Quantum Theory of Competing Orders

竞争秩序的量子理论

• 批准号: 0411931
• 负责人: Sudip Chakravarty
• 金额: $ 34.5万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-07-01 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0411931&HistoricalAwards=false
• 关键词: Quantum; Theory; Competing; Orders

Quantum mechanics forms the theoretical basis of many novel materials that continue to be discovered today, such as high temperature superconductors, ruthenates, manganates, fullerenes, and heavy electron materials. Without quantum mechanics even the most common metals, insulators, and semiconductors cannot be understood. Of fundamental interest are those properties that reflect quantum mechanics on a macroscopic scale, which are continuously challenging us to extend our perceptions of matter. New concepts, such as quantum phase transitions between fundamentally distinct states of matter at absolute zero, driven by Heisenberg's uncertainty relation lead to to spectacular consequences in observations at temperatures as high as room temperature. The ubiquity of such transitions in many varied materials of great technological interest behooves us to approach the theory of quantum phase transitions with the sophistication of theoretical physics. Control over properties of quantum states of matter involving strongly interacting, many-body degrees of freedom remains an engaging intellectual enterprise. We are only beginning to realize that underlying the materials science, there must be a set of physical principles, most likely simple in character; however, discovering these principles requires a genuine shift in thinking. One can no longer think in terms of physics on single length and energy scales, because the effects are collective.An emerging idea is the notion of competing order that underlies the complex systems of interest. It is almost a truism that in a complex system any symmetry that can be broken must be broken; however, many of the ordered states that result from these broken symmetries are effectively hidden, but surreptitiously control the general properties of matter. Thus, the discoveries of new hidden order are not only intellectually fascinating, but also enormously practical to tailor materials for our purposes, such as superconductors with the highest transition temperature. To this day, the roster of states of matter with broken symmetries is limited despite the limitless symmetries that can be broken in a strongly correlated electronic system. The difficulty is that it is not always clear what should be the effective Hamiltonian, nor is it clear how a complex quantum order fits into the phase diagram of a real material. Here, we address both of these issues by considering concrete examples from high temperature superconductors, a variety of quantum phase transitions and dissipative quantum systems. An aspect of this research consists of developing theoretical tools from the perspective of field theory, as applied to the theory of matter. Another aspect concerns the development of phenomenological ideas for direct applications to experimental systems. Yet another aspect involves computation, but augmented by sophisticated ideas of scaling and quantum criticality.The broader impacts of this work will involve educating and training graduate students to assume leadership roles in academic and industrial environments. This will be accomplished not only by mentoring students at the home institution, but also by encouraging them to attend professional meetings, where they can present results of their research activities and exchange ideas with others in the field. The existing research group already includes a woman graduate student and an effort will be made to recruit more women and minorities. Plans are underway to incorporate research activities into a modern graduate level textbook in condensed matter physics. The results of the research will also be broadly disseminated through publications in professional journals and presentations at national and international conferences. It is hoped that the research will lead to further understanding of novel materials for the benefit of society.%%% Quantum mechanics forms the theoretical basis of many novel materials that continue to be discovered today, such as high temperature superconductors, ruthenates, manganates, fullerenes, and heavy electron materials. Without quantum mechanics even the most common metals, insulators, and semiconductors cannot be understood. Of fundamental interest are those properties that reflect quantum mechanics on a macroscopic scale, which are continuously challenging us to extend our perceptions of matter. New concepts, such as quantum phase transitions between fundamentally distinct states of matter at absolute zero, driven by Heisenberg's uncertainty relation lead to to spectacular consequences in observations at temperatures as high as room temperature. The ubiquity of such transitions in many varied materials of great technological interest behooves us to approach the theory of quantum phase transitions with the sophistication of theoretical physics. Control over properties of quantum states of matter involving strongly interacting, many-body degrees of freedom remains an engaging intellectual enterprise. We are only beginning to realize that underlying the materials science, there must be a set of physical principles, most likely simple in character; however, discovering these principles requires a genuine shift in thinking. One can no longer think in terms of physics on single length and energy scales, because the effects are collective.An emerging idea is the notion of competing order that underlies the complex systems of interest. It is almost a truism that in a complex system any symmetry that can be broken must be broken; however, many of the ordered states that result from these broken symmetries are effectively hidden, but surreptitiously control the general properties of matter. Thus, the discoveries of new hidden order are not only intellectually fascinating, but also enormously practical to tailor materials for our purposes, such as superconductors with the highest transition temperature. To this day, the roster of states of matter with broken symmetries is limited despite the limitless symmetries that can be broken in a strongly correlated electronic system. The difficulty is that it is not always clear what should be the effective Hamiltonian, nor is it clear how a complex quantum order fits into the phase diagram of a real material. Here, we address both of these issues by considering concrete examples from high temperature superconductors, a variety of quantum phase transitions and dissipative quantum systems. An aspect of this research consists of developing theoretical tools from the perspective of field theory, as applied to the theory of matter. Another aspect concerns the development of phenomenological ideas for direct applications to experimental systems. Yet another aspect involves computation, but augmented by sophisticated ideas of scaling and quantum criticality.The broader impacts of this work will involve educating and training graduate students to assume leadership roles in academic and industrial environments. This will be accomplished not only by mentoring students at the home institution, but also by encouraging them to attend professional meetings, where they can present results of their research activities and exchange ideas with others in the field. The existing research group already includes a woman graduate student and an effort will be made to recruit more women and minorities. Plans are underway to incorporate research activities into a modern graduate level textbook in condensed matter physics. The results of the research will also be broadly disseminated through publications in professional journals and presentations at national and international conferences. It is hoped that the research will lead to further understanding of novel materials for the benefit of society.***

量子力学构成了当今不断发现的许多新型材料的理论基础，例如高温超导体、钌酸盐、锰酸盐、富勒烯和重电子材料。 如果没有量子力学，即使是最常见的金属、绝缘体和半导体也无法被理解。 最重要的是那些在宏观尺度上反映量子力学的性质，它们不断地挑战着我们扩展我们对物质的认知。 新概念，例如在绝对零时基本不同的物质状态之间的量子相变，由海森堡的不确定性关系驱动，导致在高达室温的温度下的观测产生惊人的结果。 这种转变在许多具有重大技术意义的材料中普遍存在，这使得我们有必要用理论物理学的复杂性来研究量子相变理论。 对涉及强相互作用、多体自由度的物质量子态特性的控制仍然是一项引人入胜的智力事业。 我们才刚刚开始认识到，在材料科学的基础上，必须有一套物理原理，而且性质很可能很简单；然而，发现这些原则需要真正的思维转变。 人们不能再从单一长度和能量尺度的物理学角度思考，因为影响是集体的。一种新兴的想法是竞争秩序的概念，它是复杂系统的基础。 几乎不言而喻的是，在复杂的系统中，任何可以打破的对称性都必须被打破。然而，由于这些对称性破缺而产生的许多有序态实际上被隐藏起来，但却秘密地控制着物质的一般性质。 因此，新隐藏秩序的发现不仅在智力上令人着迷，而且对于为我们的目的定制材料（例如具有最高转变温度的超导体）也非常实用。 直到今天，尽管在强相关电子系统中可以打破无限的对称性，但对称性破缺的物质状态仍然有限。 困难在于，并不总是清楚什么应该是有效的哈密顿量，也不清楚复杂的量子级如何适合真实材料的相图。 在这里，我们通过考虑高温超导体、各种量子相变和耗散量子系统的具体例子来解决这两个问题。 这项研究的一个方面包括从场论的角度开发理论工具，并将其应用于物质理论。 另一方面涉及现象学思想的发展以直接应用于实验系统。 另一方面涉及计算，但通过缩放和量子临界性的复杂思想得到增强。这项工作的更广泛影响将涉及教育和培训研究生在学术和工业环境中担任领导角色。 这不仅可以通过在母校指导学生来实现，还可以通过鼓励他们参加专业会议来实现，在会议上他们可以展示他们的研究活动成果并与该领域的其他人交流想法。 现有的研究小组已经包括一名女研究生，并将努力招募更多女性和少数族裔。 目前正在计划将研究活动纳入现代研究生凝聚态物理学教科书。 研究结果还将通过专业期刊上的出版物以及在国内和国际会议上的演讲来广泛传播。 希望这项研究能够进一步了解新型材料，造福社会。%%%量子力学构成了当今不断发现的许多新型材料的理论基础，例如高温超导体、钌酸盐、锰酸盐、富勒烯和重电子材料。 如果没有量子力学，即使是最常见的金属、绝缘体和半导体也无法被理解。 最重要的是那些在宏观尺度上反映量子力学的性质，它们不断地挑战着我们扩展我们对物质的认知。 新概念，例如在绝对零时基本不同的物质状态之间的量子相变，由海森堡的不确定性关系驱动，导致在高达室温的温度下的观测产生惊人的后果。 这种转变在许多具有重大技术意义的材料中普遍存在，这使得我们有必要用理论物理学的复杂性来研究量子相变理论。 对涉及强相互作用、多体自由度的物质量子态特性的控制仍然是一项引人入胜的智力事业。 我们才刚刚开始认识到，在材料科学的基础上，必须有一套物理原理，而且性质很可能很简单；然而，发现这些原则需要真正的思维转变。 人们不能再从单一长度和能量尺度的物理学角度思考，因为影响是集体的。一种新兴的想法是竞争秩序的概念，它是复杂系统的基础。 几乎不言而喻的是，在复杂的系统中，任何可以打破的对称性都必须被打破。然而，由于这些对称性破缺而产生的许多有序态实际上被隐藏起来，但却秘密地控制着物质的一般性质。 因此，新隐藏秩序的发现不仅在智力上令人着迷，而且对于为我们的目的定制材料（例如具有最高转变温度的超导体）也非常实用。 直到今天，尽管在强相关电子系统中可以打破无限的对称性，但对称性破缺的物质状态仍然有限。 困难在于，并不总是清楚什么应该是有效的哈密顿量，也不清楚复杂的量子级如何适合真实材料的相图。 在这里，我们通过考虑高温超导体、各种量子相变和耗散量子系统的具体例子来解决这两个问题。 这项研究的一个方面包括从场论的角度开发理论工具，并将其应用于物质理论。 另一方面涉及现象学思想的发展以直接应用于实验系统。 另一方面涉及计算，但通过缩放和量子临界性的复杂思想得到增强。这项工作的更广泛影响将涉及教育和培训研究生在学术和工业环境中担任领导角色。 这不仅可以通过在母校指导学生来实现，还可以通过鼓励他们参加专业会议来实现，在会议上他们可以展示他们的研究活动成果并与该领域的其他人交流想法。 现有的研究小组已经包括一名女研究生，并将努力招募更多女性和少数族裔。 目前正在计划将研究活动纳入现代研究生凝聚态物理学教科书。 研究结果还将通过专业期刊上的出版物以及在国内和国际会议上的演讲来广泛传播。 希望这项研究能够进一步了解新型材料，造福社会。***