$\mathcal{Z}_{2}$ ${\cal EEFT}$中的电路复杂性
Circuit Complexity in $\mathcal{Z}_{2}$ ${\cal EEFT}$
摘要：
受近年来弱相互作用标量场论中电路复杂性研究的启发，本文研究了$\mathcal{Z}_2$偶有效场论（$\mathcal{Z}_2$ EEFT）中电路复杂性的计算.我们考虑一个有质量的自由场论与高阶威尔逊运营商，如$ϕ^{4}$，$ϕ^{6}$和$ϕ^8.$为了方便我们的计算，我们正规化的理论，把它放在一个格子。首先，我们考虑一个简单的情况下，两个振荡器，后来推广到$N$振荡器的结果。该研究已进行了近高斯态。在我们的计算中，参考态是一个近似高斯的非纠缠态，相应的目标态，根据我们的理论计算，是一个近似高斯的纠缠态。我们计算的复杂性，使用Nielsen开发的几何方法，参数化的路径有序酉变换和最小化的测地线在酉空间。高阶算子的贡献，电路的复杂性，在我们的理论已经讨论。我们还探讨了各种情况下的复杂性与我们的理论中的其他参数的依赖关系。
英文摘要：
Motivated by recent studies of circuit complexity in weakly interacting scalar field theory, we explore the computation of circuit complexity in $\mathcal{Z}_2$ Even Effective Field Theories ($\mathcal{Z}_2$ EEFTs). We consider a massive free field theory with higher-order Wilsonian operators such as $ϕ^{4}$, $ϕ^{6}$ and $ϕ^8.$ To facilitate our computation we regularize the theory by putting it on a lattice. First, we consider a simple case of two oscillators and later generalize the results to $N$ oscillators. The study has been carried out for nearly Gaussian states. In our computation, the reference state is an approximately Gaussian unentangled state, and the corresponding target state, calculated from our theory, is an approximately Gaussian entangled state. We compute the complexity using the geometric approach developed by Nielsen, parameterizing the path ordered unitary transformation and minimizing the geodesic in the space of unitaries. The contribution of higher-order operators, to the circuit complexity, in our theory has been discussed. We also explore the dependency of complexity with other parameters in our theory for various cases.
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