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 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 a chain of spins. This article presents the "infinite" DMRG algorithm for the formula_1 antiferromagnetic Heisenberg chain, but the recipe can be applied for every translationally invariant one-dimensional lattice. DMRG is a renormalization-group technique because it offers an efficient truncation of the Hilbert space of one-dimensional quantum systems. To simulate an infinite chain, starting with four sites. The first