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Improved bounds on the spectral gap above frustration free ground states of quantum spin chains

Wolfgang L Spitzer, Shannon Starr

math-pharXiv:math-ph/0212029

Abstract

In Nac2,Nac1 Nachtergaele obtained explicit lower bounds for the spectral gap above many frustration free quantum spin chains by using the ``martingale method''. We present simple improvements to his main bounds which allow one to obtain a sharp lower bound for the spectral gap above the spin-1/2 ferromagnetic XXZ chain. As an illustration of the method, we also calculate a lower bound for the spectral gap of the AKLT model, which is about 1/3 the size of the expected gap.

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