Algorithms for Entanglement Renormalization: Boundaries, Impurities and Interfaces

2013/12/02 by Glen Evenbly, Guifre Vidal, Guifré Vidal
Chemistry · Mathematics · Physics and Astronomy · #Ansatz #Bethe ansatz #Boundary (topology) #Boundary value problem #Chemistry #Ground state #Limit (mathematics) #Mathematical analysis #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum and electron transport phenomena #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Renormalization #Statistical physics #Thermodynamic limit #Translation (biology) #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1007/s10955-014-0983-1

published as J Stat Phys (2014) 157:931-978 · 29 pages, 29 figures

arxiv created 2013/12/02 · openalex publication_date 2014/04/21 · arxiv updated 2014/10/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We propose algorithms, based on the multi-scale entanglement renormalization ansatz, to obtain the ground state of quantum critical systems in the presence of boundaries, impurities, or interfaces. By exploiting the theory of minimal updates [G. Evenbly and G. Vidal, arXiv:1307.0831], the ground state is completely characterized in terms of a number of variational parameters that is independent of the system size, even though the presence of a boundary, an impurity, or an interface explicitly breaks the translation invariance of the host system. Similarly, computational costs do not scale with the system size, allowing the thermodynamic limit to be studied directly and thus avoiding finite size effects e.g. when extracting the universal properties of the critical system.

Citations

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