Matrix product state

Summary

A matrix product state is a vector in the state space of a chain of sites whose coefficients are products of matrices. There is one matrix for each site and each local basis state. The size of the matrices, the bond dimension, bounds the entanglement between the two parts of the chain on either side of a cut. Ground states of gapped one-dimensional Hamiltonians are well approximated by matrix product states of small bond dimension. This makes them the basis of numerical methods such as the density matrix renormalization group.