Multigrid Algorithms for Tensor Network States

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 i...

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Bibliographic Details
Published inarXiv.org
Main Authors Dolfi, M, Bauer, B, Troyer, M, Ristivojevic, Z
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 12.06.2012
Subjects
Algorithms
Bosons
Computer simulation
Continuum modeling
Convergence
Dilution
Local optimization
Mathematical analysis
Optical lattices
Physics - Quantum Gases
Physics - Strongly Correlated Electrons
Tensors
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1203.6363