论文标题
$ sl_2 $变形的浮qulequet共形场理论的分类
Classification of $SL_2$ deformed Floquet Conformal Field Theories
论文作者
论文摘要
非平衡量子多体动力学的分类是凝结物理学和统计力学中的一个具有挑战性的问题。在这项工作中，我们研究了一个基本问题，即A（1+1）维度形式的野外理论（CFT）是否稳定在具有$ n $ n $ nocunds nocunting Hamiltonians的定期驾驶中。先前的工作表明，由某些$ SL_2 $变形的汉密尔顿人驱动的浮点（或定期驱动）的CFT表现出非加热（稳定）和加热（不稳定）阶段。在这项工作中，我们表明相图取决于驾驶哈密顿人的类型。通常，加热阶段是通用的，但是相图中可能不存在非加热阶段。对于不加热阶段的存在，我们为$ n = 2 $提供了足够的必要条件，以及$ n> 2 $的足够条件。这些条件由$ n $层的数据组成，每一层由驾驶汉密尔顿人的类型决定。我们的结果还适用于单个量子淬灭问题，其中$ n = 1 $。
Classification of the non-equilibrium quantum many-body dynamics is a challenging problem in condensed matter physics and statistical mechanics. In this work, we study the basic question that whether a (1+1) dimensional conformal field theory (CFT) is stable or not under a periodic driving with $N$ non-commuting Hamiltonians. Previous works showed that a Floquet (or periodically driven) CFT driven by certain $SL_2$ deformed Hamiltonians exhibit both non-heating (stable) and heating (unstable) phases. In this work, we show that the phase diagram depends on the types of driving Hamiltonians. In general, the heating phase is generic, but the non-heating phase may be absent in the phase diagram. For the existence of the non-heating phases, we give sufficient and necessary conditions for $N=2$, and sufficient conditions for $N>2$. These conditions are composed of $N$ layers of data, with each layer determined by the types of driving Hamiltonians. Our results also apply to the single quantum quench problem with $N=1$.
