Physical Properties of Strongly Correlated Quantum Liquids

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This award supports theoretical research on strongly correlated electron systems, focusing on high temperature superconductors and quantum Hall systems. Research focuses on three areas: (1) The PI takes the view that underdoped high temperature superconductors have a non-fermi liquid metallic state that exhibits spin-charge separation. Research will focus on holon dynamics and the properties of a non-condensing quantum degenerate holon gas. The transition to the superconducting state will be studied with the aim of understanding how the superconducting transition is related to spin-charge recombination and how coherent quasiparticles can grow out of incoherent spinons and holons. The transition to the striped phase will also be studied; this is expected not to be a usual CDW transition. (2) The PI plans to develop a more complete theory of fractional quantum Hall states, with an aim to elucidate the mathematical structure of topological order. The chiral operator product algebra will be examined to see if it could form the basis of a general theory of topological order. It is expected that a deeper understanding of topological order will enable the calculation of the physical properties of non-Abelian fractional quantum Hall states and so enable their identification in experiments. (3) The PI plans to study continuous phase transitions between topological orders. Continuous phase transitions can occur between clean fractional quantum Hall states as long as these states contain neutral quasiparticles. The properties of the critical point depend on the topological orders of the two states involved and so, provide a useful way to study topological order experimentally. The PI plans to find general effective theories for continuous topological phase transitions and to understand the close relation between the topological order and the critical theory. The PI will also explore how neutral gapless excitations at the critical point interact with surface acoustic phonons and other experimental probes.%%%This award supports theoretical research on strongly correlated electron systems with a particular focus on high temperature superconductors and quantum Hall systems. The PI plans to use advanced theoretical methods to understand the nature of a proposed exotic metallic state of the high temperature superconductors and the nature of the phase transition from this state to the superconducting state. The metallic state is unlike that of an ordinary metal and the transition to superconductivity may differ qualitatively from that which occurs in well-understood superconductors. The PI will also study fractional quantum Hall states that exhibit internal order. A kind of continuous phase transition can occur between two such states with the same symmetry. The PI intends to develop a more comprehensive theory of these states and the phase transitions that can occur among them. This research contributes to fundamental understanding of strongly correlated electron materials.***