Environment expansion for Matrix Product State and Tensor Network methods*

We present a method for incorporating degrees of freedom into bonds of a tensor network inspired by single-site density matrix mixing schemes and the single-site subspace expansion (3S) algorithm. This is applicable in a wide range of scenarios and we will present some benchmarks for various Matrix Product State algorithms including DMRG, TDVP, and Excitation Ansatz. The Environment Expansion approach is a simple and effective way to control bond dimension expansion, and will likely become a standard part of the MPS 'toolbox'.