Uniform matrix product states from an algebraic geometer's point of view

Adam Czapliński, Mateusz Michałek, and Tim Seynnaeve

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Submission date: 16. Apr. 2019
Pages: 26
Bibtex
MSC-Numbers: 15A69, 15A90
Keywords and phrases: uniform matrix product states, trace algebra, trace parametrization, W-state, injectivity radius
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Abstract:
We apply methods from algebraic geometry to study uniform matrix product states. Our main results concern the topology of the locus of tensors expressed as uMPS, their defining equations and identifiability. By an interplay of theorems from algebra, geometry and quantum physics we answer several questions and conjectures posed by Critch, Morton and Hackbusch.