The ground-state energy of gapped quantum chains with form-bounded short-range interactions is analytic in the coupling constant in a fixed disk independent of chain length, and the thermodynamic-limit energy per site is analytic under translation invariance.
The Stability of Free Fermi Hamiltonians
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abstract
Recent results have shown the stability of frustration-free Hamiltonians to weak local perturbations, assuming several conditions. In this paper, we prove the stability of free fermion Hamiltonians which are gapped and local. These free fermion Hamiltonians are not necessarily frustration-free, but we are able to adapt previous work to prove stability. The key idea is to add an additional copy of the system to cancel topological obstructions. We comment on applications to quantization of Hall conductance in such systems.
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Lie-Schwinger block-diagonalization and gapped quantum chains: analyticity of the ground-state energy
The ground-state energy of gapped quantum chains with form-bounded short-range interactions is analytic in the coupling constant in a fixed disk independent of chain length, and the thermodynamic-limit energy per site is analytic under translation invariance.