Microscopic theory for nematic fractional quantum Hall effect

Abstract

We analyze various microscopic properties of the nematic fractional quantum Hall effect (FQHN) in the thermodynamic limit, and present necessary conditions required of the microscopic Hamiltonians for the nematic fractional quantum Hall effect to be robust. Analytical expressions for the degenerate ground state manifold, ground state energies, and gapless nematic modes are given in compact forms with the input interaction and the corresponding ground state structure factors. We relate the long wavelength limit of the neutral excitations to the guiding center metric deformation, and show explicitly the family of trial wave functions for the nematic modes with spatially varying nematic order near the quantum critical point. For short range interactions, the dynamics of the FQHN is completely determined by the long wavelength part of the ground state structure factor. The special case of the FQHN at ν = 1/3 is discussed with theoretical insights from the Haffnian parent Hamiltonian, leading to a number of rigorous statements and experimental implications.

Fractionalization and Dynamics of Anyons and Their Experimental Signatures in the ν=n+1/3 Fractional Quantum Hall State

“…The nematic FQH state, an experimentally observed phase where the quantum Hall plateau coexists with the anisotropic longitudinal transport at low temperature [29,46], is believed to result from the quadrupole excitations going soft at ν ¼ 2 þ 1=3 [47,48]. Its underlying microscopic mechanism, however, is still not fully understood [45,48]. Here, we show that the quadrupole excitations going soft results from Hamiltonians favoring unbound GQ pairs.…”

“…These are no longer Jack polynomials, but we know immediately from LEC that the entire branch of the magnetoroton mode lives in H G (i.e., zero energy states of Ĥg ). The quadrupole excitation at L ¼ 2 is also the zero energy state of the Haffnian Hamiltonian Ĥh [45]. With the V2bdy 1 interaction, the quadrupole excitation has higher energy because it consists of an unbound pair of GQs.…”

Gaffnian and Haffnian: Physical relevance of nonunitary conformal field theory for the incompressible fractional quantum Hall effect

“…The energetic competitions between the Haffnian and Gaffnian quasiholes thus give a unifying description of the dynamics of the Laughlin phase at the finite temperature. These include the nematic FQH phase [46,47,[57][58][59][60], which is a topological phase with nontrivial geometric properties, as well as potential fractionalization of the Laughlin quasiholes at finite temperature [47]. We also show that with realistic two-body interactions, there is generally no Haffnian-type ground state similar to the case of the Gaffnian state.…”

“…Given the uniqueness of the magnetoroton model wave functions, we show here that the quadrupole excitations are exact zero-energy states of the Haffnian model Hamiltonians, thus are states within H H topo . In contrast, the dipole excitations, as well as the single Laughlin quasielectron states, are exact zero-energy states of the Gaffnian model Hamiltonian, thus living within H G topo [46,47]. To see that, let us write the root configuration of the magnetoroton modes as follows [40]:…”

“…Even in this case, H H topo can still play a relevant physical role. It is the Hilbert space of the quadrupole excitations of the Laughlin phase, and there are both numerical and experimental evidence that the quadrupole excitations can go soft in the Laughlin phase [46,47,[57][58][59][60]. As long as the charge gap is maintained, the quantum phase still has a robust Hall conductance plateau, though finite-temperature transport can be modified by the quadrupole excitations, leading to the so-called nematic FQHE phase.…”