Topological Entropy of Quantum Hall States in Rotating Bose Gases

TL;DR

This paper calculates the topological entropy of Laughlin and Pfaffian quantum Hall states in rotating Bose gases using numerical diagonalization, confirming theoretical predictions for their topological properties.

Contribution

It introduces a method to compute topological entropy in rotating Bose gases by tracing over single-particle orbitals and performs finite-size scaling analysis.

Findings

Topological entropy for Laughlin state is approximately ln(√2).

Topological entropy for Pfaffian state is approximately ln(√4).

Results agree with theoretical expectations.

Abstract

Through exact numerical diagonalization, the von Neumann entropy is calculated for the Laughlin and Pfaffian quantum Hall states in rotating interacting Bose gases at zero temperature in the lowest Landau level limit. The particles comprising the states are indistinguishable, so the required spatial bipartitioning is effected by tracing over a subset of single-particle orbitals. The topological entropy is then extracted through a finite-size scaling analysis. The results for the Laughlin and the Pfaffian states agree with the expected values of $\ln\sqrt{2}$ and $\ln\sqrt{4}$, respectively.