Entanglement branching operator

Abstract

We introduce an entanglement branching operator to split a composite entanglement flow in a tensor network which is a promising theoretical tool for many-body systems. We can optimize an entanglement branching operator by solving a minimization problem based on squeezing operators. The entanglement branching is a new useful operation to manipulate a tensor network. For example, finding a particular entanglement structure by an entanglement branching operator, we can improve a higher-order tensor renormalization group method to catch a proper renormalization flow in a tensor network space. This new method yields a new type of tensor network states. The second example is a many-body decomposition of a tensor by using an entanglement branching operator. We can use it for a perfect disentangling among tensors. Applying a many-body decomposition recursively, we conceptually derive projected entangled pair states from quantum states that satisfy the area law of entanglement entropy.

11 pages, 13 figures

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Cited by in corpus (24)

• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Anisotropic Tensor Renormalization Group
• Finding purifications with minimal entanglement
• Bond-weighted Tensor Renormalization Group
• Calculation of higher-order moments by higher-order tensor renormalization group
• Gauging tensor networks with belief propagation
• Boundary Tensor Renormalization Group
• A beginner's guide to non-abelian iPEPS for correlated fermions
• Scaling dimensions from linearized tensor renormalization group transformations
• Global optimization of tensor renormalization group using the corner transfer matrix
• Fine-Grained Tensor Network Methods
• Multi-impurity method for the bond-weighted tensor renormalization group
• Holographic analysis of boundary correlation functions for the hyperbolic-lattice Ising model
• Phase boundary location with information-theoretic entropy in tensor renormalization group flows
• Three-dimensional real space renormalization group with well-controlled approximations
• Controlling quantum many-body systems using reduced-order modelling
• Tensor-Ring Decomposition with Index-Splitting
• All-mode Renormalization for Tensor Network with Stochastic Noise
• Tensor Renormalization Group Calculations of Partition-Function Ratios
• Spectroscopy with the tensor renormalization group method
• Essential difference between 2D and 3D from the perspective of real-space renormalization group
• Variational boundary based tensor network renormalization group
• Universal spectrum structure at nonequilibrium critical points in the (1+1)-dimensional directed percolation
• Lattice and PT symmetries in tensor-network renormalization group: Case study of a hard-square lattice gas model