Renormalization of tensor networks using graph independent local truncations

Abstract

We introduce an efficient algorithm for reducing bond dimensions in an arbitrary tensor network without changing its geometry. The method is based on a novel, quantitative understanding of local correlations in a network. Together with a tensor network coarse-graining algorithm, it yields a proper renormalization group (RG) flow. Compared to existing methods, the advantages of our algorithm are its low computational cost, simplicity of implementation, and applicability to any network. We benchmark it by evaluating physical observables for the 2D classical Ising model and find accuracy comparable with the best existing tensor network methods. Because of its graph independence, our algorithm is an excellent candidate for implementation of real-space RG in higher dimensions. We discuss some of the details and the remaining challenges in 3D. Source code for our algorithm is freely available.

14 + 6 pages, 112 figures, source code in ancillary files; v2: minor changes to match journal version

References in corpus (11)

• The NumPy array: a structure for efficient numerical computation
• A class of quantum many-body states that can be efficiently simulated
• Tensor renormalization group approach to 2D classical lattice models
• DMRG and periodic boundary conditions: a quantum information perspective
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• Continuous Matrix Product States for Quantum Fields
• From Path Integrals to Tensor Networks for AdS/CFT
• Entanglement and correlations in the continuous multi-scale entanglement renormalization ansatz
• Phase transitions and thermodynamics of the two-dimensional Ising model on a distorted Kagomé lattice

Cited by in corpus (75)

• Neural Network Renormalization Group
• Tensor Network Algorithms: a Route Map
• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Anisotropic Tensor Renormalization Group
• Tensor lattice field theory with applications to the renormalization group and quantum computing
• Mapping topological to conformal field theories through strange correlators
• Gauge fixing, canonical forms and optimal truncations in tensor networks with closed loops
• Berezinskii-Kosterlitz-Thouless transition in lattice Schwinger model with one flavor of Wilson fermion
• Tensor network formulation of the massless Schwinger model
• Fast counting with tensor networks
• Bond-weighted Tensor Renormalization Group
• Efficient Simulation of Dynamics in Two-Dimensional Quantum Spin Systems with Isometric Tensor Networks
• Calculation of higher-order moments by higher-order tensor renormalization group
• Gauging tensor networks with belief propagation
• Finite-size and finite bond dimension effects of tensor network renormalization
• Entanglement branching operator
• Boundary Tensor Renormalization Group
• Computing the renormalization group flow of two-dimensional ${\varphi }^4$ theory with tensor networks
• Hyper-optimized approximate contraction of tensor networks with arbitrary geometry
• A beginner's guide to non-abelian iPEPS for correlated fermions
• Resolving the Berezinskii-Kosterlitz-Thouless transition in the 2D XY model with tensor-network based level spectroscopy
• Gentle introduction to rigorous Renormalization Group: a worked fermionic example
• Optimal Renormalization Group Transformation from Information Theory
• Efficient variational contraction of two-dimensional tensor networks with a non-trivial unit cell
• Nuclear norm regularized loop optimization for tensor network
• Tensor Renormalization Group Algorithms with a Projective Truncation Method
• Numerical linked cluster expansions for inhomogeneous systems
• Boundary conformal spectrum and surface critical behaviors of the classical spin systems: a tensor network renormalization study
• Differentiable Programming of Isometric Tensor Networks
• Scaling dimensions from linearized tensor renormalization group transformations
• Continuous tensor network renormalization for quantum fields
• Tensor RG approach to high-temperature fixed point
• Global optimization of tensor renormalization group using the corner transfer matrix
• Triad second renormalization group
• Matrix product state fixed points of non-Hermitian transfer matrices
• GrassmannTN: a Python package for Grassmann tensor network computations
• On maximum-likelihood decoding with circuit-level errors
• Tensor network calculation of the logarithmic correction exponent in the XY model
• Multi-impurity method for the bond-weighted tensor renormalization group
• Tensor Renormalization Group at Low Temperatures: Discontinuity Fixed Point
• Tensor Renormalization Group Centered About a Core Tensor
• Local order parameters for symmetry fractionalization
• Improved coarse-graining methods on two dimensional tensor networks including fermions
• Algorithms for Tensor Network Contraction Ordering
• Holographic analysis of boundary correlation functions for the hyperbolic-lattice Ising model
• Tensor Network Renormalization Study on the Crossover in Classical Heisenberg and $\mathrm{R}{\mathrm{P}}^2$ Models in Two Dimensions
• Loop Series Expansions for Tensor Networks
• Phase boundary location with information-theoretic entropy in tensor renormalization group flows
• Rotations, Negative Eigenvalues, and Newton Method in Tensor Network Renormalization Group
• Three-dimensional real space renormalization group with well-controlled approximations
• Transfer Matrix and Lattice Dilatation Operator for High-Quality Fixed Points in Tensor Network Renormalization Group
• Controlling quantum many-body systems using reduced-order modelling
• Tensor-Ring Decomposition with Index-Splitting
• 3D Tensor Renormalisation Group at High Temperatures
• Tensor Renormalization Group Calculations of Partition-Function Ratios
• Accuracy and Efficiency of Simplified Tensor Network Codes
• Phase structure analysis of 2d lattice CP(1) model with $\theta$ term using tensor renormalization group method
• Finite-size scaling on the torus with periodic projected entangled-pair states
• Tensor network simulations for nonorientable surfaces
• Spectroscopy with the tensor renormalization group method
• All-mode Renormalization for Tensor Network with Stochastic Noise
• Loop update for infinite projected entangled-pair states in two spatial dimensions
• Scalable projected entangled-pair state representation of random quantum circuit states
• Tensor network renormalization approach to antiferromagnetic 6-state clock model on the Union Jack lattice
• The Tangent Space to the Manifold of Critical Classical Hamiltonians Representable by Tensor Networks
• Lattice-reflection symmetry in tensor-network renormalization group with entanglement filtering in two and three dimensions
• Essential difference between 2D and 3D from the perspective of real-space renormalization group
• A Practical Introduction to Tensor Network Renormalization with TNRKit.jl
• Forward-mode automatic differentiation for the tensor renormalization group and its relation to the impurity method
• Variational boundary based tensor network renormalization group
• Bucket Renormalization for Approximate Inference
• Lattice and PT symmetries in tensor-network renormalization group: Case study of a hard-square lattice gas model
• Universal spectrum structure at nonequilibrium critical points in the (1+1)-dimensional directed percolation
• Holographic Aspects of Dynamical Mean-Field Theory
• Tensor renormalization group study of cold and dense QCD in the strong coupling limit