The hierarchical structure in the orbital entanglement spectrum of fractional quantum Hall systems

Abstract

We investigated the non-universal part of the orbital entanglement spectrum (OES) of the nu = 1/3 fractional quantum Hall (FQH) effect ground state using Coulomb interactions. The non-universal part of the spectrum is the part that is missing in the Laughlin model state OES, whose level counting is completely determined by its topological order. We found that the OES levels of the Coulomb interaction ground state are organized in a hierarchical structure that mimics the excitation-energy structure of the model pseudopotential Hamiltonian, which has a Laughlin ground state. These structures can be accurately modeled using Jain’s ‘composite fermion’ quasihole-quasiparticle excitation wave functions. To emphasize the connection between the entanglement spectrum and the energy spectrum, we also considered the thermodynamical OES of the model pseudopotential Hamiltonian at the finite temperature. The good match observed between the thermodynamical OES and the Coulomb OES suggests that there is a relation between the entanglement gap and the true energy gap.