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

Abstract

We construct model wavefunctions for the half-filled Landau level parameterized 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 large overlap with wavefunctions obtained by 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 wavefunctions" 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. This allows computation of the Berry phase for 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.

Theory of the disordered ν=52 quantum thermal Hall state: Emergent symmetry and phase diagram

“…It is believed to be a good starting point to assume the composite fermions in the first Landau level form a fermi liquid with a single fermi surface [21,37]. Recent studies suggest the fermi liquid may be a Dirac fermi liquid, and the fermi surface has an intrinsic π Berry phase [21,[37][38][39][40][41]. The fermi surface can then be gapped out by forming Cooper pairs.…”

Dirac composite fermions and emergent reflection symmetry about even-denominator filling fractions

“…Despite its success in incorporating PH symmetry, it still remains to understand how Son's theory might emerge from microscopics and the extent to which it can be experimentally distinguished from the HLR theory, although very interesting arguments have been put forward suggesting that Son's theory may emerge from the HLR theory upon incorporating the effect of quenched disorder [26][27][28] or as a percolation transition between the HLR theory and its PH conjugate [29]. Encouragingly, evidence for the Dirac composite fermion theory has been found in numerical studies [30,31].…”

Precise Experimental Test of the Luttinger Theorem and Particle-Hole Symmetry for a Strongly Correlated Fermionic System

“…These are puzzling at first sight, and might imply a breakdown of particle-hole symmetry. The question of whether or not the CFs obey the particle-hole symmetry has in fact sparked exciting new developments in the field of strongly interacting electron systems [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]40]. These theories mostly predict that the particle-hole symmetry should hold within the lowest LL, while Balram et al, [20] conclude that it could be broken when LLM is significant.…”