Matrix product operator representation of polynomial interactions

An efficient matrix product operator representation of the quantum chemical Hamiltonian.

We describe how to efficiently construct the quantum chemical Hamiltonian operator in matrix product form. We present its implementation as a density matrix renormalization group (DMRG) algorithm for quantum chemical applications. Existing implementations of DMRG for quantum chemistry are based on the traditional formulation of the method, which was developed from the point of view of Hilbert s...

Polynomial Matrix Inequality and Semidefinite Representation

Consider a convex set S = {x ∈ D : G(x) o 0} where G(x) is a symmetric matrix whose every entry is a polynomial or rational function, D ⊆ R is a domain on which G(x) is defined, and G(x) o 0 means G(x) is positive semidefinite. The set S is called semidefinite representable if it equals the projection of a higher dimensional set which is defined by a linear matrix inequality (LMI). This paper s...

Matrix Representation of Linear Operatorson Product

We give a condition for an operator A deened on a product space E which ensures that it can be represented in matrix form. Combining this representation with our earlier work on one-sided coupled operator matrices we can characterize various operator-theoretical properties of A in terms of its matrix entries. 1. The Matrix Representation In a series of papers, see e.g. Nag89], Nag90], EH96], En...

Differential Polynomial Rings of Triangular Matrix Rings

New coprime polynomial fraction representation of transfer function matrix