Quantum Theory of Competing Orders

University Of California-Los Angeles, Los Angeles CA

Investigators

Abstract

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. ***