Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 18 (2022), 099, 18 pages      arXiv:2204.10363

The Linear Span of Uniform Matrix Product States

Claudia De Lazzari a, Harshit J. Motwani b and Tim Seynnaeve c
a) Dipartimento di Matematica, Università di Trento, Via Sommarive 14, 38123 Povo (TN), Italy
b) Department of Mathematics: Algebra and Geometry, Ghent University, 9000 Gent, Belgium
c) Department of Computer Science, KU Leuven, Celestijnenlaan 200A, 3001 Leuven, Belgium

Received June 03, 2022, in final form December 15, 2022; Published online December 21, 2022

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.

Key words: matrix product states; invariant theory of matrices.

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