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

We study families H-n of one-dimensional (1D) quantum spin systems, where n is the number of spins, which have a spectral gap Delta E between the ground-state and first-excited state energy that scales, asymptotically, as a constant in n. We show that if the ground state parallel to Omega(m)> of the Hamiltonian H-m on m spins, where m is an O(1) constant, is locally the same as the ground state parallel to Omega(n)>, for arbitrarily large n, then an arbitrarily good approximation to the ground state of H-n 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.