Speaker
Description
The formalism for composite fermions, initially developed for bosons at filling factor ν = 1 [1, 2], has been a cornerstone in understanding the fractional quantum Hall effect (FQHE). We derive the Dirac composite fermion theory for a half-filled Landau level from first principles [3]. In this talk, we present novel insights into this phenomenon by employing a dipole representation for composite fermions that incorporates the symmetry under particle-hole exchange. By imposing a unique constraint on the degrees of freedom of composite fermions and composite holes within an enlarged space, we ensure that the resulting composite particles, known as dipoles, possess symmetric characteristics. Our investigation focuses on an effective Hamiltonian that commutes with the constraint in physical space while preserving boost invariance at the Fermi level. Remarkably, our calculations [4] of the Fermi liquid parameter F2 demonstrate remarkable agreement with previous numerical investigations [5].
Furthermore, we investigate the phase diagram of the quantum Hall bilayer (QHB) system at total filling factor ν = 1, where physics at small interlayer distances is understood in terms of Bose-Einstein condensation (BEC), while at large distances, physics is mostly understood in terms of fermionic condensation. We have now shown that composite fermions offer an accurate description of the system for all distances [6].
[1] N. Read, Phys. Rev. B 58, 16262 (1998).
[2] Z. Dong and T. Senthil, Phys. Rev. B 102, 205126 (2020).
[3] D. Gočanin, S. Predin, M. D. Ćirić, V. Radovanović, and M. Milovanović, Phys. Rev. B 104, 115150 (2021).
[4] S. Predin, A. Knežević , and M. V. Milovanović, Phys. Rev. B 107, 155132 (2023).
[5] K. Lee, J. Shao, E.-A. Kim, F. D. M. Haldane, and E. H. Rezayi, Phys. Rev. Lett. 121, 147601 (2018).
[6] S. Predin, and M. Milovanovic, to be appeared.
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