论文标题
凝结物质系统中的Landau波线
Landau poles in condensed matter systems
论文作者
论文摘要
Landau Poles的存在与否是非质量子量子场理论中最古老的开放问题之一。我们研究了两个凝结物质系统中的Landau Pole问题，它们的长波长物理是通过适当的量子场理论描述的：与远距离库仑相互作用的石墨烯中的临界量子磁体和Dirac Fermions。临界量子磁铁提供了量子相变的经典示例，并由$ ϕ^4 $理论很好地描述。我们发现，在$ ϕ^4 $理论中，$ ϕ^6 $势等无关但允许的耦合，例如$ ϕ^6 $。我们获得了$ ϕ^4 + ϕ^6 $的耦合beta函数在小订单和大订单下的潜力。从1循环计算中，Landau Pole被紫外线固定点所取代。 Lipatov在大订单上的分析表明，包含$ ϕ^6 $项在beta函数的高阶扩展方面也具有重要的影响。我们还研究了Landau Pole在2+1尺寸的Dirac Fermions中的作用，例如库仑相互作用，例如石墨烯。弱耦合扰动理论最多2个回路和低阶大N计算都表明没有Landau极。此外，我们计算β函数的渐近扩展系数。我们发现，渐近系数是由$ ϕ^4 $理论的界限，因此，如果$ ϕ^4 $理论没有表现出Landau Pole，那么石墨烯将不含Landau Poles。我们简要讨论可能在这些系统中可能探测Landau Pole的可能实验。在合适的冷凝物质系统中研究Landau杆非常重要，因为相关的Landau Pole Pole量尺度（无论是量子电动力学还是HIGGS物理学）是完全无法实现的。
The existence or not of Landau poles is one of the oldest open questions in non-asymptotic quantum field theories. We investigate the Landau pole issue in two condensed matter systems whose long-wavelength physics is described by appropriate quantum field theories: the critical quantum magnet and Dirac fermions in graphene with long-range Coulomb interactions. The critical quantum magnet provides a classic example of a quantum phase transition, and it is well described by the $ϕ^4$ theory. We find that the irrelevant but symmetry-allowed couplings, such as the $ϕ^6$ potential, can significantly change the fate of the Landau pole in the $ϕ^4$ theory. We obtain the coupled beta functions of a $ϕ^4 + ϕ^6$ potential at both small and large orders. Already from the 1-loop calculation, the Landau pole is replaced by an ultraviolet fixed point. A Lipatov analysis at large orders reveals that the inclusion of a $ϕ^6$ term also has important repercussions for the high-order expansion of the beta functions. We also investigate the role of the Landau pole in 2+1 dimensional Dirac fermions with Coulomb interactions, e.g., graphene. Both the weak-coupling perturbation theory up to 2 loops and a low-order large-N calculation show the absence of a Landau pole. Furthermore, we calculate the asymptotic expansion coefficients of the beta function. We find that the asymptotic coefficient is bounded by that of a $ϕ^4$ theory, so graphene is free from Landau poles if the $ϕ^4$ theory does not manifest a Landau pole. We briefly discuss possible experiments that could potentially probe the existence of a Landau pole in these systems. Studying Landau poles in suitable condensed matter systems is of considerable fundamental importance since the relevant Landau pole energy scales in particle physics, whether it is quantum electrodynamics or Higgs physics, are completely unattainable.
