Boundary supersymmetry of 1+1 d fermionic SPT phases

TL;DR

This paper proves that boundaries of all non-trivial 1+1D fermionic SPT phases with finite symmetries inherently exhibit supersymmetry, stemming from boundary anomalies, without fine-tuning the Hamiltonian.

Contribution

It establishes a universal link between boundary anomalies of fermionic SPT phases and emergent supersymmetry, revealing a fundamental property of these topological phases.

Findings

Boundaries are supersymmetric quantum systems.

Supersymmetry arises from boundary 't Hooft anomalies.

No fine-tuning needed for supersymmetry to emerge.

Abstract

We prove that the boundaries of all non-trivial 1+1 dimensional intrinsically fermionic symmetry-protected-topological phases, protected by finite on-site symmetries (unitary or anti-unitary), are supersymmetric quantum mechanical systems. This supersymmetry does not require any fine-tuning of the underlying Hamiltonian, arises entirely as a consequence of the boundary 't Hooft anomaly that classifies the phase and is related to a `Bose-Fermi' degeneracy different in nature from other well known degeneracies such as Kramers doublets.