The Linear Span of Uniform Matrix Product States
Claudia De Lazzari, Harshit J Motwani, Tim Seynnaeve
TL;DR
This paper investigates the linear span of uniform matrix product states, connecting algebraic geometry and quantum physics, using advanced mathematical tools to understand their structure and properties.
Contribution
It introduces a novel analysis of the linear span of uniform matrix product states employing linear algebra, representation theory, and invariant theory.
Findings
Characterization of the linear span of uniform matrix product states
Connections established between algebraic geometry and quantum many-body physics
Mathematical tools developed for analyzing translation-invariant systems
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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Matrix Theory and Algorithms