Heisenberg group by 90°. The other reflections are "xyx" and "yxy", and rotation by 180° is "xyxy" (="yxyx"). The Lie algebra formula_16 of the Heisenberg group formula_1 (over the real numbers) is the space of formula_18 matrices of the form with formula_20. The following three elements form a basis for formula_16: The basis elements satisfy the commutation relations: The name "Heisenberg group" is motivated by the preceding relations, which have the same form as the canonical commutation relations in quantum mechanics: where formula_25 is the position operator, formula_26 is the momentum operator, and formula_27 is Planck's constant. The Heisenberg group formula_1 has
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