Algorithms for Entanglement Renormalization: Boundaries, Impurities and Interfaces

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 (Evenbly and Vidal, arXiv:1307.0831, 2013 ), the ground st...

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Bibliographic Details
Published in:Journal of statistical physics 2014-12, Vol.157 (4-5), p.931-978
Main Authors: Evenbly, G., Vidal, G.
Format: Article
Language:English
Subjects:
Algorithms
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Thermodynamics
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Summary: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 (Evenbly and Vidal, arXiv:1307.0831, 2013 ), 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.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-014-0983-1