Quantum Fluctuations and Broken Symmetries in Correlated Electron Systems

University Of California-Los Angeles, Los Angeles CA

Investigators

Abstract

TECHNICAL SUMMARY This award supports theoretical research and education on a variety of problems that are interlinked by the common threads of quantum fluctuations and broken symmetries when electronic correlations are important. This project will address: high temperature superconductivity in cuprates, dissipative quantum phase transitions in general, and in particular, in low dimensional systems such as nanowires, and the role of disorder in quantum phase transitions applicable to many condensed matter systems, from cuprates to heavy fermions to organics. The recent discovery of quantum oscillations in cuprate superconductors has ushered in a new era of this twenty-year old unsolved major problem in physics. A theoretical understanding of this phenomenon may result in a major breakthrough. The PI's approach is to model the various broken symmetry states, with particular attention paid to coexisting states of competing order parameters in the vortex liquid state. The PI will employ exact transfer matrix technique and Landauer-Pichard formula to compute Shubnikov-de Haas oscillations. Dissipative quantum phase transitions are addressed because of their potential importance in shedding light on the foundations of quantum mechanics, as well as their key role in a novel class of quantum criticality, with many applications. Numerical simulations as well as scaling theories will be used. A specific application of the theory is the ongoing experiments in quantum phase slips in nanowires. In the same broad framework, the PI will also investigate the role of disorder in phase transitions, in particular quantum phase transitions. Many complex materials of great importance in understanding correlated electron systems are inevitably rife with disorder. Both the tools of rigorous mathematical statistical mechanics as well as numerical simulations in well-defined quantum models will be addressed. There are many cases where some unorthodox thinking may be required; the notion of quantum mechanical entanglement entropy, the von Neumann entropy, is one of them. This award also supports training graduate students in theoretical condensed matter physics. Research activities will enhance teaching in undergraduate classes, where there are now many more minorities and women students. It is at this undergraduate level that the PI will encourage students to pursue careers in science. NONTECHNICAL SUMMARY This award supports theoretical research and education on quantum phase transitions. These are an intensely studied phenomenon that has become cutting edge research in condensed matter physics. Ordinary phase transitions, like the transition of water to ice, take place at non-zero temperature and are driven by thermal fluctuations. Quantum phase transitions can take place at the absolute zero of temperature driven by the quantum fluctuations of Heisenberg's uncertainty principle. The PI aims to explore novel materials that have been discovered in recent years in this new light and to explain their observable, and so far puzzling, properties. This research may lead to further progress in predicting useful materials, such as materials that might exhibit superconductivity at room temperatures. Superconductivity is a quantum mechanical state of matter that so far occurs at low temperatures, at most about twice the frigid temperature where the element nitrogen, a gaseous component of our atmosphere, boils. Superconductors can carry electricity without loss. At the same time we would be learning fundamental aspects of quantum properties of matter. This research may lead to further understanding of novel materials that may form the foundations of future technologies. This award also supports training graduate students in theoretical condensed matter physics. Research activities will enhance teaching in undergraduate classes, where there are now many more minorities and women students. It is at this undergraduate level that the PI will encourage students to pursue careers in science.