Non-abelian symmetries in tensor networks: a quantum symmetry space approach

DOI10.1016/j.aop.2012.07.009zbMath1311.81065arXiv1202.5664OpenAlexW2149287125WikidataQ62442962 ScholiaQ62442962MaRDI QIDQ1933576

Andreas Weichselbaum

Publication date: 24 January 2013

Published in: Annals of Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.5664

zbMATH Keywords

Lie algebraClebsch-Gordan coefficientstensor networksdensity matrix renormalization groupnumerical renormalization groupnon-abelian symmetries

Mathematics Subject Classification ID

Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Quantum information, communication, networks (quantum-theoretic aspects) (81P45)

Related Items (8)

A practical introduction to tensor networks: Matrix product states and projected entangled pair states ⋮ The PointGroupNRG code for numerical renormalization group calculations with discrete point-group symmetries ⋮ Matrix product states forsu(2) invariant quantum spin chains ⋮ Lattice regularisation and entanglement structure of the Gross-Neveu model ⋮ Phases of one-dimensional \(\mathrm{SU}(N)\) cold atomic Fermi gases -- from molecular Luttinger liquids to topological phases ⋮ Unnamed Item ⋮ Time-evolution methods for matrix-product states ⋮ SU(3) Clebsch–Gordan coefficients and some of their symmetries

Uses Software

• LiE
• JDQR
• JDQZ

Cites Work

• The density-matrix renormalization group in the age of matrix product states
• \(SU(N)\) quantum Racah coefficients and non-torus links
• Colloquium: Area laws for the entanglement entropy
• The density-matrix renormalization group
• Diagrammatics forSU(2) invariant matrix product states
• Area Laws in Quantum Systems: Mutual Information and Correlations
• Renormalization and tensor product states in spin chains and lattices
• Templates for the Solution of Algebraic Eigenvalue Problems
• A numerical algorithm for the explicit calculation of SU(N) and $\mbox{SL}(N,\mathbb {C})$SL(N,C) Clebsch–Gordan coefficients
• Black Holes and Entropy
• Mesoscopic scattering of spinsparticles

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