$(2+1)$维量子临界点附近的Higgs振幅模
Higgs amplitude mode in the vicinity of a $(2+1)$-dimensional quantum critical point
摘要：
研究了二维相对论量子O（$N$）模型中的“Higgs”振幅模.利用非微扰重整化群计算了零温量子临界点附近的O（$N$）不变标量磁化率。在零温有序相中，我们发现了一个定义良好的Higgs共振的$N=2$与量子蒙特卡罗模拟协议的普遍性质。共振在低于Berezinskiii-Kosterlitz-Erborless转变温度的有限温度下持续存在。在零温度无序相，我们发现一个最大的光谱函数，但不相关的一个假定的希格斯共振。此外，我们表明，强烈抑制的共振$N\geq 3$。
英文摘要：
We study the "Higgs" amplitude mode in the relativistic quantum O($N$) model in two space dimensions. Using the nonperturbative renormalization group we compute the O($N$)-invariant scalar susceptibility in the vicinity of the zero-temperature quantum critical point. In the zero-temperature ordered phase, we find a well defined Higgs resonance for $N=2$ with universal properties in agreement with quantum Monte Carlo simulations. The resonance persists at finite temperature below the Berezinskii-Kosterlitz-Thouless transition temperature. In the zero-temperature disordered phase, we find a maximum in the spectral function which is however not related to a putative Higgs resonance. Furthermore we show that the resonance is strongly suppressed for $N\geq 3$.
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