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Bhattacharyya, Arpan; Shekar, Arvind; Sinha, Aninda

Circuit complexity in interacting QFTs and RG flows. (English) Zbl 1402.81203

J. High Energy Phys. 2018, No. 10, Paper No. 140, 44 p. (2018).
Summary: We consider circuit complexity in certain interacting scalar quantum field theories, mainly focusing on the \(\phi^4\) 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 \(\phi^4\) interaction eventually causing the perturbative calculation to breakdown. We discuss how circuit complexity relates with the renormalization group.

Cited in 53 Documents

MSC:

81T25 Quantum field theory on lattices
81T17 Renormalization group methods applied to problems in quantum field theory
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics

Keywords:

effective field theories; lattice quantum field theory; renormalization group; AdS-CFT correspondence
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References:

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