The Linear Span of Uniform Matrix Product States

Abstract

The variety of uniform matrix product states arises both in algebraic geometry as a natural generalization of the Veronese variety, and in quantum many-body physics as a model for a translation-invariant system of sites placed on a ring. Using methods from linear algebra, representation theory, and invariant theory of matrices, we study the linear span of this variety.

References in corpus (3)

• On the closedness and geometry of tensor network state sets
• Dimension of Tensor Network varieties
• The Linear Span of Uniform Matrix Product States

Cited by in corpus (3)

• The resource theory of tensor networks
• The Linear Span of Uniform Matrix Product States
• Quantum max-flow in the bridge graph