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math-ph2019★ 1 cited
Uniform matrix product states from an algebraic geometer's point of view
Adam Czapliński, Mateusz Michałek, Tim Seynnaeve
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 equ…
math-ph2018
A tensor version of the quantum Wielandt theorem
Mateusz Michałek, Tim Seynnaeve, Frank Verstraete
We prove boundedness results for the injectivity regions for PEPS. Our result is a higher-dimensional generalization of the quantum Wielandt inequality.