Werner Heisenberg foundation of the matrix formulation of quantum mechanics through only the use of observables. In February 1943, Heisenberg was appointed to the Chair for Theoretical Physics at the "Friedrich-Wilhelms-Universität" (today, the Humboldt-Universität zu Berlin). In April, his election to the "Preußische Akademie der Wissenschaften" (Prussian Academy of Sciences) was approved. That same month, he moved his family to their retreat in as Allied bombing increased in Berlin. In the summer, he dispatched the first of his staff at the "Kaiser-Wilhelm Institut für Physik" to Hechingen and its neighboring town of Haigerloch, on the edge of the Black Forest, for the
DMRG of the Heisenberg model for example: formula_68 formula_69 formula_70 formula_71 Now, form the formula_72 matrix representations of the new block and universe-block operators, form a new block by changing basis with the transformation formula_58, for example: formula_74 At this point the iteration is ended and the algorithm goes back to step 1. The algorithm stops successfully when the observable converges to some value. DMRG of the Heisenberg model Within the study of the quantum many-body problem in physics, the DMRG analysis of the Heisenberg model is an important theoretical example applying techniques of the density matrix renormalization group (DMRG) to the Heisenberg model of