Energy renormalization-group method for electronic structure of large systems

A renormalization-group method for electronic structure of large systems within a tight-binding framework is presented. A telescopic series of nested Hilbert spaces is constructed, having exponentially decreasing dimensions and electrons. The Hamiltonian matrices have exponentially converging energy ranges focusing to the Fermi level. The computational effort scales near linearly with system size even when the density matrix is highly nonlocal. This is illustrated by calculations on a model metal and a metallic finite carbon nanotube, for which standard linear scaling methods are inapplicable.