03-70 Wolfgang L. Spitzer, Shannon Starr

Improved Bounds on the Spectral Gap above Frustration Free Ground States of Quantum Spin Chains (43K, AMS-TeX) Feb 22, 03

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Abstract. In \cite{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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