Hierarchical structure in the orbital entanglement spectrum in Fractional Quantum Hall systems

TL;DR

This paper explores the hierarchical structure of the orbital entanglement spectrum in fractional quantum Hall systems, revealing connections to excitation structures and energy gaps through modeling and thermodynamical analysis.

Contribution

It uncovers a hierarchical organization in the orbital entanglement spectrum of Coulomb ground states, linking it to excitation energies and finite-temperature spectra using composite fermion models.

Findings

Hierarchical structure mimics excitation-energy levels

Good modeling with Jain's composite fermion wavefunctions

Thermodynamical OES matches Coulomb OES, indicating a relation to energy gaps

Abstract

We investigate the non-universal part of the orbital entanglement spectrum (OES) of the nu = 1/3 fractional quantum Hall effect (FQH) ground-state with 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 find that the OES levels of the Coulomb interaction ground-state are organized in a hierarchical structure that mimic 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 wavefunctions. To emphasize the connection between the entanglement spectrum and the energy spectrum, we also consider the thermodynamical OES of the model pseudopotential Hamiltonian at finite temperature. The observed good match between the thermodynamical OES and the Coulomb OES suggests a relation between the entanglement gap and the true energy gap.