Tensor network representations from the geometry of entangled states
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Tensor network representations from the geometry of entangled states. / Christandl, Matthias; Lucia, Angelo; Vrana, Peter; Werner, Albert H.
In: SciPost Physics, Vol. 9, No. 3, 042, 2020.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Tensor network representations from the geometry of entangled states
AU - Christandl, Matthias
AU - Lucia, Angelo
AU - Vrana, Peter
AU - Werner, Albert H.
PY - 2020
Y1 - 2020
N2 - Tensor network states provide successful descriptions of strongly correlated quantum systems with applications ranging from condensed matter physics to cosmology. Any family of tensor network states possesses an underlying entanglement structure given by a graph of maximally entangled states along the edges that identify the indices of the tensors to be contracted. Recently, more general tensor networks have been considered, where the maximally entangled states on edges are replaced by multipartite entangled states on plaquettes. Both the structure of the underlying graph and the dimensionality of the entangled states influence the computational cost of contracting these networks. Using the geometrical properties of entangled states, we provide a method to construct tensor network representations with smaller effective bond dimension. We illustrate our method with the resonating valence bond state on the kagome lattice.
AB - Tensor network states provide successful descriptions of strongly correlated quantum systems with applications ranging from condensed matter physics to cosmology. Any family of tensor network states possesses an underlying entanglement structure given by a graph of maximally entangled states along the edges that identify the indices of the tensors to be contracted. Recently, more general tensor networks have been considered, where the maximally entangled states on edges are replaced by multipartite entangled states on plaquettes. Both the structure of the underlying graph and the dimensionality of the entangled states influence the computational cost of contracting these networks. Using the geometrical properties of entangled states, we provide a method to construct tensor network representations with smaller effective bond dimension. We illustrate our method with the resonating valence bond state on the kagome lattice.
U2 - 10.21468/SciPostPhys.9.3.042
DO - 10.21468/SciPostPhys.9.3.042
M3 - Journal article
VL - 9
JO - SciPost Physics
JF - SciPost Physics
SN - 2542-4653
IS - 3
M1 - 042
ER -
ID: 249302901