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Title: Berry phase in composite Fermi liquids
Authors: Wang, Jie
Advisors: Haldane, Duncan
Contributors: Physics Department
Keywords: Berry phase
composite Fermi liquid
particle hole symmetry
Subjects: Physics
Quantum physics
Issue Date: 2019
Publisher: Princeton, NJ : Princeton University
Abstract: Two-dimensional electron gas in high magnetic field exhibits a wide variety of interesting physical properties. Perhaps most notable of these is the quantum Hall effect, which is a classic example of a topological phase. Another interesting phase occurs at even denominator filling fraction is the so-called ``composite Fermi liquid''. Such compressible phase is traditionally thought of as a Fermi liquid of ``composite fermions'' due to B. I. Halperin, P. A. Lee and N. Read (HLR). Composite Fermi liquid has gained renewed interest recently due to the particle-hole symmetry and Berry phase: when the lowest Landau level is half filled, the effective Hamiltonian is particle-hole symmetric. However, it is unclear how the HLR description realizes this symmetry. A key ingredient that was missing in HLR's treatment seems to be a PI Fermi sea Berry phase associated with transporting a composite fermion around the Fermi surface. Motivated by the symmetry and Berry phase, recently D. T. Son conjectured that composite fermions are relativistic Dirac particles. In Son's theory, particle-hole symmetry acts in a way akin to time reversal on Dirac fermions, and the PI Berry phase is a curvature singularity at Dirac node. A direct measurement of this PI Berry phase is one of the main results in this dissertation. We examined a model wavefunction that explicitly exhibits a Fermi surface, and has been shown to give good agreement with states found in exact diagonalization studies. We then formulated a many-body version of Berry phase for transporting a single composite fermion around a path in momentum space, and evaluated the Berry phase. To study the property of model wavefunction and Berry phase on larger system sizes, we developed ``lattice Monte Carlo'' technique based on a mathematically exact discretized formulation of holomorphic quantum Hall states on torus. Besides half filling, the Berry phase at 1/4 was found to be remarkably interesting: it suggests the emergence of Dirac fermion at generic filling fraction. Motived by this, an effective theory, dubbed as ``flux attached Dirac fermion theory'', which generalizes Son's theory and covers all filling fractions was proposed.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog:
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Physics

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