚态理论的新兴领域的相互作用。这些领域之间的协同作用可能会带来新的进展和新的方向。这项研究还可能对一些基本原理产生影响，这些原理可能使利用量子力学状态进行计算和通信的能力成为可能。除了用先进的理论方法教育下一代科学家外，该奖项还支持与洛杉矶地区贫困市中心高中的当地物理教师合作的推广工作。这项活动通过年度研讨会、培训课程和频繁的校园访问，为参与的教师提供了一个网络。

TECHNICAL SUMMARY:This award supports theoretical and computational research, and education with an aim to develop a quantum information geometry approach to critical phenomena, and to apply it to correlated many-body systems of high physical relevance. Specifically, the PIs will combine analytical, for example development of quantum distinguishability measures, application to exactly solvable models, and computational techniques, such as Quantum Monte Carlo and strong-disorder renormalization group, to investigate the emergence of topological order in quantum spin systems, analyze the effects of disorder on quantum phase transitions, and study the consequences of environment-induced decoherence on quantum criticality.In contrast to traditional approaches, the proposed information geometry analysis of phase transitions is not based on an a priori identification of order parameters, and hence does not require knowledge of symmetry breaking patterns. Instead, systems are analyzed using fidelity measures which quantify the proximity of two system states with different parameter sets. So, the PIs hope this strategy will enable them to gain physical insight into traditionally hard problems, systems for which the order parameter is either unknown, hidden or not defined.This metric approach shifts the traditional emphasis from Hamiltonians to the analysis of quantum states themselves, or put another way, from studying order parameters to universal geometrical structures underlying the way quantum matter organizes itself into different phases.This award supports an outreach effort that involves a collaboration with local physics teachers who work at underprivileged inner-city high schools in the Los Angeles area. This activity supports a network for participating teachers through annual workshops, training sessions and frequent campus visits.NONTECHNICAL SUMMARY:This award supports theoretical and computational research, and education with an aim to develop a different approach to understanding how one state of matter transforms into another. The way atoms are organized can distinguish different sates of matter, for example atoms arranged on a regular array in crystalline solid verses a random arrangement of atoms in liquid. Recent research suggests that this notion is not complete and there are more subtle distinctions between states of matter. This research combines ideas from the emerging area of quantum information theory and computer simulation methods used to study magnetism and other states of matter in complex materials, to investigate new states of matter that may emerge from strong interactions among electrons that may have more subtle differences that are not distinguished in the standard theory of phase transitions. The research is fundamental but involves the interaction of the emerging area of quantum information science with condensed matter theory. The synergy between these areas may lead to new advances and new directions. The research may also have impact on the fundamental principles that may enable the exploitation of the ability to manipulate quantum mechanical states for computation and communication.Apart from educating the next generation of scientists in advanced theoretical methods, this award supports an outreach effort that involves a collaboration with local physics teachers who work at underprivileged inner-city high schools in the Los Angeles area. This activity supports a network for participating teachers through annual workshops, training sessions and frequent campus visits.