Local matrix product operators: Canonical form, compression, and control theory

Dirac's theory of constraints in field theory and the canonical form of Hamiltonian differential operators

In the classical theory of Hamiltonian systems, great emphasis is placed on the introduction of canonical coordinates-the positions and conjugate momenta of classical mechanics. I Canonical coordinates serve to simplify many of the equations and transformations required in the study of finite-dimensional Hamiltonian systems. Most quantization procedures require that the Hamiltonian system be in...

Jordan Canonical Form: Theory and Practice

Canonical density matrix perturbation theory.

Density matrix perturbation theory [Niklasson and Challacombe, Phys. Rev. Lett. 92, 193001 (2004)] is generalized to canonical (NVT) free-energy ensembles in tight-binding, Hartree-Fock, or Kohn-Sham density-functional theory. The canonical density matrix perturbation theory can be used to calculate temperature-dependent response properties from the coupled perturbed self-consistent field equat...

Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms.

Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In t...

Canonical matrices of isometric operators on indefinite inner product spaces

We give canonical matrices of a pair (A,B) consisting of a nondegenerate form B and a linear operator A satisfying B(Ax,Ay) = B(x, y) on a vector space over F in the following cases: • F is an algebraically closed field of characteristic different from 2 or a real closed field, and B is symmetric or skew-symmetric; • F is an algebraically closed field of characteristic 0 or the skew field of qu...