一类一维非临界量子自旋系统的基态可以有效地近似
The ground state of a class of noncritical 1D quantum spin systems can be approximated efficiently
摘要：
研究了一维量子自旋系统族H_n，其中n是自旋数，在基态和第一激发态能量之间存在一个谱隙ΔE，该谱隙渐近地以n为常数.我们证明了如果基态|当m为O（1）常数时，m自旋上的哈密顿量H_m的Ω_m>与基态局域相同|Ω_n>，则对任意大的n，H_n的基态的任意好的近似可以有效地存储。我们提出了一个猜想，如果这个猜想成立的话，就意味着我们的结果适用于所有非临界的一维自旋系统。我们还包括一个附录准绝热演化。
英文摘要：
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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