Dynamical density-matrix renormalization group

The dynamical density-matrix renormalization group (DDMRG) method is a numerical technique for calculating the zero-temperature dynamical properties in low-dimensional quantum many-body systems. For the onedimensional Hubbard model and its extensions, DDMRG allows for accurate calculations of these properties for lattices with hundreds of sites and particles and for any excitation energy. The key idea of this approach is a variational principle for dynamical correlation functions. The variational problem can be solved with a standard density-matrix renormalization group (DMRG) method. Combined with a finite-size-scaling analysis for dynamical spectra, the DDMRG method enables us to study dynamical properties in the thermodynamic limit. An efficient calculation of momentum-dependent quantities with DMRG is achieved using open boundary conditions and quasi-momenta. These techniques are illustrated with the photoemission spectral function of the half-filled one-dimensional Hubbard model.