Journal of High Energy Physics

, 2019:276 | Cite as

Circuit complexity and 2D bosonisation

  • Dongsheng GeEmail author
  • Giuseppe Policastro
Open Access
Regular Article - Theoretical Physics


We consider the circuit complexity of free bosons and free fermions in 1+1 dimensions. Motivated by the results of [1, 2, 3] who found different behavior in the complexity of free bosons and fermions, in any dimension, we consider the 1+1 dimensional case where, thanks to the bosonisation equivalence of the Hilbert spaces, we can consider the same state from both the bosonic and the fermionic perspectives. This allows us to study the dependence of the complexity on the choice of the set of gates, which explains the discrepancy. We study the effect in two classes of states: i) bosonic-coherent / fermionic- gaussian states; ii) states that are both bosonic- and fermionic-gaussian. We consider the complexity relative to the ground state. In the first class, the different complexities can be related to each other by introducing a mode-dependent cost function in one of the descriptions. The differences in the second class are more important, in terms of the structure of UV divergencies and the overall behavior of the complexity.


AdS-CFT Correspondence Effective Field Theories Field Theories in Lower Dimensions 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Laboratoire de Physique de l’Ećole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne UniversitéUniversité Paris-DiderotParisFrance

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