Title: A Path Integral for Chord Diagrams and Chaotic-Integrable Transitions in Double Scaled SYK Show Chinese title

Title: 弦图的路径积分及双尺度SYK中的混沌-可积过渡

Abstract: We study transitions from chaotic to integrable Hamiltonians in the double scaled SYK and $p$-spin systems. The dynamics of our models is described by chord diagrams with two species. We begin by developing a path integral formalism of coarse graining chord diagrams with a single species of chords, which has the same equations of motion as the bi-local ($G\Sigma$) Liouville action, yet appears otherwise to be different and in particular well defined. We then develop a similar formalism for two types of chords, allowing us to study different types of deformations of double scaled SYK and in particular a deformation by an integrable Hamiltonian. The system has two distinct thermodynamic phases: one is continuously connected to the chaotic SYK Hamiltonian, the other is continuously connected to the integrable Hamiltonian, separated at low temperature by a first order phase transition. We also analyze the phase diagram for generic deformations, which in some cases includes a zero-temperature phase transition. Show Chinese abstract

Abstract: 我们研究双标度SYK和$p$自旋系统中从混沌到可积哈密顿量的转变。 我们的模型的动力学由两种种类的弦图描述。 我们首先开发了一种单一种类弦图的粗粒化路径积分形式，其运动方程与双局域($G\Sigma$)李维维尔作用量相同，但除此之外似乎不同，并且特别是良好定义的。 然后，我们为两种类型的弦开发了类似的格式，使我们能够研究双标度SYK的不同类型变形，特别是通过一个可积哈密顿量的变形。 该系统有两个不同的热力学相：一个是连续连接到混沌SYK哈密顿量的相，另一个是连续连接到可积哈密顿量的相，在低温下通过一阶相变分隔。 我们还分析了通用变形的相图，其中在某些情况下包括零温相变。