Wolfgang L. Spitzer, Shannon Starr
Improved Bounds on the Spectral Gap above Frustration Free Ground States of Quantum Spin Chains
(43K, AMS-TeX)

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.