Quantum Multiscale Entanglement Renormalization Ansatz Channels

2008/04/30 by Vittorio Giovannetti, Simone Montangero, Rosario Fazio · 6 citations
Mathematics · Physics and Astronomy · #Ansatz #Critical exponent #Critical phenomena #Density matrix renormalization group #Mathematics #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum and electron transport phenomena #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Renormalization #Renormalization group #Statistical physics #Tensor (intrinsic definition) #Thermodynamic limit #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physrevlett.101.180503

published as Phys. Rev. Lett. 101, 180503 (2008) · 4 pages, 2 figures

openalex publication_date 2008/10/30 · arxiv created 2008/11/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Tensor network representations of many-body quantum systems can be described in terms of quantum channels. We focus on channels associated with the multiscale entanglement renormalization ansatz tensor network that has been recently introduced to efficiently describe critical systems. Our approach allows us to compute the multiscale entanglement renormalization ansatz correspondent to the thermodynamical limit of a critical system introducing a transfer matrix formalism, and to relate the system critical exponents to the convergence rates of the associated channels.

Citations

• Simulation of time evolution with multiscale entanglement renormalization ansatz
• Density Matrix Renormalization Group and Periodic Boundary Conditions: A Quantum Information Perspective
• Density-matrix algorithms for quantum renormalization groups
• Strictly contractive quantum channels and physically realizable quantum computers
• New trends in density matrix renormalization
• The generalized Lyapunov theorem and its application to quantum channels

Cited by

• Acoustic plasmons in extrinsic free-standing graphene
• Entanglement renormalization, scale invariance, and quantum criticality
• Multiscale entanglement renormalization ansatz for spin chains with continuously varying criticality
• Theory of minimal updates in holography
• Hyperinvariant Tensor Networks and Holography
• Quantum Machine Learning Tensor Network States

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