Equality of bulk wave functions and edge correlations in topological superconductors: A spacetime derivation

Abstract

For certain systems, the N-particle ground-state wavefunctions of the bulk happen to be exactly equal to the N-point space-time correlation functions at the edge, in the infrared limit. We show why this had to be so for a class of topological superconductors, beginning with the p+ip state in D=2+1. Varying the chemical potential as a function of Euclidean time between weak and strong pairing states is shown to extract the wavefunction. Then a Euclidean rotation that exchanges time and space and approximate Lorentz invariance lead to the edge connection. We illustrate straightforward extension to other dimensions (eg. 3He- B phase in D=3+1) and to correlated states like fractionalized topological superconductors.

4 pages + 1 page Appendix. 1 Figure

References in corpus (9)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Non-Abelian Anyons and Topological Quantum Computation
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
• Fractional topological insulators in three dimensions
• Lattice model of three-dimensional topological singlet superconductor with time-reversal symmetry

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