Circuit complexity in proca theory

TL;DR

This paper investigates the circuit complexity of Proca theory using Nielsen's and Fubini-Study approaches, revealing logarithmic and linear growth patterns in ground and TFD states, respectively.

Contribution

It introduces a combined analysis of circuit complexity in Proca theory using two different metrics and provides explicit calculations for ground and TFD states.

Findings

TFD complexity grows logarithmically over time

Ground state complexity is obtained via lattice regularization

TFD state complexity increases linearly with time

Abstract

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, and obtain the ground state by adopting proper coordinates. We calculate complexities of the ground and thermofield double (TFD) states with Nielsen's approach, complexity of the TFD state is found to grows like a logarithmic function. We quantize the Proca fields and give the approximate ground state and TFD state by acting unitary circuit operators on the associated reference states. The circuit lengths are calculated with FS metric, the minimal lengths are given according to the associated geometric spaces. The complexity of TFD state is found to grows linearly with time.