发表机构
Fudan University; Hefei National Laboratory（复旦大学; 合肥国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出费米高斯斯克鲁奇系综，用以描述自由费米子系统的深度热化，并在SYK$_2$模型及电荷守恒随机高斯电路中验证其普适性。
AI 中文摘要
测量多体波函数的一部分会在未测量的子系统中生成一个纯量子态的投影系综。深度热化的最新进展表明，在混沌系统中，该系综普遍收敛到与其平均密度矩阵相容的最大随机系综，即斯克鲁奇系综。相比之下，自由费米子系统是非混沌的，其量子态被约束为保持高斯形式。受这一区别的启发，我们引入了费米高斯斯克鲁奇系综来描述一般自由费米子系统中的深度热化。该系综被定义为平均密度矩阵对高斯哈尔系综的扭曲，其矩揭示了复制希尔伯特空间中高斯态的一种扩大的对称性。我们在两个互补的场景中证明了费米高斯斯克鲁奇系综的出现：（1）我们解析地证明了SYK$_2$模型的投影系综在任意演化时间都遵循费米高斯斯克鲁奇系综；（2）我们提供了数值证据，表明在具有电荷守恒的随机高斯电路中，它在足够长的时间后出现。我们的结果确立了费米高斯斯克鲁奇系综作为自由费米子系统中深度热化的普遍描述。
英文摘要
Measuring part of a many-body wave function generates a projected ensemble of pure quantum states on the unmeasured subsystem. Recent advances in deep thermalization have shown that, in chaotic systems, this ensemble universally converges to the maximally random ensemble compatible with its average density matrix, known as the Scrooge ensemble. By contrast, free-fermion systems are nonchaotic, and their quantum states are constrained to remain Gaussian. Motivated by this distinction, we introduce the fermionic Gaussian Scrooge ensemble to describe deep thermalization in generic free-fermion systems. This ensemble is defined as a distortion of the Gaussian Haar ensemble by the average density matrix, and its moments reveal an enlarged symmetry of Gaussian states in the replicated Hilbert space. We demonstrate the emergence of the fermionic Gaussian Scrooge ensemble in two complementary settings: (1) we analytically prove that the projected ensemble of the SYK$_2$ model follows the fermionic Gaussian Scrooge ensemble at arbitrary evolution times; (2) we provide numerical evidence that it emerges at sufficiently long times in random Gaussian circuits with charge conservation. Our results establish the fermionic Gaussian Scrooge ensemble as a universal description of deep thermalization in free-fermion systems.
Comments10 pages, 3 figures + supplementary materials
