Multigrid Algorithms for Tensor Network States

TL;DR

This paper introduces a multigrid algorithm for tensor network states that improves convergence in systems with multiple length scales, demonstrated through boson simulations and applicable to various lattice models.

Contribution

The paper presents a multigrid approach that enhances tensor network algorithms' convergence, especially for systems with multiple length scales, and can be integrated with existing methods like CORE.

Findings

Effective in simulating bosons in continuous space

Improves convergence in systems with multiple length scales

Can be combined with CORE for lattice models

Abstract

The widely used density matrix renormalization group (DRMG) method often fails to converge in systems with multiple length scales, such as lattice discretizations of continuum models and dilute or weakly doped lattice models. The local optimization employed by DMRG to optimize the wave function is ineffective in updating large-scale features. Here we present a multigrid algorithm that solves these convergence problems by optimizing the wave function at different spatial resolutions. We demonstrate its effectiveness by simulating bosons in continuous space, and study non-adiabaticity when ramping up the amplitude of an optical lattice. The algorithm can be generalized to tensor network methods, and be combined with the contractor renormalization group (CORE) method to study dilute and weakly doped lattice models.