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The question concerns the topology and dimensions of Helium 3A and 3B

A. The Helium 3A phase shows the same low energy excitations as those of a 2 spatial dimensional chiral p-wave superconductor --- with the half-quantum vortex in a chiral p-wave superconductor of spinful fermions (as the order parameter of A phase of 3He). The chiral p-wave superconductor is a gapped long range entangled state with topological order.

B. The Helium 3B phase shows the nature of 3 spatial dimensional topological superconductor (TSC) with time reversal symmetry $T^2=(-1)^f$. The TSC is a gapped short range entangled state protected by the time reversal symmetry known as symmetry protected order.

questions

  • (Why) are Helium 3A and 3B are realized in different dimensions? 2 spatial vs. 3 spatial dimensions? Should they live in the same phase diagram with the same dimensions?

  • Why are Helium 3A and 3B have realized different long vs short range entanglement?

See ref for a statement on Helium 3A.

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