Topological Entanglement Entropy of Realistic Quantum Hall States

Shiying Dong, Eduardo Fradkin, Robert G Leigh +1 more

Masudul Haque, O. S. Zozulya, Kareljan Schoutens +2 more

Barry Friedman, Gregory Levine

The entanglement entropy of the incompressible states of a realistic quantum Hall system is studied by direct diagonalization. The subdominant term to the area law, the topological entanglement entropy (which is believed to carry information about topologic order in the ground state), was extracted for filling factors $\ensuremath{\nu}=1/3$, $\ensuremath{\nu}=1/5$, and $\ensuremath{\nu}=5/2$. The results for $\ensuremath{\nu}=1/3$ and $\ensuremath{\nu}=1/5$ are consistent with the topological entanglement entropy for the Laughlin wave function. The $\ensuremath{\nu}=5/2$ state exhibits a topological entanglement entropy consistent with the Moore-Read wave function.

Barry Friedman, Gregory Levine

The entanglement entropy of the incompressible states of a realistic quantum Hall system in the second Landau level is studied by direct diagonalization. The subdominant term of the area law, the topological entanglement entropy, which is believed to carry information about topological order in the ground state, was extracted for filling factors ν = 12/5 and ν = 7/3. While it is difficult to make strong conclusions about ν = 12/5, the ν = 7/3 state appears to be very consistent with the topological entanglement entropy for the k = 4 Read–Rezayi state. The effect of finite thickness corrections to the Coulomb potential used in the direct diagonalization is also systematically studied.

Barry Friedman, Greg Levine

Ramanjit Sohal, Bo Han, Luiz H. Santos +1 more

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.