A Renormalized-Hamiltonian-Flow Approach to Eigenenergies and Eigenfunctions *

Wen-Ge Wang

Fig. 2 Variation of $|E^{(n)}-E|$ (circles connected by dashed lines) with $E$ for $n=5$, the parameters $N=300$, $b=100$, $\lambda =10$, and $E=247+0.06m$ with $m=1,2,\ldots , 100$. At each step of the renormalized Hamiltonian flow, 30 basis states are decimated. Within the energy region shown in this figure, the original Hamiltonian has three eigenenergies with positions indicated by the three vertical dotted lines. Approximate values of the eigenenergies can be get from extrapolation of the circles close to the local minima of $|E^{(n)}-E|$.