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entanglement area law

Cambridge University Press (1)

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5 - Tensor Network Ansatz of Wave Functions
Tao Xiang, Chinese Academy of Sciences, Beijing
Book:

Density Matrix and Tensor Network Renormalization

Published online:

18 January 2024

Print publication:

31 August 2023, pp 77-95
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Summary

This chapter introduces the tensor network ansatz for a quantum state whose entanglement entropy obeys the so-called area law with or without logarithmic corrections. This ansatz represents a quantum many-body wave function by a network product of local tensors defined on the lattice sites and treats all tensor elements as variational parameters. It includes, for example, one-dimensional matrix product states (MPS) and two-dimensional projected entangled pair states (PEPS) or projected entangled simplex states (PESS). A typical example is the spin-1 AKLT chain, whose ground state can be exactly represented as an MPS. If a logarithmic correction to the entanglement area law emerges, a tensor network state termed the multi-scale entanglement renormalization ansatz (MERA) describes the entanglement structure of the ground state more accurately in one dimension.