Multigrid Algorithms for Tensor Network States

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.

5 pages, 7 figures. Accepted for publication in PRL

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• One-dimensional Continuum Electronic Structure with the Density Matrix Renormalization Group and Its Implications For Density Functional Theory
• Pair Correlations in Doped Hubbard Ladders
• Quantum Flutter: Signatures and Robustness
• Riemannian optimization of isometric tensor networks
• Continuous Matrix Product States for Quantum Fields: an Energy Minimization Algorithm
• Unitary dynamics of strongly-interacting Bose gases with time-dependent variational Monte Carlo in continuous space
• Understanding repulsively mediated superconductivity of correlated electrons via massively parallel DMRG
• Minimizing nonadiabaticities in optical-lattice loading
• Continuous matrix product states for non-relativistic quantum fields: a lattice algorithm for inhomogeneous systems
• Variational optimization of continuous matrix product states
• Efficient representation of long-range interactions in tensor network algorithms
• Ground state phase diagram of the one-dimensional $t$-$J$ model with pair hopping terms
• On the generalization of the exponential basis for tensor network representations of long-range interactions in two and three dimensions
• Functional Tensor Network Solving Many-body Schrödinger Equation
• Multiple phase separation in one-dimensional mixtures of mass- and population-imbalanced attractive Fermi gases
• Density-Matrix Renormalization Group for Continuous Quantum Systems
• Variational adiabatic transport of tensor networks
• The matrix product approximation for the dynamic cavity method
• A Multi-Scale Tensor Network Architecture for Classification and Regression
• Performance of the rigorous renormalization group for first order phase transitions and topological phases
• Continuous matrix-product states in inhomogeneous systems with long-range interactions
• Numerical continuum tensor networks in two dimensions
• Accuracy and Efficiency of Simplified Tensor Network Codes
• Quantum Cramer-Rao Precision Limit of Noisy Continuous Sensing
• Redundant string symmetry-based error correction: Demonstrations on quantum devices
• The Software Landscape for the Density Matrix Renormalization Group
• Density redistribution effects in fermionic optical lattices
• Electric Field Propagation Through Singular Value Decomposition