Non-Gaussian entanglement renormalization for quantum fields
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Springer
Received: May 4, Revised: June 15, Accepted: June 21, Published: July 22,
2020 2020 2020 2020
J.J. Fern´ andez-Melgarejoa and J. Molina-Vilaplanab a
Departamento de F´ısica, Universidad de Murcia, Campus de Espinardo, Murcia 30100, Spain b Department of Automatics, Electrical Engineering and Electronic Technology, Universidad Polit´ecnica de Cartagena, C/Dr Fleming S/N, Cartagena 30202, Spain
E-mail: [email protected], [email protected] Abstract: In this work, a non-Gaussian cMERA tensor network for interacting quantum field theories (icMERA) is presented. This consists of a continuous tensor network circuit in which the generator of the entanglement renormalization of the wavefunction is nonperturbatively extended with nonquadratic variational terms. The icMERA circuit nonperturbatively implements a set of scale dependent nonlinear transformations on the fields of the theory, which suppose a generalization of the scale dependent linear transformations induced by the Gaussian cMERA circuit. Here we present these transformations for the case of self-interacting scalar and fermionic field theories. Finally, the icMERA tensor network is fully optimized for the λφ4 theory in (1 + 1) dimensions. This allows us to evaluate, nonperturbatively, the connected parts of the two- and four-point correlation functions. Our results show that icMERA wavefunctionals encode proper non-Gaussian correlations of the theory, thus providing a new variational tool to study phenomena related with strongly interacting field theories. Keywords: Holography and condensed matter physics (AdS/CMT), Nonperturbative Effects, Renormalization Group ArXiv ePrint: 2003.08438
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)149
JHEP07(2020)149
Non-Gaussian entanglement renormalization for quantum fields
Contents 1 Introduction and summary
1
2 cMERA formalism 2.1 Non-Gaussian states: beyond quadratic entanglers
5 7 10 10 11 12
4 Non-Gaussian cMERA 4.1 Nonlinear canonical transformations 4.2 Non-Gaussian cMERA formalism 4.3 Fermionic non-Gaussian cMERA
13 14 17 19
5 icMERA: non-Gaussian cMERA circuits 5.1 Nonquadratic entangler 5.2 icMERA correlation functions 5.3 icMERA circuit for the scalar λφ4 theory
20 20 24 26
6 Discussion
31
A icMERA at a perturbative regime in λφ4 (2) (4) A.1 Connected diagrams for Gc and Gc (n) A.2 Perturbative analysis of Gc in icMERA
32 32 33
B χ integrals
35
1
Introduction and summary
The multiscale entanglement renormalization ansatz (MERA) [1, 2], which was originally proposed as a variational method to obtain the ground state of spin chains systems, consists of a real space renormalization group technique that, iteratively, removes the quantum correlations between small adjacent regions of space at each length scale. A continuous version of MERA (cMERA) was proposed for free field theories [3, 4]. Motivated, among others, by the conjecture that cMERA is a realization of the AdS/CFT correspondence [5– 11], a rigorous and (non)perturbative formalis
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