Tensor network representations from the geometry of entangled states

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Standard

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

Harvard

Christandl, M, Lucia, A, Vrana, P & Werner, AH 2020, 'Tensor network representations from the geometry of entangled states', SciPost Physics, vol. 9, no. 3, 042. https://doi.org/10.21468/SciPostPhys.9.3.042

APA

Christandl, M., Lucia, A., Vrana, P., & Werner, A. H. (2020). Tensor network representations from the geometry of entangled states. SciPost Physics, 9(3), [042]. https://doi.org/10.21468/SciPostPhys.9.3.042

Vancouver

Christandl M, Lucia A, Vrana P, Werner AH. Tensor network representations from the geometry of entangled states. SciPost Physics. 2020;9(3). 042. https://doi.org/10.21468/SciPostPhys.9.3.042

Author

Christandl, Matthias ; Lucia, Angelo ; Vrana, Peter ; Werner, Albert H. / Tensor network representations from the geometry of entangled states. In: SciPost Physics. 2020 ; Vol. 9, No. 3.

Bibtex

@article{ecae411477c74147ada85cbbf1a08029,
title = "Tensor network representations from the geometry of entangled states",
abstract = "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.",
author = "Matthias Christandl and Angelo Lucia and Peter Vrana and Werner, {Albert H.}",
year = "2020",
doi = "10.21468/SciPostPhys.9.3.042",
language = "English",
volume = "9",
journal = "SciPost Physics",
issn = "2542-4653",
publisher = "SCIPOST FOUNDATION",
number = "3",

}

RIS

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