Renormalization method for proving frustration-free local spin chains are gapped

Abstract

Key properties of a physical system depend on whether it is gapped, i.e. whether its spectral gap has a positive lower bound that is independent of system size. In quantum information theory, the question of whether a system is gapped has essential computational significance as well. Here, we introduce a rigorous renormalization method to prove that a spin chain is gapped. This approach exploits the fact that ground states of gapped systems exhibit decaying correlations. We apply the method to show that two interesting models are gapped, successfully completing proofs even where the previously established methods are inconclusive.

40 pages, 13 figures

References in corpus (3)

• Simple proof of equivalence between adiabatic quantum computation and the circuit model
• Spectral gaps of frustration-free spin systems with boundary
• Performance of the rigorous renormalization group for first order phase transitions and topological phases