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J. J. Fernández-Melgarejo, J. Molina-Vilaplana, E. Torrente-Lujan, Entanglement Renormalization for Interacting Field Theories
Original
1904
Earlier work this paper cites.
G. Evenbly Number-State Preserving Tensor Networks as Classifiers for Supervised Learning
Original
1905
Earlier work this paper cites.
M. Fannes, B. Nachtergaele, and R. F. Werner, Finitely correlated states on quantum spin chains
1992
Earlier work this paper cites.
S.R. White, Density matrix formulation for quantum renormalization groups
1992
Earlier work this paper cites.
T. Nishino, K. Okunishi Corner Transfer Matrix Renormalization Group Method
1996
Earlier work this paper cites.
G. Sierra and M.A. Martin-Delgado, The Density Matrix Renormalization Group, Quantum Groups and Conformal Field Theory
1998
Earlier work this paper cites.
T. Nishino and K. Okunishi, A Density Matrix Algorithm for 3D Classical Models
1998
Earlier work this paper cites.
S. R. White, R. L. Martin, Ab Initio Quantum Chemistry using the Density Matrix Renormalization Group
1999
Earlier work this paper cites.
G. Vidal, Efficient classical simulation of slightly entangled quantum computations
2003
Earlier work this paper cites.
F. Verstraete, and J. I. Cirac, Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
2004
Earlier work this paper cites.
U. Schollwoeck, The density-matrix renormalization group
2005
Earlier work this paper cites.
D. Perez-Garcia, F. Verstraete, M. M.Wolf, and J. I. Cirac, Matrix Product State Representations
2007
Earlier work this paper cites.
G. Vidal, Entanglement renormalization
2007
Earlier work this paper cites.
M. Levin, C. P. Nave, Tensor renormalization group approach to 2D classical lattice models
2007
Earlier work this paper cites.
G. Vidal, A class of quantum many-body states that can be efficiently simulated
2008
Earlier work this paper cites.
G. Evenbly, G. Vidal, Algorithms for entanglement renormalization, Phys. Rev. B 79, 144108 (2009), arXiv: 0707.1454
2009
Earlier work this paper cites.
J. I. Cirac, F. Verstraete, Renormalization and tensor product states in spin chains and lattices
Original
2009
Earlier work this paper cites.
Z.-C. Gu, X.-G. Wen, Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
Original
2009
Earlier work this paper cites.
F. Verstraete and J. I. Cirac, Continuous Matrix Product States for Quantum Fields
Original
2010
Earlier work this paper cites.

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2019

Magic entanglement renormalization for quantum fields

Zou, Yijian, Ganahl, Martin, Vidal, Guifre

Understand

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.

Built on

J. J. Fernández-Melgarejo, J. Molina-Vilaplana, E. Torrente-Lujan, Entanglement Renormalization for Interacting Field Theories
Original
1904
Earlier work this paper cites.
G. Evenbly Number-State Preserving Tensor Networks as Classifiers for Supervised Learning
Original
1905
Earlier work this paper cites.
M. Fannes, B. Nachtergaele, and R. F. Werner, Finitely correlated states on quantum spin chains
1992
Earlier work this paper cites.
S.R. White, Density matrix formulation for quantum renormalization groups
1992
Earlier work this paper cites.
T. Nishino, K. Okunishi Corner Transfer Matrix Renormalization Group Method
1996
Earlier work this paper cites.
G. Sierra and M.A. Martin-Delgado, The Density Matrix Renormalization Group, Quantum Groups and Conformal Field Theory
1998
Earlier work this paper cites.
T. Nishino and K. Okunishi, A Density Matrix Algorithm for 3D Classical Models
1998
Earlier work this paper cites.
S. R. White, R. L. Martin, Ab Initio Quantum Chemistry using the Density Matrix Renormalization Group
1999
Earlier work this paper cites.
G. Vidal, Efficient classical simulation of slightly entangled quantum computations
2003
Earlier work this paper cites.
F. Verstraete, and J. I. Cirac, Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
2004
Earlier work this paper cites.
U. Schollwoeck, The density-matrix renormalization group
2005
Earlier work this paper cites.
D. Perez-Garcia, F. Verstraete, M. M.Wolf, and J. I. Cirac, Matrix Product State Representations
2007
Earlier work this paper cites.
G. Vidal, Entanglement renormalization
2007
Earlier work this paper cites.
M. Levin, C. P. Nave, Tensor renormalization group approach to 2D classical lattice models
2007
Earlier work this paper cites.
G. Vidal, A class of quantum many-body states that can be efficiently simulated
2008
Earlier work this paper cites.
G. Evenbly, G. Vidal, Algorithms for entanglement renormalization, Phys. Rev. B 79, 144108 (2009), arXiv: 0707.1454
2009
Earlier work this paper cites.
J. I. Cirac, F. Verstraete, Renormalization and tensor product states in spin chains and lattices
Original
2009
Earlier work this paper cites.
Z.-C. Gu, X.-G. Wen, Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
Original
2009
Earlier work this paper cites.
F. Verstraete and J. I. Cirac, Continuous Matrix Product States for Quantum Fields
Original
2010
Earlier work this paper cites.