周期、准周期和随机驱动共形场论：I
Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories: Part I
摘要：
在本文及其续集中，我们研究了驱动1+1D共形场论（CFTs）中的非平衡动力学，包括周期、准周期和随机驱动。我们研究一个可溶性家庭的驱动器，其中的哈密顿量只涉及在一个单一的波长空间调制的能量动量密度。由此产生的时间演化，然后捕获的莫比乌斯坐标变换。在第一部分中，我们建立了总体框架，并重点介绍了前两个类。在周期性驱动的CFTs中，我们推广了早期的工作，并研究了不同阶段，即加热，非加热阶段和它们之间的相变的纠缠/能量演化的一般特征。在准周期驱动的CFTs中，我们主要关注的是用Fibonacci序列驱动的情况。我们发现：（i）非加热相形成一个零测度的Cantor集;（ii）在加热相，李雅普诺夫指数（其表征纠缠熵和能量的增长率）表现出自相似性，并且可以是任意小的;（iii）加热阶段在斐波那契时间的空间结构的位置中表现出周期性;（iv）我们可以精确地找到非加热不动点，在那里，纠缠熵/能量在Fibonacci数处振荡，但在非Fibonacci数处以多项式方式增长;（v）对于驱动哈密顿算子的某些选择，Fibonacci驱动CFT的非加热阶段可以映射到Fibonacci准晶体中传播的电子的能谱。此外，还研究了另一种具有Aubry-André类序列的准周期驱动CFT。我们比较CFT结果晶格计算，发现显着的协议。
英文摘要：
In this paper and its sequel, we study non-equilibrium dynamics in driven 1+1D conformal field theories (CFTs) with periodic, quasi-periodic, and random driving. We study a soluble family of drives in which the Hamiltonian only involves the energy-momentum density spatially modulated at a single wavelength. The resulting time evolution is then captured by a Möbius coordinate transformation. In this Part I, we establish the general framework and focus on the first two classes. In periodically driven CFTs, we generalize earlier work and study the generic features of entanglement/energy evolution in different phases, i.e. the heating, non-heating phases and the phase transition between them. In quasi-periodically driven CFTs, we mainly focus on the case of driving with a Fibonacci sequence. We find that (i) the non-heating phases form a Cantor set of measure zero; (ii) in the heating phase, the Lyapunov exponents (which characterize the growth rate of the entanglement entropy and energy) exhibit self-similarity, and can be arbitrarily small; (iii) the heating phase exhibits periodicity in the location of spatial structures at the Fibonacci times; (iv) one can find exactly the non-heating fixed point, where the entanglement entropy/energy oscillate at the Fibonacci numbers, but grow logarithmically/polynomially at the non-Fibonacci numbers; (v) for certain choices of driving Hamiltonians, the non-heating phases of the Fibonacci driving CFT can be mapped to the energy spectrum of electrons propagating in a Fibonacci quasi-crystal. In addition, another quasi-periodically driven CFT with an Aubry-André like sequence is also studied. We compare the CFT results to lattice calculations and find remarkable agreement.
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