Emergence of Jack ground states from two-body pseudopotentials in fractional quantum Hall systems

Abstract

The family of "Jack states" related to antisymmetric Jack polynomials are the exact zero-energy ground states of particular model short-range many-body repulsive interactions, defined by a few non-vanishing leading pseudopotentials. Some Jack states are known or anticipated to accurately describe many-electron incompressible ground states emergent from the two-body Coulomb repulsion in fractional quantum Hall effect. By extensive numerical diagonalization we demonstrate emergence of Jack states from suitable pair interactions. We find empirically a simple formula for the optimal two-body pseudopotentials for the series of most prominent Jack states generated by contact manybody repulsion. Furthermore, we seek realization of arbitrary Jack states in realistic quantum Hall systems with Coulomb interaction, i.e., in partially filled lowest and excited Landau levels in quasi-two-dimensional layers of conventional semiconductors like GaAs or in graphene.

Fractional quantum Hall effect at ν=2+4/9

“…The pseudopotentials {V m } (V m denotes the energy penalty for placing two particles in the relative angular momentum m state) of CFs [12,[16][17][18][19][20][21] indicate that the residual interaction between two CFs occupying the SΛL in the presence of the filled lowest ΛL (LΛL) is hollow-core like, i.e., the interaction is dominated by a strong repulsion in the m = 3 channel. For comparison, the Coulomb interaction between electrons in the LLL, which stabilizes the 1/5 Laughlin state [22][23][24], is dominated by the hardcore V 1 pseudopotential. Thus, for interactions where V 3 V m ∀m = 3, the case realized for CFs in the SΛL, it is not clear if the 1/5 Laughlin state could be stabilized.…”

Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond

“…Taken together with our previous works [35,63], the results presented in this Rapid Communication suggest that almost all fractional quantum Hall states observed in the second Landau level of GaAs could be described by then21 3 orn2 2 1 4 parton ansatz, with n = 1, 2, 3, or their particle-hole conjugates. The states observed in the second LL that do not fall in these sequences or their particle-hole conjugates, e.g., at filling factor 1/5 and 2/7, are likely well described by composite fermion states [16,51] (which are also parton states). In all, except for the lowest Landau level states at ν = 4/11 and 5/13 (see, e.g., Refs.…”

“…(2)], and the ground state obtained by exact diagonalization using the SLL Coulomb pseudopotentials SLL 2/5 . The numbers for | were previously given in Refs [5,6,20,23,51]…”

Automatic design of Hamiltonians

“…The possibility to produce the approximation to the RR state as a ground state of a twobody Hamiltonian has been discussed in literature recently [26,27]. In ref.…”

“…In ref. [26] an extensive parameter scan of the 3 lowest pseudopotentials (V 1 , V 3 , V 5 ) was performed and in Ref. [27] an analytic mean-field calculation.…”