Magic entanglement renormalization for quantum fields
arXiv:1906.04218
Abstract
Continuous tensor networks are variational wavefunctions proposed in recent years to efficiently simulate quantum field theories (QFTs). Prominent examples include the continuous matrix product state (cMPS) and the continuous multi-scale entanglement renormalization ansatz (cMERA). While the cMPS can approximate ground states of a class of QFT Hamiltonians that are both local and interacting, cMERA is only well-understood for QFTs that are quasi-local and non-interacting. In this paper we propose the magic cMERA, a concrete realization of cMERA for a free boson QFT that simultaneously satisfies four remarkable properties: (i) it is the exact ground state of a strictly local Hamiltonian; (ii) in the massless case, its spectrum of scaling operators is exactly soluble in real space; (iii) it has the short-distance structure of a cMPS; (iv) it is generated by a quasi-local entangler that can be written as a continuous matrix product operator. None of these properties is fulfilled by previous cMERA proposals. Properties (iii)-(iv) establish a firm connection between cMERA and cMPS wavefunctionals, opening the path to applying powerful cMPS numerical techniques, valid for interacting QFTs, also to cMERA calculations.
4+8 pages, 4 figures
References in corpus (32)
- The density-matrix renormalization group
- Efficient classical simulation of slightly entangled quantum computations
- Entanglement renormalization
- Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
- A class of quantum many-body states that can be efficiently simulated
- Time-dependent variational principle for quantum lattices
- Tensor renormalization group approach to 2D classical lattice models
- Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
- Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks
- Tensor Network Renormalization
- Algorithms for entanglement renormalization
- Tensor product methods and entanglement optimization for ab initio quantum chemistry
- Continuous Matrix Product States for Quantum Fields
- Entanglement renormalization for quantum fields
- Surface/State Correspondence as a Generalized Holography
- cMERA as Surface/State Correspondence in AdS/CFT
- Matrix product ansatz for Fermi fields in one dimension
- A Density Matrix Algorithm for 3D Classical Models
- Fermionic orbital optimisation in tensor network states
- Applying the variational principle to (1+1)-dimensional quantum field theories
- Continuous Matrix Product States for Quantum Fields: an Energy Minimization Algorithm
- Spacetime symmetries and conformal data in the continuous multi-scale entanglement renormalization ansatz
- Lieb-Liniger model with exponentially-decaying interactions: a continuous matrix product state study
- Holographic Entanglement Renormalization of Topological Insulators
- Continuous matrix product states for coupled fields: Application to Luttinger Liquids and quantum simulators
- Continuous matrix product states with periodic boundary conditions and an application to atomtronics
- Information Geometry of Entanglement Renormalization for free Quantum Fields
- Entanglement and correlations in the continuous multi-scale entanglement renormalization ansatz
- Unitary Networks from the Exact Renormalization of Wave Functionals
- Continuous matrix product states for non-relativistic quantum fields: a lattice algorithm for inhomogeneous systems
- Quantum Gross-Pitaevskii Equation
- Entanglement Renormalization and Two Dimensional String Theory