Symmetries and local transformations of translationally invariant Matrix
Product States
- URL: http://arxiv.org/abs/2111.02457v1
- Date: Wed, 3 Nov 2021 18:22:55 GMT
- Title: Symmetries and local transformations of translationally invariant Matrix
Product States
- Authors: Martin Hebenstreit, David Sauerwein, Andras Molnar, J. Ignacio Cirac,
Barbara Kraus
- Abstract summary: We determine the local symmetries and local transformation properties of translationally in matrix product states (MPS)
We identify and classify the local transformations (SLOCC) that are allowed among MPS.
These results reflect the variety of local properties of MPS, even if restricted to translationally in states with low bond dimension.
- Score: 0.6299766708197883
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We determine the local symmetries and local transformation properties of
translationally invariant matrix product states (MPS). We focus on physical
dimension $d=2$ and bond dimension $D=3$ and use the procedure introduced in D.
Sauerwein et al., Phys. Rev. Lett. 123, 170504 (2019) to determine all
(including non--global) symmetries of those states. We identify and classify
the stochastic local transformations (SLOCC) that are allowed among MPS. We
scrutinize two very distinct sets of MPS and show the big diversity (also
compared to the case $D=2$) occurring in both, their symmetries and the
possible SLOCC transformations. These results reflect the variety of local
properties of MPS, even if restricted to translationally invariant states with
low bond dimension. Finally, we show that states with non-trivial local
symmetries are of measure zero for $d = 2$ and $D > 3$.
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