We show here that an extension of the Hamiltonian theory developed by us over the years furnishes a composite fermion (CF) description of the ν=1/2 state that is particle-hole (PH) symmetric, has a charge density that obeys the magnetic translation algebra of the lowest Landau level (LLL), and exhibits cherished ideas from highly successful wave functions, such as a neutral quasiparticle with a certain dipole moment related to its momentum. We also a provide an extension away from ν=1/2, which has the features from ν=1/2 and implements the PH transformation on the LLL as an antiunitary operator T with T2=-1. This extension of our past work was inspired by Son, who showed that the CF may be viewed as a Dirac fermion on which the particle-hole transformation of LLL electrons is realized as time-reversal, and Wang and Senthil, who provided a very attractive interpretation of the CF as the bound state of a semion and antisemion of charge ±e/2. Along the way, we also found a representation with all the features listed above except that now T2=+1. We suspect it corresponds to an emergent charge-conjugation symmetry of the μ=1 boson problem analyzed by Read.
|Physical Review B
|Published - Feb 2 2016
Bibliographical noteFunding Information:
We are grateful to Son for extended discussions at the Aspen Center for Physics. We thank Senthil for sharing with us his work with Wang and the physical picture in terms of semions. His input, through extensive email and phone communications, was crucial to our understanding of the central issues. R.S. thanks Ashvin Viswanath for conversations. We thank the Aspen Center for Physics, where this work was conceived and completed, and which is supported by National Science Foundation Grant PHY-1066293. Murthy also acknowledges partial support from the NSF via DMR-1306897 (G.M.) and from the US-Israel Binational Science Foundation via Grant No. 2012120.
© 2016 American Physical Society.
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics