Non-local scaling operators with entanglement renormalization

Abstract

The multi-scale entanglement renormalization ansatz (MERA) can be used, in its scale invariant version, to describe the ground state of a lattice system at a quantum critical point. From the scale invariant MERA one can determine the local scaling operators of the model. Here we show that, in the presence of a global symmetry $\mathcal{G}$, it is also possible to determine a class of non-local scaling operators. Each operator consist, for a given group element $g\in \mathcal{G}$, of a semi-infinite string $\tGamma_g$ with a local operator $\varphi$ attached to its open end. In the case of the quantum Ising model, $\mathcal{G}={\mathbb{Z}}_2$, they correspond to the disorder operator $\mu$, the fermionic operators $\psi$ and $\bar{\psi }$, and all their descendants. Together with the local scaling operators identity $\mathbb{I}$, spin $\sigma$ and energy $\epsilon$, the fermionic and disorder scaling operators $\psi$, $\bar{\psi }$ and $\mu$ are the complete list of primary fields of the Ising CFT. Thefore the scale invariant MERA allows us to characterize all the conformal towers of this CFT.

4 pages, 4 figures. Revised version

References in corpus (6)

• A class of quantum many-body states that can be efficiently simulated
• Entanglement renormalization and topological order
• Entanglement renormalization, scale invariance, and quantum criticality
• Quantum MERA Channels
• Exact entanglement renormalization for string-net models
• Boundary quantum critical phenomena with entanglement renormalization

Cited by in corpus (21)

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• Anomalies and entanglement renormalization
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• Emergence of conformal symmetry in quantum spin chains: anti-periodic boundary conditions and supersymmetry
• Quantum dimensions from local operator excitations in the Ising model
• Holographic Dynamics from Multiscale Entanglement Renormalization Ansatz
• Entanglement compression in scale space: from the multiscale entanglement renormalization ansatz to matrix product operators
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• Entanglement renormalization and symmetry fractionalization
• Qubit frugal entanglement determination with the deep multi-scale entanglement renormalization ansatz
• Note on Localized Objects as Constrained States of Holographic Variables