Heisenberg picture formulation of matrix mechanics in an arbitrary basis, in which the Hamiltonian is not necessarily diagonal. It further serves to define a third, hybrid, picture, the interaction picture. In the Heisenberg picture of quantum mechanics the state vectors, |"ψ("t")"〉, do not change with time, while observables satisfy where is the Hamiltonian and <nowiki>[•,•]</nowiki> denotes the commutator of two operators (in this case and ). Taking expectation values automatically yields the Ehrenfest theorem, featured in the correspondence principle. By the Stone–von Neumann theorem, the Heisenberg picture and the Schrödinger picture are unitarily equivalent, just a basis change in Hilbert space. In
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