Geometry of Matrix Product States: metric, parallel transport and curvature

Understand

We study the geometric properties of the manifold of states described as (uniform) matrix product states.

• Due to the parameter redundancy in the matrix product state representation, matrix product states have the mathematical structure of a (principal) fiber bundle.
• The total space or bundle space corresponds to the parameter space, i.e.
• the space of tensors associated to every physical site.