Renormalization group contraction of tensor networks in three dimensions

Abstract

We present a new strategy for contracting tensor networks in arbitrary geometries. This method is designed to follow as strictly as possible the renormalization group philosophy, by first contracting tensors in an exact way and, then, performing a controlled truncation of the resulting tensor. We benchmark this approximation procedure in two dimensions against an exact contraction. We then apply the same idea to a three dimensional system. The underlying rational for emphasizing the exact coarse graining renormalization group step prior to truncation is related to monogamy of entanglement.

5 pages, 8 figures

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Cited by in corpus (37)

• Tensor Network Renormalization
• Lecture Notes of Tensor Network Contractions
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• Gauge fixing, canonical forms and optimal truncations in tensor networks with closed loops
• Monogamy of entanglement without inequalities
• X-Symbols for Non-Abelian Symmetries in Tensor Networks
• General monogamy relation of multi-qubit systems in terms of squared Rényi-$\alpha$ entanglement
• Monogamy equalities for qubit entanglement from Lorentz invariance
• Multipartite Entanglement Measure and Complete Monogamy Relation
• Simulation of three-dimensional quantum systems with projected entangled-pair states
• Spectral gaps of AKLT Hamiltonians using Tensor Network methods
• The area law and real-space renormalization
• Monogamy relation of multi-qubit systems for squared Tsallis-\emph{q} entanglement
• Three-dimensional isometric tensor networks
• Few-body systems capture many-body physics: tensor network approach
• Efficient evaluation of high-order moments and cumulants in tensor network states
• Renormalization Group Circuits for Gapless States
• Density of Yang-Lee zeros in the thermodynamic limit from tensor network methods
• Conclusive Identification of Quantum Channels via Monogamy of Quantum Correlations
• Monogamy of quantum entanglement
• Complete monogamy of the multipartite quantum mutual information
• Tighter constraints of multiqubit entanglement in terms of Rényi-$\alpha$ entropy
• Polygamy relation for the Rényi-$\alpha$ entanglement of assistance in multi-qubit systems
• Generalization of the tensor renormalization group approach to 3-D or higher dimensions
• Tensor Renormalization Group Centered About a Core Tensor
• Complete Genuine Multipartite Entanglement Monotone
• Numerical studies of entanglement properties in one- and two-dimensional quantum Ising and XXZ models
• Partial-Norm of Entanglement: Entanglement Monotones That are not Monogamous
• Single-layer tensor network approach for three-dimensional quantum systems
• Spectral gaps of two- and three-dimensional many-body quantum systems in the thermodynamic limit
• Polygamy relation of quantum correlations with equality
• Maximum Violation of Monogamy of Entanglement for Indistinguishable Particles by Measures that are Monogamous for Distinguishable Particles
• Variational boundary based tensor network renormalization group
• Implicitly disentangled renormalization
• Tighter monogamy and polygamy relations using Rényi-$\alpha$ entropy
• Dispersion Relations in Two- and Three-Dimensional Quantum Systems