Interactions are crucial in driving topological phenomena in bosonic systems. Here, the authors construct exactly solvable models of topological phases of interacting bosons that preserve electric charge. They focus on the ${E}_{8}$ bosonic integer quantum Hall state and show how its intrinsic ${E}_{8}$ symmetry allows for the emergence of fractional topological phases of bosons. They detail the charge and statistics of the quasiparticle excitations of the resulting fractional quantum Hall states.Interactions are crucial in driving topological phenomena in bosonic systems. Here, the authors construct exactly solvable models of topological phases of interacting bosons that preserve electric charge. They focus on the ${E}_{8}$ bosonic integer quantum Hall state and show how its intrinsic ${E}_{8}$ symmetry allows for the emergence of fractional topological phases of bosons. They detail the charge and statistics of the quasiparticle excitations of the resulting fractional quantum Hall states.

arXiv:2212.14559Physical review. B./Physical review. BJul 18, 20232 citations

Higher stability filling fractions in the hierarchy theory of the fractional quantum Hall effect

Jian Cheng Yang, W. P. Su

The effective partition function of a fractional quantum Hall system, which is described by the Laughlin quasiparticle wave function, is obtained in the path-integral representation. It shows that the quasiparticles cannot be treated as ordinary anyons in view of the freeze of the kinetic energy and the ``bosonic aspect'' of the Hilbert space. By using the constrained anyon systems, we find that one type of filling fractions is more stable than other fractions predicted by the standard hierarchy theory. This work also sheds considerable light on the possible equivalence between the hierarchy theory and the composite-fermion approach proposed by Jain recently.The effective partition function of a fractional quantum Hall system, which is described by the Laughlin quasiparticle wave function, is obtained in the path-integral representation. It shows that the quasiparticles cannot be treated as ordinary anyons in view of the freeze of the kinetic energy and the ``bosonic aspect'' of the Hilbert space. By using the constrained anyon systems, we find that one type of filling fractions is more stable than other fractions predicted by the standard hierarchy theory. This work also sheds considerable light on the possible equivalence between the hierarchy theory and the composite-fermion approach proposed by Jain recently.

Physical Review LettersApr 13, 19927 citations

Fractionalization via Z2 Gauge Fields at a Cold-Atom Quantum Hall Transition

Yafis Barlas, Kun Yang

We study a single species of fermionic atoms in an "effective" magnetic field at total filling factor ν(f)=1, interacting through a p-wave Feshbach resonance, and show that the system undergoes a quantum phase transition from a ν(f)=1 fermionic integer quantum Hall state to ν(b)=1/4 bosonic fractional quantum Hall state as a function of detuning. The transition is in the (2+1)D Ising universality class. We formulate a dual theory in terms of quasiparticles interacting with a Z(2) gauge field and show that charge fractionalization follows from this topological quantum phase transition. Experimental consequences and possible tests of our theoretical predictions are discussed.We study a single species of fermionic atoms in an "effective" magnetic field at total filling factor ν(f)=1, interacting through a p-wave Feshbach resonance, and show that the system undergoes a quantum phase transition from a ν(f)=1 fermionic integer quantum Hall state to ν(b)=1/4 bosonic fractional quantum Hall state as a function of detuning. The transition is in the (2+1)D Ising universality class. We formulate a dual theory in terms of quasiparticles interacting with a Z(2) gauge field and show that charge fractionalization follows from this topological quantum phase transition. Experimental consequences and possible tests of our theoretical predictions are discussed.

arXiv:1012.0046Physical Review LettersApr 29, 20113 citations

Strong Fermion Interactions in Fractional Quantum Hall States

S. B. Mulay, John J. Quinn, Mark Shattuck

Springer series in solid-state sciencesJan 1, 20180 citations

{E}_{8}

bosonic integer quantum Hall state and show how its intrinsic

{E}_{8}

symmetry allows for the emergence of fractional topological phases of bosons. They detail the charge and statistics of the quasiparticle excitations of the resulting fractional quantum Hall states.