热场动力学中广义相干态的电路复杂性
Circuit complexity for generalised coherent states in thermal field dynamics
摘要：
本文采用协方差矩阵方法研究了热系统中广义相干态的电路复杂性。我们专注于相干热（CT）状态，这是非高斯的，并有一个非零的一点函数。我们发现，即使CT状态不能完全确定的对称两点函数，电路的复杂性仍然可以计算的协方差矩阵形式主义的框架内适当扩大的协方差矩阵。现在由酉生成的群是平移和辛群的半积。如果参考状态是高斯的，则最优测地线仍然由水平生成器生成，使得可以通过将成本函数取为$F_2$来从与目标状态相关联的广义协方差矩阵读取电路复杂度。对于单谐振子，我们详细讨论了参考态为高斯态，目标空间为单模或双模激发时的复杂性及其形成。我们的研究可以推广到自由标量场理论。
英文摘要：
In this work, we study the circuit complexity for generalized coherent states in thermal systems by adopting the covariance matrix approach. We focus on the coherent thermal (CT) state, which is non-Gaussian and has a nonvanishing one-point function. We find that even though the CT state cannot be fully determined by the symmetric two-point function, the circuit complexity can still be computed in the framework of the covariance matrix formalism by properly enlarging the covariance matrix. Now the group generated by the unitary is the semiproduct of translation and the symplectic group. If the reference state is Gaussian, the optimal geodesic is still be generated by a horizontal generator such that the circuit complexity can be read from the generalized covariance matrix associated to the target state by taking the cost function to be $F_2$. For a single harmonic oscillator, we discuss carefully the complexity and its formation in the cases that the reference states are Gaussian and the target space is excited by a single mode or double modes. We show that the study can be extended to the free scalar field theory.
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