Circuit complexity in fermionic field theory

By Rifath Khan, Chethan Krishnan, Sanchita Sharma. Physical Review D, 2018

224 citations recorded by the source corpus.

We define and calculate versions of complexity for free fermionic quantum field theories in 1 + 1 and 3 + 1 dimensions, adopting Nielsen's geodesic perspective in the space of circuits. We do this both by discretizing and identifying appropriate classes of Bogoliubov-Valatin transformations, and also directly in the continuum by defining squeezing operators and their generalizations. As a closely related problem, we consider cMERA tensor networks for fermions: viewing them as paths in circuit space, we compute their path lengths. Certain ambiguities that arise in some of these results because of cutoff dependence are discussed.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/14c551afc466d7226f76c4e2383b42aafe5dfdc0

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In Atomic and Molecular Physics, and Optics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Circuit complexity in interacting QFTs and RG flows (2018, background): “These calculations have been generalized for free fermions in [17,19].”
Complexity and entanglement for thermofield double states (2018, background): “[23,55,56,58,59]) focused on circuits which remain within the space of Gaussian states, and hence the group of Bogoliubov transformations played an important role.”
Holographic complexity in Vaidya spacetimes. Part II (2018, background): “In this case, the boundary of the WDW patch is defined by two timelike geodesics that originate at the past joint (30)We note that the logarithmic factor does not seem to arise for a free fermion [35, 57].”