Global symmetries in tensor network states: symmetric tensors versus minimal bond dimension

Understand

Tensor networks offer a variational formalism to efficiently represent wave-functions of extended quantum many-body systems on a lattice.

• In a tensor network N, the dimension \chi of the bond indices that connect its tensors controls the number of variational parameters and associated computational costs.
• In the absence of any symmetry, the minimal bond dimension \chi^{min} required to represent a given many-body wave-function |\Psi> leads to the most compact, computationally efficient tensor network description of |\Psi>.
• In the presence of a global, on-site symmetry, one can use a tensor network N_{sym} made of symmetric tensors.