Information Geometry of Quantum Phase Transitions

量子相变的信息几何

• 批准号: 0804914
• 负责人: Paolo Zanardi
• 金额: $ 39万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-15 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0804914&HistoricalAwards=false
• 关键词: Information; Geometry; Quantum; Phase; Transitions

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.

技术摘要：该奖项支持理论和计算研究以及教育，目的是开发一种研究临界现象的量子信息几何方法，并将其应用于具有高度物理相关性的相关多体系统。具体地说，PI将结合分析方法，例如量子可分辨度量的发展，应用于精确可解模型，以及计算技术，如量子蒙特卡罗和强无序重整化群，来研究量子自旋系统中拓扑秩序的出现，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的影响。与传统方法不同，所提出的相变的信息几何分析不基于序参数的先验识别，因此不需要对称破缺模式的知识。取而代之的是，使用保真度度量来分析系统，该度量量化具有不同参数集的两个系统状态的接近程度。因此，PI希望这一策略将使他们能够从物理上洞察传统上的困难问题，即有序参数未知、隐藏或未定义的系统。这种度量法将传统的重点从哈密尔顿转移到量子态本身的分析上，或者换句话说，从研究有序参数到量子物质组织成不同阶段的普遍几何结构。这个奖项支持与洛杉矶地区贫困市中心高中工作的当地物理教师的合作。这项活动通过年度研讨会、培训课程和频繁的校园访问来支持参与教师的网络。非技术摘要：该奖项支持理论和计算研究以及教育，目的是开发一种不同的方法来理解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不同的物质状态，例如在晶体固体中规则排列的原子和在液体中随机排列的原子。最近的研究表明，这一概念并不完整，物质状态之间存在着更微妙的区别。这项研究结合了新兴的量子信息理论领域的想法，以及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，以研究电子之间可能存在的强相互作用可能出现的新物质状态，这些电子之间可能存在更细微的差异，而标准相变理论中没有区分这些差异。这项研究是基础性的，但涉及到量子信息科学的新兴领域与凝聚态理论的相互作用。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。这项研究还可能对利用操纵量子力学状态进行计算和通信的基本原理产生影响。除了教育下一代科学家掌握先进的理论方法外，该奖项还支持一项外展努力，涉及与在洛杉矶地区贫困市中心高中工作的当地物理教师的合作。这项活动通过年度讲习班、培训课程和频繁的校园访问，为参与的教师网络提供支持。