Tensor network
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Tensor networks or tensor network states are a class of variational wave functions used in the study of many-body quantum systems.[1] Tensor networks extend one-dimensional matrix product states to higher dimensions while preserving some of their useful mathematical properties.
The wave function is encoded as a tensor contraction of a network of individual tensors. The structure of the individual tensors can impose global symmetries on the wave function (such as antisymmetry under exchange of fermions) or restrict the wave function to specific quantum numbers, like total charge, angular momentum, or spin. It is also possible to derive strict bounds on quantities like entanglement and correlation length using the mathematical structure of the tensor network.[2] This has made tensor networks useful in theoretical studies of quantum information in many-body systems. They have also proved useful in variational studies of ground states, excited states, and dynamics of strongly correlated many-body systems.[3]
References
- ^ Orús, Román (2014-10-01). "A practical introduction to tensor networks: Matrix product states and projected entangled pair states". Annals of Physics. 349: 117–158. doi:10.1016/j.aop.2014.06.013. ISSN 0003-4916.
- ^ Verstraete, F.; Wolf, M. M.; Perez-Garcia, D.; Cirac, J. I. (2006-06-06). "Criticality, the Area Law, and the Computational Power of Projected Entangled Pair States". Physical Review Letters. 96 (22): 220601. doi:10.1103/PhysRevLett.96.220601.
- ^ Montangero, Simone,. Introduction to tensor network methods : numerical simulations of low-dimensional many-body quantum systems. Cham, Switzerland. ISBN 978-3-030-01409-4. OCLC 1076573498.
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