Composite Fermi liquid
Fig-1: Main numerical results of Ref ; the main theoretical result is illustrated in Fig-2.
The Berry curvature distribution on the emergent Fermi sea at 1/4 filled Landau level. The strong peak at the Fermi sea center strongly suggest the emergence of relativistic Dirac particle. Motivated by this numerical observation, I proposed an effective theory generalizing the Son-Dirac theory to all other filling fractions that composite Fermi liquids can occur. See Ref.  for details.
During the graduate school at Princeton, where I mainly worked with my advisor Duncan Haldane, I worked on the emergent phenomena in a partially filled Landau level. Much of my Ph.D. work is about the Composite Fermi Liquid phase, a strongly correlated gapless phase occurring in an even denominator (v=1/2m, such as 1/2, 1/4, ...) filled lowest Landau level.
My work [1,2,3] contribute to the fundamental understandings about the nature of composite fermion in this phase.
 Jie Wang (2019). Dirac Fermion Hierarchy of Composite Fermi Liquids. PhysRevLett.122.257203
 Jie Wang, S. Geraedts, E.H. Rezayi and F.D.M. Haldane (2019). Lattice Monte Carlo for Quantum Hall States on a Torus. PhysRevB.99.125123
 S. Geraedts, Jie Wang, E.H. Rezayi and F.D.M. Haldane (2018). Berry phase and model wavefunctions in the half-filled Landau level. PhysRevLett.121.147202 (Editor's suggestion)
The composite Fermi liquids (CFL) was initially understood by B.I. Halperin, Patrick Lee, Nicholas Read in 1993 [PRB.47.7312] as Fermi seas of composite fermions, which are bound states of one electron and 2m flux quanta at filling fraction v=1/(2m). A long-standing open problem of Halperin-Lee-Read theory is the lack of particle-hole symmetry at half filling (m=1). This motivated Dam Thanh Son in 2015 to propose an alternative low energy effective theory [PRX.5.031027]. According to Son, the composite fermions are instead relativistic Dirac particles.
Important contributions of our works include the definition and the numerical detection of the many-body Berry phase associated to the adiabatic transportation of the composite fermion around the Fermi surface. The Berry phase at half filling was found to have a Z2 character , supporting Son’s theory.
The Z2 phase was further confirmed on much larger system sizes by a fast Lattice Monte Carlo technique developed by us, based on our exact discretized lattice formulation of the continuum torus quantum Hall problems .
In an independent study , I generalized Son-Dirac theory from half filling to all other filling fractions motivated by the Berry phase studied in a one-quarter filled Landau level [Fig-1]. According to my theory, composite fermions at generic filling fractions are flux-attached Dirac fermions [Fig-2]. Same effective theory is proposed at the same time by H. Goldman and E. Fradkin [PRB.98.165137] from a different but complementary point of view.
Fig-2: Main theoretical results of Ref : illustration of my Dirac effective theory for composite Fermi liquids at all filling fractions.
My theory generalizes Son-Dirac theory (only for half filling) by internal gauge flux-attachment represented by 'a' in the effective theory. 'eta' and 'm' determines the filling fraction.