Tensor operators: constructions and applications for long-range interaction systems
arXiv:1003.1047 · doi:10.1103/PhysRevA.81.062337
Abstract
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.
19 pages, 13 figures
References in corpus (9)
- Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
- A class of quantum many-body states that can be efficiently simulated
- Matrix product states represent ground states faithfully
- From density-matrix renormalization group to matrix product states
- Minimally Entangled Typical Thermal State Algorithms
- Applying matrix product operators to model systems with long-range interactions
- Finite automata for caching in matrix product algorithms
- Classical simulation versus universality in measurement based quantum computation
- Renormalization algorithm with graph enhancement