ABSTRACT
Ulrich Schollwo¨ck Arnold Sommerfeld Center for Theoretical Physics, University of Munich, Germany
Since its invention in 1992 by White [1,2], the density matrix renormalization group (DMRG) has firmly established itself as the currently most powerful method to calculate static and more recently also dynamic [3-5] properties of low-lying eigenstates of strongly correlated Hamiltonians defined on onedimensional quantum lattices. At the same time, its extension to the analysis of two-dimensional classical [6] and one-dimensional quantum [7,8] transfer matrices has given access to highly precise thermodynamics in classical two-dimensional and quantum one-dimensional systems. It has even been extended to the numerically much more demanding study of non-Hermitian (pseudo-)Hamiltonians emerging in the analysis of classical steady states in one-dimensional systems [9-11]. However, it also turned out quite quickly that extending DMRG to the study of two-dimensional systems did not lead to similarly huge successes.
