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The ground state of a class of noncritical 1D quantum spin systems can be approximated efficiently

Tobias J. Osborne
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Abstract

We study families H_n of 1D quantum spin systems, where n is the number of spins, which have a spectral gap ΔE between the ground-state and first-excited state energy that scales, asymptotically, as a constant in n. We show that if the ground state |Ω_m> of the hamiltonian H_m on m spins, where m is an O(1) constant, is locally the same as the ground state |Ω_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 quasi-adiabatic evolutions.

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Tobias J. Osborne. 2007-03-01. The ground state of a class of noncritical 1D quantum spin systems can be approximated efficiently. https://doi.org/10.1103/physreva.75.042306

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