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Tensor networks for complex quantum systems

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arxiv 1812.04011 v2 pith:Y732ZTL3 submitted 2018-12-10 cond-mat.str-el hep-latquant-ph

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classification cond-mat.str-elhep-latquant-ph
keywords quantumtensornetworksystemsartificialcontextentanglementfield
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Tensor network states and methods have erupted in recent years. Originally developed in the context of condensed matter physics and based on renormalization group ideas, tensor networks lived a revival thanks to quantum information theory and the understanding of entanglement in quantum many-body systems. Moreover, it has been not-so-long realized that tensor network states play a key role in other scientific disciplines, such as quantum gravity and artificial intelligence. In this context, here we provide an overview of basic concepts and key developments in the field. In particular, we briefly discuss the most important tensor network structures and algorithms, together with a sketch on advances related to global and gauge symmetries, fermions, topological order, classification of phases, entanglement Hamiltonians, AdS/CFT, artificial intelligence, the 2d Hubbard model, 2d quantum antiferromagnets, conformal field theory, quantum chemistry, disordered systems, and many-body localization.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Connecting Magic Dynamics in Thermofield Double States to Spectral Form Factors

    quant-ph 2026-01 conditional novelty 7.0 of 10

    For chaotic all-to-all systems, the stabilizer Rényi entropy of thermofield double states is set by the spectral form factor and saturates through a first-order dynamical transition.

  2. Simulating matrix models with tensor networks

    hep-th 2024-12 conditional novelty 6.0 of 10

    Tensor-network DMRG simulations of SU(2) and small-SU(N) bosonic and supersymmetric matrix models give convergent ground states and entanglement measures, with costs that appear to grow polynomially with the number of...

  3. SU(4) Heisenberg model on the hyperhoneycomb lattice

    cond-mat.str-el 2026-06 unverdicted novelty 5.0 of 10

    Numerical iPEPS with loop expansions indicates the SU(4) Heisenberg model on the hyperhoneycomb lattice has a gapless quantum spin-liquid ground state, consistent with prior variational Monte Carlo results.

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