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Circuit complexity in proca theory

2021 
In this paper, we study circuit complexity in proca theory with Nielsen's approach and Fubini-Study (FS) metric approach. We place the fields on a lattice to gain a regularized theory. The ground state is obtained by adopting proper coordinates. We calculate complexities of the ground and thermofield double (TFD) states with Nielsen's approach. We find complexity of the TFD state grows like a logarithmic function. We quantize the proca fields and construct the approximate ground and TFD states by action unitary circuit operators on the associated reference states. We calculate complexities of the ground and TFD states with FS metric approach, and find complexity of the TFD state grows linearly with time.
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