We consider the fractional quantum Hall effect at the filling factor $\ensuremath{\nu}=4/11$, where two independent experiments have observed a well-developed and quantized Hall plateau. We examine the Abelian state described by the `` $4\overline{2}{1}^{3}$ '' parton wave function and numerically demonstrate it to be a plausible candidate for the ground state at $\ensuremath{\nu}=4/11$. We work out the low-energy effective theory of the $4\overline{2}{1}^{3}$ edge and make predictions for experimentally measurable properties of the state.We consider the fractional quantum Hall effect at the filling factor $\ensuremath{\nu}=4/11$, where two independent experiments have observed a well-developed and quantized Hall plateau. We examine the Abelian state described by the ``$4\overline{2}{1}^{3}$'' parton wave function and numerically demonstrate it to be a plausible candidate for the ground state at $\ensuremath{\nu}=4/11$. We work out the low-energy effective theory of the $4\overline{2}{1}^{3}$ edge and make predictions for experimentally measurable properties of the state.

arXiv:2102.04414Physical review. B./Physical review. BApr 1, 202122 citations

Theory of the Fractional Quantum Hall Effect

Allan H. MacDonald

Recent Progress in Many-Body TheoriesJan 1, 19880 citations

A non-Abelian parton state for the $ν=2+3/8$ fractional quantum Hall effectA non-Abelian parton state for the $ν=2+3/8$ fractional quantum Hall effect

Ajit Coimbatore Balram

Fascinating structures have arisen from the study of the fractional quantum Hall effect (FQHE) at the even denominator fraction of 5/2 5 / 2 . We consider the FQHE at another even denominator fraction, namely \nu=2+3/8 ν = 2 + 3 / 8 , where a well-developed and quantized Hall plateau has been observed in experiments. We examine the non-Abelian state described by the `` \bar{3}\bar{2}^{2}1^{4} 3 ‾ 2 ‾ 2 1 4 " parton wave function and numerically demonstrate it to be a feasible candidate for the ground state at \nu=2+3/8 ν = 2 + 3 / 8 . We make predictions for experimentally measurable properties of the \bar{3}\bar{2}^{2}1^{4} 3 ‾ 2 ‾ 2 1 4 state that can reveal its underlying topological structure.Fascinating structures have arisen from the study of the fractional quantum Hall effect (FQHE) at the even denominator fraction of 5/2 5 / 2 . We consider the FQHE at another even denominator fraction, namely \nu=2+3/8 ν = 2 + 3 / 8 , where a well-developed and quantized Hall plateau has been observed in experiments. We examine the non-Abelian state described by the `` \bar{3}\bar{2}^{2}1^{4} 3 ‾ 2 ‾ 2 1 4 " parton wave function and numerically demonstrate it to be a feasible candidate for the ground state at \nu=2+3/8 ν = 2 + 3 / 8 . We make predictions for experimentally measurable properties of the \bar{3}\bar{2}^{2}1^{4} 3 ‾ 2 ‾ 2 1 4 state that can reveal its underlying topological structure.

arXiv:2010.08965SciPost PhysicsApr 15, 202132 citations

Crossover from integer to fractional quantum Hall effect

Koji Kudo, Jonathan Schirmer, Jainendra K. Jain

The parton theory constructs candidate fractional quantum Hall states by decomposing the physical particles into unphysical partons, placing the partons in integer quantum Hall states, and then gluing the partons back into the physical particles. Field theoretical formulations execute the gluing process through the device of emergent gauge fields. Here we study numerically the process of going from the integer quantum Hall effect of two species of fermionic partons to the fractional quantum Hall effect of bosons by introducing an attractive interaction between the fermions of different species and continuously increasing its strength to glue them into bosons. To properly capture the physics in the bulk, we implement this process in a lattice version of the spherical geometry, which allows us to keep the full Hilbert space. Even though the two end-point states are topologically distinct, we find that, for the small system sizes accessible to our study, the energy gap remains open, indicating a crossover between these two states.The parton theory constructs candidate fractional quantum Hall states by decomposing the physical particles into unphysical partons, placing the partons in integer quantum Hall states, and then gluing the partons back into the physical particles. Field theoretical formulations execute the gluing process through the device of emergent gauge fields. Here we study numerically the process of going from the integer quantum Hall effect of two species of fermionic partons to the fractional quantum Hall effect of bosons by introducing an attractive interaction between the fermions of different species and continuously increasing its strength to glue them into bosons. To properly capture the physics in the bulk, we implement this process in a lattice version of the spherical geometry, which allows us to keep the full Hilbert space. Even though the two end-point states are topologically distinct, we find that, for the small system sizes accessible to our study, the energy gap remains open, indicating a crossover between these two states.

arXiv:2401.06965Physical review. B./Physical review. BFeb 26, 20240 citations

4\overline{2}{1}^{3}

'' parton wave function and numerically demonstrate it to be a plausible candidate for the ground state at $\ensuremath{\nu}=4/11$. We work out the low-energy effective theory of the

4\overline{2}{1}^{3}

edge and make predictions for experimentally measurable properties of the state.

A non-Abelian parton state for the

ν=2+3/8

fractional quantum Hall effect