Circuit complexity in interacting QFTs and RG flows
Aug 9, 2018
50 pages
Published in:
- JHEP 10 (2018) 140
- Published: Oct 23, 2018
e-Print:
- 1808.03105 [hep-th]
DOI:
- 10.1007/JHEP10(2018)140 (publication)
Report number:
- YITP-18-89
View in:
Citations per year
Abstract: (Springer)
We consider circuit complexity in certain interacting scalar quantum field theories, mainly focusing on the ϕ theory. We work out the circuit complexity for evolving from a nearly Gaussian unentangled reference state to the entangled ground state of the theory. Our approach uses Nielsen’s geometric method, which translates into working out the geodesic equation arising from a certain cost functional. We present a general method, making use of integral transforms, to do the required lattice sums analytically and give explicit expressions for the d = 2, 3 cases. Our method enables a study of circuit complexity in the epsilon expansion for the Wilson-Fisher fixed point. We find that with increasing dimensionality the circuit depth increases in the presence of the ϕ interaction eventually causing the perturbative calculation to breakdown. We discuss how circuit complexity relates with the renormalization group.Note:
- 50 pages, 2 figures; references updated; version to appear in JHEP
- Effective Field Theories
- Lattice Quantum Field Theory
- Renormalization Group
- AdS-CFT Correspondence
- field theory: interaction
- interaction: scalar
- field theory: scalar
- renormalization group: flow
- epsilon expansion
- ground state
References(94)
Figures(2)
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