A Variational Principle for Ground Spaces

The ground space of every element of a vector space of Hermitian matrices is an intersection of maximal ground spaces of matrices from the same space. We characterize the ground spaces and the maximal ground spaces in terms of operator cones. This contributes to the geometry of quantum marginals, as...

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Bibliographic Details
Published in:Reports on mathematical physics 2018-12, Vol.82 (3), p.317-336
Main Author: Weis, Stephan
Format: Article
Language:English
Subjects:
coatom
convex set
exposed face
ground space
local Hamiltonian
normal cone
operator cone
quantum marginals
variational principle
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Summary:The ground space of every element of a vector space of Hermitian matrices is an intersection of maximal ground spaces of matrices from the same space. We characterize the ground spaces and the maximal ground spaces in terms of operator cones. This contributes to the geometry of quantum marginals, as their exposed faces are in one-to-one correspondence with ground spaces of local Hamiltonians.
ISSN:0034-4877
1879-0674
DOI:10.1016/S0034-4877(19)30005-9