Real-space renormalization yields finite correlations

Abstract

Real-space renormalization approaches for quantum lattice systems generate certain hierarchical classes of states that are subsumed by the multi-scale entanglement renormalization ansatz (MERA). It is shown that, with the exception of one spatial dimension, MERA states are actually finitely correlated states, i.e., projected entangled pair states (PEPS) with a bond dimension independent of the system size. Hence, real-space renormalization generates states which can be encoded with local effective degrees of freedom, and MERA states form an efficiently contractible class of PEPS that obey the area law for the entanglement entropy. It is shown further that there exist other efficiently contractible schemes violating the area law.

7 pages, 6 figures; final version, featuring an addendum to the published article

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• Resonating valence bond states in the PEPS formalism
• Neural Network Renormalization Group
• Tensor Network Algorithms: a Route Map
• Unconstrained Tree Tensor Network: An adaptive gauge picture for enhanced performance
• Renormalization group constructions of topological quantum liquids and beyond
• Scaling of entanglement entropy in the (branching) multi-scale entanglement renormalization ansatz
• Lieb-Robinson bounds and the simulation of time evolution of local observables in lattice systems
• Practical learning method for multi-scale entangled states
• Topological Multipartite Entanglement in a Fermi Liquid
• The area law and real-space renormalization
• Algebraically contractible topological tensor network states
• Numerical study of incommensurability of the spiral state on spin-1/2 spatially anisotropic triangular antiferromagnets using entanglement renormalization
• Isometric tensor network optimization for extensive Hamiltonians is free of barren plateaus
• On the closedness and geometry of tensor network state sets
• Tensor network methods with graph enhancement
• Convergence and Quantum Advantage of Trotterized MERA for Strongly-Correlated Systems
• Single-shot holographic compression from the area law
• Entanglement renormalization for chiral topological phases
• Security of quantum position-verification limits Hamiltonian simulation via holography
• Scaling of contraction costs for entanglement renormalization algorithms including tensor Trotterization and variational Monte Carlo
• Scale-Invariant Continuous Entanglement Renormalization of a Chern Insulator