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arXiv · 1808.03105

Circuit complexity in interacting QFTs and RG flows

Arpan Bhattacharyya·Arvind Shekar·Aninda Sinha
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Abstract

We consider circuit complexity in certain interacting scalar quantum field theories, mainly focusing on the $ϕ^4$ 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 $ϕ^4$ interaction eventually causing the perturbative calculation to breakdown. We discuss how circuit complexity relates with the renormalization group.

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Arpan Bhattacharyya, Arvind Shekar, Aninda Sinha. 2018-10-18. Circuit complexity in interacting QFTs and RG flows. https://doi.org/10.1007/jhep10(2018)140

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