Stability of Gapped Ground State Phases of Spins and Fermions in One Dimension

Abstract

We investigate the persistence of spectral gaps of one-dimensional frustration free quantum lattice systems under weak perturbations and with open boundary conditions. Assuming the interactions of the system satisfy a form of local topological quantum order, we prove explicit lower bounds on the ground state spectral gap and higher gaps for spin and fermion chains. By adapting previous methods using the spectral flow, we analyze the bulk and edge dependence of lower bounds on spectral gaps.

arXiv commentVersion published in J. Math. Phys

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• Stability of the spectral gap and ground state indistinguishability for a decorated AKLT model
• Dynamical Phase Error in Interacting Topological Quantum Memories
• Lie-Schwinger block-diagonalization and gapped quantum chains: analyticity of the ground-state energy