In two dimensions strongly interacting bosons in a magnetic field can form an integer quantum Hall state. This state has a bulk gap, no fractional charges or topological order in the bulk, but nevertheless quantized Hall transport and symmetry-protected edge excitations. Here we study a simple microscopic model for such a state in a system of two-component bosons in a strong orbital magnetic field. We show through exact-diagonalization calculations that the model supports the boson integer quantum Hall ground state in a range of parameters.In two dimensions strongly interacting bosons in a magnetic field can form an integer quantum Hall state. This state has a bulk gap, no fractional charges or topological order in the bulk, but nevertheless quantized Hall transport and symmetry-protected edge excitations. Here we study a simple microscopic model for such a state in a system of two-component bosons in a strong orbital magnetic field. We show through exact-diagonalization calculations that the model supports the boson integer quantum Hall ground state in a range of parameters.

arXiv:1305.0298Physical Review BOct 22, 201362 citations

Theory of the Fractional Quantum Hall Effect

Allan H. MacDonald

Recent Progress in Many-Body TheoriesJan 1, 19880 citations

Ground State for Fractional Quantum Hall Effect

Ahmed Jellal

International Journal of Theoretical PhysicsFeb 1, 20000 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

Non-Abelian S U ( N − 1 ) -singlet fractional quantum Hall states from coupled wires

Yohei Fuji, P. Lecheminant

The construction of fractional quantum Hall (FQH) states from the two-dimensional array of quantum wires provides a useful way to control strong interactions in microscopic models and has been successfully applied to the Laughlin, Moore-Read, and Read-Rezayi states. We extend this construction to the Abelian and non-Abelian $SU(N\ensuremath{-}1)$-singlet FQH states at filling fraction $\ensuremath{\nu}=k(N\ensuremath{-}1)/[N+k(N\ensuremath{-}1)m]$ labeled by integers $k$ and $m$ , which are potentially realized in multicomponent quantum Hall systems or $SU(N)$ spin systems. Utilizing the bosonization approach and conformal field theory (CFT), we show that their bulk quasiparticles and gapless edge excitations are both described by an $(N\ensuremath{-}1)$-component free-boson CFT and the $SU{(N)}_{k}/{[U(1)]}^{N\ensuremath{-}1}$ CFT known as the Gepner parafermion. Their generalization to different filling fractions is also proposed. In addition, we argue possible applications of these results to two kinds of lattice systems: bosons interacting via occupation-dependent correlated hoppings and an $SU(N)$ Heisenberg model.The construction of fractional quantum Hall (FQH) states from the two-dimensional array of quantum wires provides a useful way to control strong interactions in microscopic models and has been successfully applied to the Laughlin, Moore-Read, and Read-Rezayi states. We extend this construction to the Abelian and non-Abelian $SU(N\ensuremath{-}1)$-singlet FQH states at filling fraction $\ensuremath{\nu}=k(N\ensuremath{-}1)/[N+k(N\ensuremath{-}1)m]$ labeled by integers $k$ and $m$, which are potentially realized in multicomponent quantum Hall systems or $SU(N)$ spin systems. Utilizing the bosonization approach and conformal field theory (CFT), we show that their bulk quasiparticles and gapless edge excitations are both described by an $(N\ensuremath{-}1)$-component free-boson CFT and the $SU{(N)}_{k}/{[U(1)]}^{N\ensuremath{-}1}$ CFT known as the Gepner parafermion. Their generalization to different filling fractions is also proposed. In addition, we argue possible applications of these results to two kinds of lattice systems: bosons interacting via occupation-dependent correlated hoppings and an $SU(N)$ Heisenberg model.

arXiv:1611.07968Physical review. B./Physical review. BMar 24, 201738 citations

Fractional Quantum Hall Effect: Recent Developments

R. Morf

NATO ASI series. Series B : PhysicsJan 1, 19890 citations

k

and

m

, which are potentially realized in multicomponent quantum Hall systems or

SU(N)

spin systems. Utilizing the bosonization approach and conformal field theory (CFT), we show that their bulk quasiparticles and gapless edge excitations are both described by an $(N\ensuremath{-}1)$-component free-boson CFT and the $SU{(N)}_{k}/{[U(1)]}^{N\ensuremath{-}1}$ CFT known as the Gepner parafermion. Their generalization to different filling fractions is also proposed. In addition, we argue possible applications of these results to two kinds of lattice systems: bosons interacting via occupation-dependent correlated hoppings and an

SU(N)

Heisenberg model.