近似模型中光子凝聚的非微扰No-Go定理
A non-perturbative no-go theorem for photon condensation in approximate models
摘要：
正常态和光子凝聚态之间的平衡相变（也称为超辐射相变）是一个备受争议的研究课题，在过去的四十年里，关于它们的发生和不去定理的提议一直在相互追逐。最近的不通过定理表明，规范不变性禁止二阶相变的光子凝聚态时，腔-光子模式被假定为{ \it空间均匀}。然而，理论上已经预测，耦合到光的三能级系统的集合可以显示到光子凝聚态的一阶相变。最近还表明，物质系统的希尔伯特空间的截断可以影响理论的规范不变性。然而，在截断的希尔伯特空间中总是可以得到遵守规范原理的近似哈密顿量。在这里，我们证明了一个一般的不去定理也适用于截断，规范不变的模型，禁止一阶以及二阶超辐射相变在没有耦合的情况下与磁场。特别是，我们明确考虑的情况下，相互作用的电子在晶格和$M$能级系统。
英文摘要：
Equilibrium phase transitions between a normal and a photon condensate state (also known as superradiant phase transitions) are a highly debated research topic, where proposals for their occurrence and no-go theorems have chased each other for the past four decades. Recent no-go theorems have demonstrated that gauge invariance forbids second-order phase transitions to a photon condensate state when the cavity-photon mode is assumed to be {\it spatially uniform}. However, it has been theoretically predicted that a collection of three-level systems coupled to light can display a first-order phase transition to a photon condensate state. %{It has also been recently shown that truncation of the Hilbert space of the matter system can affect the gauge invariance of the theory. However, it is always possible to obtain approximate Hamiltonians obeying the gauge principle in the truncated Hilbert space.} Here, we demonstrate a general no-go theorem valid also for truncated, gauge-invariant models which forbid first-order as well as second-order superradiant phase transitions in the absence of a coupling with a magnetic field. In particular, we explicitly consider the cases of interacting electrons in a lattice and $M$-level systems.
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