Year: 2014
Type: article
Abstract: We present several results relating to the contraction of generic tensor networks and discuss their application to the simulation of quantum many-body systems using variational approaches based upon tensor network states. Given a closed tensor network $\mathcal{T}$, we prove that if the environment of a single tensor from the network can be evaluated with computational cost $\ensuremath{\kappa}$, then the environment of any other tensor from $\mathcal{T}$ can be evaluated with identical cost $\ensuremath{\kappa}$. Moreover, we describe how the set of all single tensor environments from $\mathcal{T}$ can be simultaneously evaluated with fixed cost $3\ensuremath{\kappa}$. The usefulness of these results, which are applicable to a variety of tensor network methods, is demonstrated for the optimization of a multiscale entanglement renormalization Ansatz for the ground state of a one-dimensional quantum system, where they are shown to substantially reduce the computation time.
Source: Physical Review B
Authors: Glen Evenbly, Robert N. C. Pfeifer
Institutions: California Institute of Technology, Perimeter Institute
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2128319993