Abstract
We investigated the non-universal part of the orbital entanglement spectrum (OES) of the ν = 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.
Highlights
Most condensed matter phases can be characterized using local order parameters
We show that the higher energy levels in the Coulomb orbital entanglement spectrum (OES) are organized into branches whose structure can be related to virtual particle-hole excitations that dress the simpler entanglement spectrum of the model ground-state that just characterizes the topological order of the Fractional Quantum Hall (FQH) state
The entanglement spectrum can be used to determine the universality class of realistic Hamiltonians in a topologically ordered phase: by identifying the state-count of the lowest-lying entanglement branch of the spectrum with the state-count of the conformal field theory (CFT) of an edge theory, we can in principle predict that the ground-state of the system lies in a certain topological phase
Summary
Most condensed matter phases (states of matter) can be characterized using local order parameters. In systems exhibiting the Fractional Quantum Hall (FQH) effect, the first topological phases to be experimentally realized, such an entanglement measure providing a single number does not provide a unique characterization of the many possible states that can occur. We show that the higher energy levels in the Coulomb OES are organized into branches whose structure can be related to virtual particle-hole excitations that dress the simpler entanglement spectrum of the model ground-state that just characterizes (in its purest form) the topological order of the FQH state. This interpolation explains the hierarchical structure observed in the OES.
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