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Berry Phase and Model Wave Function in the Half-Filled Landau Level

Journal Article · · Physical Review Letters
 [1];  [2];  [3];  [2]
  1. Princeton Univ., NJ (United States); DOE/OSTI
  2. Princeton Univ., NJ (United States)
  3. California State Univ., Los Angeles, CA (United States)
+ Show Author Affiliations
We construct model wave functions for the half-filled Landau level parametrized by “composite fermion occupation-number configurations” in a two-dimensional momentum space, which correspond to a Fermi sea with particle-hole excitations. When these correspond to a weakly excited Fermi sea, they have a large overlap with wave functions obtained by the exact diagonalization of lowest-Landau-level electrons interacting with a Coulomb interaction, allowing exact states to be identified with quasiparticle configurations. We then formulate a many-body version of the single-particle Berry phase for adiabatic transport of a single quasiparticle around a path in momentum space, and evaluate it using a sequence of exact eigenstates in which a single quasiparticle moves incrementally. In this formulation the standard free-particle construction in terms of the overlap between “periodic parts of successive Bloch wave functions” is reinterpreted as the matrix element of a “momentum boost” operator between the full Bloch states, which becomes the matrix elements of a Girvin-MacDonald-Platzman density operator in the many-body context. Here, this allows the computation of the Berry phase for the transport of a single composite fermion around the Fermi surface. In addition to a phase contributed by the density operator, we find a phase of exactly π for this process.
Research Organization:
Princeton Univ., NJ (United States)
Sponsoring Organization:
USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
SC0002140
OSTI ID:
1610645
Alternate ID(s):
OSTI ID: 1475468
Journal Information:
Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 14 Vol. 121; ISSN 0031-9007
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Cited By (10)

Dirac Fermion Hierarchy of Composite Fermi Liquids journal June 2019
Geometric resonance of four-flux composite fermions journal July 2019
Non-Abelian quasiholes in lattice Moore-Read states and parent Hamiltonians journal October 2018
Modular covariance properties of composite fermions on the torus journal February 2019
Lattice Monte Carlo for quantum Hall states on a torus journal March 2019
Hall viscosity of composite fermions journal February 2020
Lattice Monte Carlo for Quantum Hall States on a Torus text January 2017
Non-Abelian quasiholes in lattice Moore-Read states and parent Hamiltonians text January 2018
Dirac Fermion Hierarchy of Composite Fermi Liquids text January 2018
Hall Viscosity of Composite Fermions text January 2019

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