RUI: Physics of Interacting Quantum Systems with Phase Transitions

Yeshiva University, New York NY

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports theoretical research and education on quantum systems that have many interacting particles. The main goal is to identify the conditions for the onset of transitions between different states of organization of the constituent particles, and to put forward a set of proposals to detect such transitions experimentally. In classical physics, a thermal phase transition occurs when the temperature of a material reaches a critical point and the material undergoes a change in state, such as the transition from water to ice. At very low temperatures, classical laws break down and quantum physics takes over. At that level, different quantum phases can emerge from the competition between different interactions in the system. Distinct phases are associated with different macroscopic properties that can be experimentally detected, such as good or bad conductivity. This topic of research is tightly connected with the development of new materials. New phases of matter are critical components of emerging technologies, which may revolutionize how we use and produce energy, may lead to new types of electronic devices, and may facilitate the scaling up of quantum computers. The potential economical and social impact of the discovery of novel phases of matter is immense. Yet, one needs to know where to look to have a higher chance to find them. The project will also foster the participation of women in physics and improve the educational infrastructure at the Stern College for Women of Yeshiva University by offering new research opportunities and training in core areas of physics and in computational methods. Female undergraduate students will continue to coauthor papers with the PI and disseminate their results at conferences. Students from local high schools will also have the opportunity to experience research at Stern College for Women. This effort is facilitated by the PI's collaboration with three of her former students, who are now physics teachers in high schools for girls. Furthermore, the plan to expand a webpage designed for posting computer programs from courses and research findings will contribute to the integration of teaching and research at other undergraduate institutions. TECHNICAL SUMMARY This award supports theoretical research and education on computational and analytical methods to advance our understanding of low-dimensional quantum systems with short- and long-range interactions. The focus will be on two main topics that carry potential to open new research avenues. They are: 1. Identifying the conditions for the onset of quantum phase transitions at excited states and putting forward a set of proposals to detect such transitions experimentally. Studies of ground state quantum phase transitions are of crucial importance to fields as diverse as nuclear physics, condensed matter physics, and cosmology. Progress in this field may carry the key to unsolved problems in condensed matter physics and may lead to novel phases of matter. Recently, a new element has been brought to the picture: the existence of excited-state quantum phase transitions. They have mainly been examined in models from quantum optics, molecular and nuclear physics. This project will expand the analysis to also include condensed matter models. This will bring new perspectives, tools, and approaches to the understanding of many-body condensed matter systems as well as to the existing studies of excited-state quantum phase transitions. 2. Exploring the counterintuitive scenario of achieving localization by increasing the range of the interactions, instead of increasing on-site disorder or the amplitude of the interactions. Despite innumerable studies about the metal-insulator transition, the subject is still partially understood. These transitions are usually divided in two categories: disorder-driven Anderson transitions and interaction-driven Mott transitions. The main current interest, however, is on the richer and more complicated case where both interaction and disorder are taken into account simultaneously. The usual expectation is that in the presence of long-range interactions, localization should become more difficult. Yet, long-range interactions can also lead to subspaces inside of which the states are highly localized. This project will explore new scenarios, such as the latter, which will bring a new viewpoint to the subject of localization. The project will also foster the participation of women in physics and improve the educational infrastructure at the Stern College for Women of Yeshiva University by offering new research opportunities and training in core areas of physics and in computational methods. Female undergraduate students will continue to coauthor papers with the PI and disseminate their results at conferences. Students from local high schools will also have the opportunity to experience research at Stern College for Women. This effort is facilitated by the PI's collaboration with three of her former students, who are now physics teachers in high schools for girls. Furthermore, the plan to expand a webpage designed for posting computer programs from courses and research findings will contribute to the integration of teaching and research at other undergraduate institutions.