ABSTRACT

This grant supports theoretical research on fundamental condensed matter physics. Condensed matter physics has been dominated by two primary themes. The first is Landau's Fermi liquid theory and the second is Landau's symmetry breaking theory along with renormalization group theory. Recent studies suggest that new themes are emerging in condensed matter physics. The research supported by this grant will explore these new themes.

One of the new developments is the quantum/topological order introduced by the principal investigator (PI). Topological order describes a new kind of order in fractional quantum Hall (FQH) states. Quantum order describes the internal structure of over one hundred different quantum spin liquids. Quantum/topological order represents new types of order that cannot be described by Landau's symmetry breaking theory. More recent research indicates that quantum/topological order is closely related to the phenomenon of string condensation. The theory of quantum/topological order and string condensation is still in its infancy. This research will attempt to develop a more complete theory. In particular, the following projects will be studied:

The theory of string condensation has a potential to become a well-developed theory like Landau's theory of symmetry breaking. The mathematical framework behind symmetry breaking states is group theory. This project will try to reveal the mathematical framework behind string condensation. The new knowledge will lead to a systematic understanding of phase transitions between different string condensed states as well as the collective excitations above string condensed states. The new knowledge will also lead to a classification of different string condensed states.

Under prior support, the PI showed that a continuous transition between clean FQH states can occur as long as the FQH states contain non-bosonic neutral quasiparticles. Using the relationship between topological order and string condensation, continuous transitions between more general FQH states will be studied, as well as their experimental consequences. These theoretical studies will lead to systematic experimental studies of continuous transitions between clean FQH states. Since FQH states can be viewed as string condensed states, these experiments can also reveal the properties of transitions between different string condensations.

The underdoped high Tc superconductors have some very unusual properties. Their normal state contains electron-like quasiparticles. However, the Fermi surfaces of the quasiparticles are small segments that violate the Luttinger theorem. This project will develop a theory for this strange underdoped normal state. The quantum order and the associated spin liquids will play a key role in the research. The new theory of the underdoped normal state will lead to better understanding of the mechanism and nature of the superconducting transition.

The research accomplished under this grant will have a broad and deep impact on many areas of physics. The string condensed states have robust quantum entanglements that can be used to perform fault tolerant quantum computing. Since the collective excitations in a string condensed state are gauge bosons and fermions, it deepens our understanding of the origin of elementary particles.
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This grant supports theoretical research on fundamental condensed matter physics. Condensed matter physics has been dominated by two primary themes. The first is Landau's Fermi liquid theory and the second is Landau's symmetry breaking theory along with renormalization group theory. Recent studies suggest that new themes are emerging in condensed matter physics. The research supported by this grant will explore these new themes.
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