Matrix product operator representations

Matrix product state representations

This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical forms and provide efficient methods for obtaining them. Results on frustration free Hamiltonians and the generation of MPS are extended, and the use of the MPS-r...

Representations of the Direct Product of Matrix Algebras

Suppose B is the unital algebra consisting of the algebraic product of full matrix algebras over an index set X. A bijection is set up between the equivalence classes of irreducible representations of B as operators on a Banach space and the σ-complete ultrafilters on X, Theorem 2.6. Therefore, if X has less than measurable cardinality (e.g. accessible), the equivalence classes of the irreducib...

The matrix product representations for all valence bond states

We introduce a simple representation for irreducible spherical tensor operators of the rotation group of arbitrary integer or half integer rank and use these tensor operators to construct matrix product states corresponding to all the variety of valence-bond states proposed in the Affleck-Kennedy-Lieb-Tasaki (AKLT) construction. These include the fully dimerized states of arbitrary spins, the p...

Operator Representations on Quantum Spaces

We deal with quantum spaces of particular importance in physics, i.e., q-deformed Minkowski space and q-deformed Euclidean space in three and four dimensions. For all these cases representations of their covariant differential calculi have been worked out. The explicit formulae refer to left representations, as right representations can be easily deduced from left ones. We are going to show for...

Irreducible Representations of Operator Algebras