Gershgorin gap bound for an adiabatic history path
= Gershgorin gap bound for an adiabatic history path
{c}
{title2=$\Delta(M(s))\geq1-2s$}
For $M(s)=(1-s)D+sE$ in the unary history subspace, the first <Gershgorin disc> lies in $[0,s]$ and every other disc has real part at least $1-s$. For $s<1/2$, the first disc is isolated and contains the unique <ground state> energy. Thus the <spectral gap> is at least $1-2s$, in particular at least $1/3$ for $s\leq1/3$.