Physics – Quantum Physics
Scientific paper
2010-03-04
Phys. Rev. A 81, 062337 (2010)
Physics
Quantum Physics
19 pages, 13 figures
Scientific paper
10.1103/PhysRevA.81.062337
We consider the representation of operators in terms of tensor networks and their application to ground-state approximation and time evolution of systems with long-range interactions. We provide an explicit construction to represent an arbitrary many-body Hamilton operator in terms of a one-dimensional tensor network, i.e. as a matrix product operator. For pairwise interactions, we show that such a representation is always efficient and requires a tensor dimension growing only linearly with the number of particles. For systems obeying certain symmetries or restrictions we find optimal representations with minimal tensor dimension. We discuss the analytic and numerical approximation of operators in terms of low-dimensional tensor operators. We demonstrate applications for time evolution and ground-state approximation, in particular for long-range interaction with inhomogeneous couplings. The operator representations are also generalized to other geometries such as trees and 2D lattices, where we show how to obtain and use efficient tensor network representations respecting a given geometry.
Dür Wolfgang
Fröwis Florian
Nebendahl V.
No associations
LandOfFree
Tensor operators: constructions and applications for long-range interaction systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Tensor operators: constructions and applications for long-range interaction systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Tensor operators: constructions and applications for long-range interaction systems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-560169