FoCM 2014 conference

Workshop C1 - Computational Algebraic Geometry

No date set

## Algebraic geometry of tree tensor network states

### Sara Jamshidi

### Pennsylvania State University, USA - jamshidi@math.psu.edu

Tree tensor networks have been used to model the ground states of Hamiltonians in condensed matter physics and quantum chemistry. Exactly which quantum states can be represented by a tree tensor network with a given topology and given restrictions on the parameter tensors? When the restrictions are algebraic, the set of states is a projective algebraic variety. We describe those varieties, using techniques originally developed for phylogenetics.

Joint work with Jason Morton (Pennsylvania State University, USA).