Abstract
This chapter is to introduce some basic definitions and concepts of TN. We will show that the TN can be used to represent quantum many-body states, where we explain MPS in 1D and PEPS in 2D systems, as well as the generalizations to thermal states and operators. The quantum entanglement properties of the TN states including the area law of entanglement entropy will also be discussed. Finally, we will present several special TNs that can be exactly contracted, and demonstrate the difficulty of contracting TNs in general cases.
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CITATION STYLE
Ran, S. J., Tirrito, E., Peng, C., Chen, X., Tagliacozzo, L., Su, G., & Lewenstein, M. (2020). Tensor network: Basic definitions and properties. In Lecture Notes in Physics (Vol. 964, pp. 25–62). Springer. https://doi.org/10.1007/978-3-030-34489-4_2
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