量子多临界点附近的振荡保真度磁化率
Oscillating fidelity susceptibility near a quantum multicritical point
摘要：
以横截面XY模型为例，研究了几何张量$χ_{α,β}(λ_1,λ_2)$和保真度磁化率$(χ_{\rm F})$在量子多临界点附近的标度行为.我们表明，几何张量的行为（从而$χ_{\rm F}$）是从附近的临界点看到的截然不同。特别是，我们发现，是高度非单调函数的$λ$沿通用方向$λ_1\simλ_2 = λ$时，系统大小$L$之间的较短和较长的相关长度表征MCP：$1/|λ|^{ν_1}\ll L\ll 1/|λ|^{ν_2}$，其中$ν_1<ν_2$是两个相关长度指数表征系统的边界。我们发现，$χ_{αβ}$的组件的最大值的标度与准临界点的出现在$λ\sim 1/L^{1/ν_1}$，有关的接近有限动量各向异性过渡的临界线。这种标度不同于由常规临界指数确定的热力学极限$L\gg 1/|λ|^{ν_2}$中的标度。我们使用我们的结果来计算缺陷密度从MCP开始的快速淬火，并表明，它施加一个小的淬火幅度的阶梯状行为。热密度和对角熵密度的研究也显示出准临界点的特征。
英文摘要：
We study scaling behavior of the geometric tensor $χ_{α,β}(λ_1,λ_2)$ and the fidelity susceptibility $(χ_{\rm F})$ in the vicinity of a quantum multicritical point (MCP) using the example of a transverse XY model. We show that the behavior of the geometric tensor (and thus of $χ_{\rm F}$) is drastically different from that seen near a critical point. In particular, we find that is highly non-monotonic function of $λ$ along the generic direction $λ_1\simλ_2 = λ$ when the system size $L$ is bounded between the shorter and longer correlation lengths characterizing the MCP: $1/|λ|^{ν_1}\ll L\ll 1/|λ|^{ν_2}$, where $ν_1<ν_2$ are the two correlation length exponents characterizing the system. We find that the scaling of the maxima of the components of $χ_{αβ}$ is associated with emergence of quasi-critical points at $λ\sim 1/L^{1/ν_1}$, related to the proximity to the critical line of finite momentum anisotropic transition. This scaling is different from that in the thermodynamic limit $L\gg 1/|λ|^{ν_2}$, which is determined by the conventional critical exponents. We use our results to calculate the defect density following a rapid quench starting from the MCP and show that it exerts a step-like behavior for small quench amplitudes. Study of heat density and diagonal entropy density also show signatures of quasi-critical points.
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