Heisenberg group Heisenberg group In mathematics, the Heisenberg group formula_1, named after Werner Heisenberg, is the group of 3×3 upper triangular matrices of the form under the operation of matrix multiplication. Elements "a, b" and "c" can be taken from any commutative ring with identity, often taken to be the ring of real numbers (resulting in the "continuous Heisenberg group") or the ring of integers (resulting in the "discrete Heisenberg group"). The continuous Heisenberg group arises in the description of one-dimensional quantum mechanical systems, especially in the context of the Stone–von Neumann theorem. More generally, one can consider Heisenberg groups associated to
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