The topological entanglement entropy is a robust measurement of the quantum many-body state with topological order. In fractional quantum Hall (FQH) state, it has a connection to the quantum dimension of the state itself and its quasihole excitations from the conformal field theory (CFT) description. We systematically study the entanglement entropy in the Laughlin, Moore-Read, and Read-Rezayi FQH states. The Abelian nature of the quasihole manifests in the invariant of the entanglement entropy and spectrum while it is created in the subsystem. Whereas the non-Abelian quasihole excitation induces an extra correction of the topological entanglement entropy and the changing of the structure of the entanglement spectrum. The quantum dimension of the quasihole can be obtained from the entropy difference before and after inserting the quasihole. On the other hand, the entanglement entropy behaviors similarly to the density profile and has less oscillations far away from the center of quasihole. It gives us a better definition of the quasihole boundary and the measurement of the size of the quasihole.
We present analytic and numerical calculations on the bipartite entanglement entropy in fractional quantum Hall states of the fermionic Laughlin sequence. The partitioning of the system is done both by dividing Landau-level orbitals and by grouping the fermions themselves. For the case of orbital partitioning, our results can be related to spatial partitioning, enabling us to extract a topological quantity (the "total quantum dimension") characterizing the Laughlin states. For particle partitioning we prove a very close upper bound for the entanglement entropy of a subset of the particles with the rest, and provide an interpretation in terms of exclusion statistics.
We present a detailed analysis of bipartite entanglement in the non-Abelian Moore-Read fractional quantum Hall state of bosons and fermions on the torus. In particular, we show that the entanglement spectra can be decomposed into intricate combinations of different sectors of the conformal field theory describing the edge physics, and that the edge level counting and tower structure can be microscopically understood by considering the vicinity of the thin-torus limit. We also find that the boundary entropy density of the Moore-Read state is markedly higher than in the Laughlin states investigated so far. Despite the torus geometry being somewhat more involved than in the sphere geometry, our analysis and insights may prove useful when adopting entanglement probes to other systems that are more easily studied with periodic boundary conditions, such as fractional Chern insulators and lattice problems in general.
Using the newly developed matrix product state formalism for non-Abelian fractional quantum Hall (FQH) states, we address the question of whether a FQH trial wave function written as a correlation function in a nonunitary conformal field theory (CFT) can describe the bulk of a gapped FQH phase. We show that the nonunitary Gaffnian state exhibits clear signatures of a pathological behavior. As a benchmark we compute the correlation length of a Moore-Read state and find it to be finite in the thermodynamic limit. By contrast, the Gaffnian state has an infinite correlation length in (at least) the non-Abelian sector, and is therefore gapless. We also compute the topological entanglement entropy of several non-Abelian states with and without quasiholes. For the first time in the FQH effect the results are in excellent agreement in all topological sectors with the CFT prediction for unitary states. For the nonunitary Gaffnian state in finite size systems, the topological entanglement entropy seems to behave like that of the composite fermion Jain state at equal filling.
We theoretically examine entanglement in fractional quantum hall states, explicitly taking into account and emphasizing the quasi-two-dimensional nature of experimental quantum Hall systems. In particular, we study the entanglement entropy and the entanglement spectrum as a function of the finite layer thickness,
d, of the quasi-two-dimensional system for a number of filling fractions $\ensuremath{\nu}$ in the lowest and the second Landau levels: $\ensuremath{\nu}$ = 1/3, 7/3, 1/2, and 5/2. We observe that the entanglement measures are dependent on which Landau level the electrons fractionally occupy, and find that filling fractions 1/3 and 7/3, which are considered to be Laughlin states, weaken with
d in the lowest Landau level ($\ensuremath{\nu}=1/3$) and strengthen with
d in the second Landau level ($\ensuremath{\nu}=7/3$). For the enigmatic even-denominator $\ensuremath{\nu}=5/2$ state, we find that entanglement in the ground state is consistent with that of the non-Abelian Moore-Read Pfaffian state at an optimal thickness,
d. We also find that the single-layer $\ensuremath{\nu}=1/2$ system is not a fractional quantum Hall state consistent with the experimental observation. In general, our theoretical findings based on entanglement considerations are completely consistent with the results based on wave-function overlap calculations.
Topologically ordered phases of matter can be characterized by the presence of a universal, constant contribution to the entanglement entropy known as the topological entanglement entropy (TEE). The TEE can be calculated for Abelian phases via a ``cut-and-glue'' approach by treating the entanglement cut as a physical cut, coupling the resulting gapless edges with explicit tunneling terms, and computing the entanglement between the two edges. We provide a first step towards extending this methodology to non-Abelian topological phases, focusing on the generalized Moore-Read (MR) fractional quantum Hall states at filling fractions $\ensuremath{\nu}=1/n$. We consider interfaces between different MR states, write down explicit gapping interactions, which we motivate using an anyon condensation picture, and compute the entanglement entropy for an entanglement cut lying along the interface. Our work provides new insight towards understanding the connections between anyon condensation, gapped interfaces of non-Abelian phases, and TEE.