论文标题
临界点附近全息复杂性的非分析性
Non-analyticity in Holographic Complexity near Critical points
论文作者
论文摘要
使用二阶相变的全息模型研究了临界点附近的区域。在上一篇论文中，我们认为真空的量子电路复杂性（$ c_0 $）是关键点最大的。当通过$ \ int d^d x \，τ\，o_Δ$复杂性$ c（τ）$从临界点变形时，在$τ$中具有非分析性，即$ c_0 -c（τ）在这里，像往常一样，$ν= \ frac {1} {d-δ} $和$ξ$是相关长度$ξ\ sim | sim | | wism |谢| |τ-τ_c|^{ - ν} $，并且可能对此表达式进行对数更正。这是使用Bose-Hubbard模型和一般缩放考虑因素的数值结果得出的。在本文中，我们表明，在全息复杂性的情况下，情况也是有效的，证明了结果是普遍的，同时也提供了复杂性全息计算的证据。
The region near a critical point is studied using holographic models of second-order phase transitions. In a previous paper, we argued that the quantum circuit complexity of the vacuum ($C_0$) is the largest at the critical point. When deforming away from the critical point by a term $\int d^d x \, τ\, O_Δ$ the complexity $C(τ)$ has a piece non-analytic in $τ$, namely $C_0 -C(τ) \sim |τ-τ_c|^{ν(d-1)} + \mathrm{analytic} $. Here, as usual, $ν=\frac{1}{d-Δ}$ and $ξ$ is the correlation length $ξ\sim |τ-τ_c|^{-ν}$ and there are possible logarithmic corrections to this expression. That was derived using numerical results for the Bose-Hubbard model and general scaling considerations. In this paper, we show that the same is valid in the case of holographic complexity providing evidence that the results are universal, and at the same time providing evidence for holographic computations of complexity.
