Algorithms for entanglement renormalization: boundaries, impurities and interfaces

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.

29 pages, 29 figures

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• Isometric Tensor Network States in Two Dimensions
• Tensor network renormalization yields the multi-scale entanglement renormalization ansatz
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• Entanglement renormalization and wavelets
• Transfer Matrices and Excitations with Matrix Product States
• Holographic Quantum Circuits from Splitting/Joining Local Quenches
• Topological conformal defects with tensor networks
• Finding purifications with minimal entanglement
• Riemannian geometry and automatic differentiation for optimization problems of quantum physics and quantum technologies
• Operator content of entanglement spectra after global quenches in the transverse field Ising chain
• Continuous Tensor Network States for Quantum Fields
• MERA for Spin Chains with Continuously Varying Criticality
• Efficient Simulation of Dynamics in Two-Dimensional Quantum Spin Systems with Isometric Tensor Networks
• Mixed global anomalies and boundary conformal field theories
• Representation and design of wavelets using unitary circuits
• QGOpt: Riemannian optimization for quantum technologies
• A defect in holographic interpretations of tensor networks
• Entanglement renormalization for disordered systems
• Matrix product state renormalization
• Relativistic continuous matrix product states for quantum fields without cutoff
• Certifying ground-state properties of quantum many-body systems
• Gaussian Continuous Tensor Network States for Simple Bosonic Field Theories
• Disentangling Interacting Systems with Fermionic Gaussian Circuits: Application to Quantum Impurity Models
• Quantum Impurity in Luttinger Liquid: Universal Conductance with Entanglement Renormalization
• Spectral properties of critical 1+1D Abelian-Higgs model
• Bulk-boundary correspondence from hyper-invariant tensor networks
• Large-$S$ and tensor-network methods for strongly-interacting topological insulators
• Diagonal Isometric Form for Tensor Network States in Two Dimensions
• Entanglement renormalization for quantum fields with boundaries and defects