Controlled Bond Expansion for Density Matrix Renormalization Group Ground State Search at Single-Site Costs

Abstract

DMRG ground state search algorithms employing symmetries must be able to expand virtual bond spaces by adding or changing symmetry sectors if these lower the energy. Traditional single-site DMRG does not allow bond expansion; two-site DMRG does, but at much higher computational costs. We present a controlled bond expansion (CBE) algorithm that yields two-site accuracy and convergence per sweep, at single-site costs. Given a matrix product state $\mathrm{\ensuremath{\Psi}}$ defining a variational space, CBE identifies parts of the orthogonal space carrying significant weight in $H\mathrm{\ensuremath{\Psi}}$ and expands bonds to include only these. CBE-DMRG uses no mixing parameters and is fully variational. Using CBE-DMRG, we show that the Kondo-Heisenberg model on a width 4 cylinder features two distinct phases differing in their Fermi surface volumes.