Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01v118rh42g
 Title: Berry phase in composite Fermi liquids Authors: Wang, Jie Advisors: Haldane, Duncan Contributors: Physics Department Keywords: Berry phasecomposite Fermi liquidparticle hole symmetry Subjects: PhysicsQuantum 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. URI: http://arks.princeton.edu/ark:/88435/dsp01v118rh42g Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: catalog.princeton.edu Type of Material: Academic dissertations (Ph.D.) Language: en Appears in Collections: Physics