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We propose an experiment to identify the topological order of the $ u=frac{5}{2}$ state through a measurement of the electric conductance of a mesoscopic device. Our setup is based on interfacing $ u=2, frac{5}{2}$ and $3$ in the same device. Its conductance can unambiguously establish or rule out the particle-hole symmetric Pfaffian topological order, which is supported by recent thermal measurements. Additionally, it distinguishes between the Moore-Read and Anti-Pfaffian topological orders, which are favored by numerical calculations.
The topological order is equivalent to the pattern of long-range quantum entanglements, which cannot be measured by any local observable. Here we perform an exact diagonalization study to establish the non-Abelian topological order through entangleme
We present the quantitative phase diagram of the bilayer bosonic fractional quantum Hall system on the torus geometry at total filling factor $ u=1$ in the lowest Landau level. We consider short-range interactions within and between the two layers, a
The Landau description of phase transitions relies on the identification of a local order parameter that indicates the onset of a symmetry-breaking phase. In contrast, topological phase transitions evade this paradigm and, as a result, are harder to
In this short paper, we argue that the chiral central charge $c_-$ of a (2+1)d topological ordered state is sometimes strongly constrained by t Hooft anomaly of anti-unitary global symmetry. For example, if a (2+1)d fermionic TQFT has a time reversal
We present the first numerical computation of the neutral fermion gap, $Delta_psi$, in the $ u=5/2$ quantum Hall state, which is analogous to the energy gap for a Bogoliubov-de Gennes quasiparticle in a superconductor. We find $Delta_psi approx 0.027