Quantum Theory of Competing Orders

量子力学构成了许多新材料的理论基础，这些新材料今天仍在不断被发现，如高温超导体、钌酸盐、锰酸盐、富勒烯和重电子材料。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。最基本的兴趣是那些在宏观尺度上反映量子力学的特性，它们不断挑战我们扩展我们对物质的感知。在海森堡的不确定性关系的推动下，在绝对零度下物质基本不同状态之间的量子相变等新概念导致了在室温下观察到的惊人结果。这种转变在许多具有重大技术兴趣的不同材料中无处不在，使我们有必要用理论物理的复杂性来研究量子相变理论。控制涉及强相互作用的物质的量子态特性，多体自由度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，一定有一套物理原理，很可能是简单的；然而，发现这些原则需要思维上的真正转变。人们不能再用单一长度和能量尺度的物理学来思考，因为这些影响是集体的。一个新兴的观点是竞争秩序的概念，它是复杂的利益系统的基础。在一个复杂的系统中，任何可以被打破的对称都必须被打破，这几乎是不言自明的；然而，由这些破缺对称性产生的许多有序态实际上是隐藏的，但却秘密地控制着物质的一般性质。因此，新的隐藏秩序的发现不仅在智力上令人着迷，而且在为我们的目的定制材料方面也非常实用，例如具有最高转变温度的超导体。直到今天，尽管在强相关的电子系统中可以打破无限的对称性，但具有破缺对称性的物质状态的名单是有限的。困难在于，人们并不总是清楚有效的哈密顿量应该是什么，也不清楚复杂的量子顺序如何与真实材料的相图相适应。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。本研究的一个方面包括从场论的角度发展理论工具，应用于物质理论。另一个方面涉及发展现象学思想，以便直接应用于实验系统。另一个方面涉及计算，但被复杂的缩放和量子临界性概念所增强。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。这不仅要通过在国内机构指导学生，而且要鼓励他们参加专业会议，在那里他们可以展示他们的研究活动的结果，并与该领域的其他人交换意见。现有的研究小组已经包括一名女研究生，并将努力招募更多的女性和少数民族。将研究活动纳入凝聚态物理现代研究生水平教科书的计划正在进行中。研究结果也将通过专业期刊的出版物和在国家和国际会议上的发言广泛传播。希望这项研究将导致对新型材料的进一步了解，以造福社会。量子力学构成了许多新材料的理论基础，这些新材料今天仍在不断被发现，如高温超导体、钌酸盐、锰酸盐、富勒烯和重电子材料。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。最基本的兴趣是那些在宏观尺度上反映量子力学的特性，它们不断挑战我们扩展我们对物质的感知。在海森堡的不确定性关系的推动下，在绝对零度下物质基本不同状态之间的量子相变等新概念导致了在室温下观察到的惊人结果。这种转变在许多具有重大技术兴趣的不同材料中无处不在，使我们有必要用理论物理的复杂性来研究量子相变理论。控制涉及强相互作用的物质的量子态特性，多体自由度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，一定有一套物理原理，很可能是简单的；然而，发现这些原则需要思维上的真正转变。人们不能再用单一长度和能量尺度的物理学来思考，因为这些影响是集体的。一个新兴的观点是竞争秩序的概念，它是复杂的利益系统的基础。在一个复杂的系统中，任何可以被打破的对称都必须被打破，这几乎是不言自明的；然而，由这些破缺对称性产生的许多有序态实际上是隐藏的，但却秘密地控制着物质的一般性质。因此，新的隐藏秩序的发现不仅在智力上令人着迷，而且在为我们的目的定制材料方面也非常实用，例如具有最高转变温度的超导体。直到今天，尽管在强相关的电子系统中可以打破无限的对称性，但具有破缺对称性的物质状态的名单是有限的。困难在于，人们并不总是清楚有效的哈密顿量应该是什么，也不清楚复杂的量子顺序如何与真实材料的相图相适应。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。本研究的一个方面包括从场论的角度发展理论工具，应用于物质理论。另一个方面涉及发展现象学思想，以便直接应用于实验系统。另一个方面涉及计算，但被复杂的缩放和量子临界性概念所增强。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。这不仅要通过在国内机构指导学生，而且要鼓励他们参加专业会议，在那里他们可以展示他们的研究活动的结果，并与该领域的其他人交换意见。现有的研究小组已经包括一名女研究生，并将努力招募更多的女性和少数民族。将研究活动纳入凝聚态物理现代研究生水平教科书的计划正在进行中。研究结果也将通过专业期刊的出版物和在国家和国际会议上的发言广泛传播。希望这项研究将导致对新材料的进一步了解，以造福社会

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.***