Quantum Phases and Transitions

Yale University, New Haven CT

Investigators

Abstract

TECHNICAL SUMMARY This award supports theoretical research and education on quantum phases and phase transitions as well as the PI's constant efforts to communicate developments in his field to a wide audience using a variety of vehicles like summer school courses, dialogs, public lectures, books, and review articles. Quantum phase transitions occur when the ground state of a system undergoes a change of phase, say from superconductor to insulator, in response to a changing parameter in the Hamiltonian. Equally interesting as the transitions, are the phases themselves: the excitations they support, their degeneracies and their responses to external probes. The PI has developed two tools to this end: (i) the renormalization group for fermions in which low-energy states near the Fermi surface are systematically eliminated to display the ultimate properties of the ground state and its instabilities (ii) and the Hamiltonian Theory of the Fractional Quantum Hall Effect which is an operator treatment of the problem that allows the computation of gaps, relaxation rates etc. He plans to extend and apply the renormalization group in many ways: to describe the singular Coulomb interaction, to describe ferromagnetism, to describe Fermions with more than one momentum direction normal to the Fermi surface, to describe the vexing but important problem of how to formulate a renormalization group for bosons and fermions at the same time and bilayer graphene. He plans to apply the Hamiltonian theory to describe the response of the Hall system near half-filling to microwave radiation. Finally he proposes to pursue a rather tantalizing connection between Lie groups and fermion motion on several lattices- where Lie groups generate the very lattice and determine its unusual spectrum. The PI plans to continue disseminating ideas here and abroad, to a broad audience, ranging from school children to advanced graduate students in summer schools, from professionals to the lay public via review articles, public lectures, web-based lectures, and his third text book, this time on the methods of quantum field theory in condensed matter physics. He will continue to actively disseminate his work on renormalization group to sister disciplines like Nuclear Physics and Particle Physics which have adapted it to describe matter at finite density. NON-TECHNICAL SUMMARY This award supports theoretical research and education on quantum phase transitions and quantum states of matter. Unlike the more familiar phase transformations, like water to steam, quantum phase transitions occur at the absolute zero of temperature as an external variable, like pressure, is tuned through the transformation from one phase to another. It is believed that these phase transitions can influence the electronic properties of materials for a wide range of temperatures and hold promise to explain anomalous electronic properties of some classes of materials. The PI will further develop and apply a powerful technique first developed in particle physics but later applied to theory of phase transitions. The technique, called the renormalization group, enables one to examine the physics contained in a theory across expanding length scales. While this approach has yielded great insights into a number of important problems to condensed matter and materials physics, its application to others has proven more difficult. The PI aims to clear conceptual roadblocks and harvest the valuable insights it offers into quantum phase transitions and quantum mechanical systems of interacting particles more generally. The PI plans to continue disseminating ideas here and abroad, to a broad audience, ranging from school children to advanced graduate students in summer schools, from professionals to the lay public via review articles, public lectures, web-based lectures, and his third text book, this time on the methods of quantum field theory in condensed matter physics. He will continue to actively disseminate his work on renormalization group to sister disciplines like Nuclear Physics and Particle Physics which have adapted it to describe matter at finite density.