Entanglement renormalization, scale invariance, and quantum criticality

2008/10/31 by Robert N. C. Pfeifer, Glen Evenbly, Guifre Vidal +1 · 7 citations
Mathematics · Physics and Astronomy · #Ansatz #Conformal field theory #Conformal map #Conformal symmetry #Critical dimension #Critical exponent #Critical phenomena #Gauge theory #Lattice field theory #Mathematical physics #Mathematics #Observable #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum and electron transport phenomena #Quantum entanglement #Quantum field theory #Quantum many-body systems #Quantum mechanics #Renormalization #Renormalization group #Scale invariance #cond-mat.str-el

paper · pdf · doi:10.1103/physreva.79.040301

published as Physical Review A 79(4), 040301(R) (2009) · 4 pages, 3 figures, RevTeX 4. Revised for greater clarity

openalex publication_date 2009/04/06 · arxiv created 2009/04/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The use of entanglement renormalization in the presence of scale invariance is investigated. We explain how to compute an accurate approximation of the critical ground state of a lattice model and how to evaluate local observables, correlators, and critical exponents. Our results unveil a precise connection between the multiscale entanglement renormalization ansatz and conformal field theory (CFT). Given a critical Hamiltonian on the lattice, this connection can be exploited to extract most of the conformal data of the CFT that describes the model in the continuum limit.

Citations

• Quantum Multiscale Entanglement Renormalization Ansatz Channels
• Density-matrix algorithms for quantum renormalization groups
• Conformal invariance and universality in finite-size scaling
• The renormalization group: Critical phenomena and the Kondo problem
• Class of Quantum Many-Body States That Can Be Efficiently Simulated
• Conformal Field Theory

Cited by

• Foundations and Applications of Entanglement Renormalization
• Emergent geometry, thermal CFT and surface/state correspondence
• Scaling of entanglement entropy in the (branching) multiscale entanglement renormalization ansatz
• Multiscale entanglement renormalization ansatz for spin chains with continuously varying criticality
• Theory of minimal updates in holography
• Hyperinvariant Tensor Networks and Holography
• Algorithms for Entanglement Renormalization: Boundaries, Impurities and Interfaces

Related

• Quantum Criticality with the Multi-scale Entanglement Renormalization\n Ansatz
• A generalized multi-scale entanglement renormalization ansatz: more accurate conformal data from a critical lattice model
• Scaling and universality of multipartite entanglement at criticality
• Entanglement Entropies in One-Dimensional Systems
• Universal entanglement correction induced by relevant deformations at the quantum critical point