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Entanglement Theory Quantum Correlations Quantum Simulation

Tensor networks for frustrated systems: emergence of order from simplex entanglement

arXiv
Authors: Daniel Alsina, José Ignacio Latorre

Year

2013

Paper ID

31609

Status

Preprint

Abstract Read

~2 min

Abstract Words

105

Citations

N/A

Abstract

We consider a frustrated anti-ferromagnetic triangular lattice Hamiltonian and show that the properties of the manifold of its degenerated ground state are represented by a novel type of tensor networks. These tensor networks are not based on ancillary maximally entangled pairs, but rather on triangular W-like simplices. Anti-ferromagnetic triangular frustration is then related to ancillary W-states in contrast to ferromagnetic order which emerges from the contraction of GHZ-like triangular simplices. We further discuss the outwards entangling power of various simplices. This analysis suggests the emergence of distinct macroscopic types of order from the classification of entanglement residing on the simplices that define a tensor network.

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  • We consider a frustrated anti-ferromagnetic triangular lattice Hamiltonian and show that the properties of the manifold of its degenerated ground state are represented by a...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1312.0952 [2] arXiv https://arxiv.org/abs/1312.0952 [3] Publisher https://arxiv.org/abs/1312.0952

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