Ground state of a class of noncritical one-dimensional quantum spin systems can be approximated efficiently

We study families H₍ of one-dimensional (1D) quantum spin systems, where n is the number of spins, which have a spectral gap between the ground-state and first-excited state energy that scales, asymptotically, as a constant in n. We show that if the ground state ₌⟩ of the Hamiltonian H₌ on m spins, where m is an O (1) constant, is locally the same as the ground state ₍⟩, for arbitrarily large n, then an arbitrarily good approximation to the ground state of H₍ can be stored efficiently for all n. We formulate a conjecture that, if true, would imply our result applies to all noncritical 1D spin systems. We also include an appendix on quasiadiabatic evolutions.