AI 中文总结
针对孤立量子系统相变难以捉摸的问题，本文在全息共形场论中证明本征态热化系统可产生Lee-Yang范式的类热力学相变，揭示了其瞬子气体映射机制和大中心荷下的相变标度特征。
AI 中文摘要
由于孤立量子系统中的相变问题仍难以捉摸，本文阐明了一种属于Lee-Yang范式的类热力学相变如何在展现本征态热化的系统中产生。具体而言，我们发现在全息共形场论中，自关联函数的本征态期望值可映射为虚拟相互作用瞬子气体的配分函数${\cal Z}_{gauge}(z)$，其中虚时的共形映射$z=1-e^{-τ}$和中心荷$c$分别模拟瞬子的逸度和体积。我们发现，与Lee-Yang范式类似，当$c\to\infty$时，${\cal Z}_{gauge}(z)$的一对复共轭零点会向实轴移动，最终落在著名的禁戒奇点处。穿过该奇点时，系统会从低逸度相转变为高逸度相，同时自由能的标度行为和主导微观构型会发生剧烈变化。我们的研究结果表明，本征态热化中的相变物理内涵十分丰富。
英文摘要
As phase transitions in isolated quantum systems remain elusive, here we show how a thermodynamic-like phase transition, falling into the Lee-Yang paradigm, can arise in systems displaying eigenstate thermalization. Specifically, we show that in holographic conformal field theories, the eigenstate expectation of the auto-correlation function can be mapped to the partition function ${\cal Z}_{gauge}(z)$ of a virtual interacting instanton gas, with the conformal mapping of the imaginary time: $z=1-e^{-τ}$ and the central charge $c$ mimicking the instanton fugacity and volume, respectively. We find that akin to the Lee-Yang paradigm, for $c\to\infty$ a pair of complex conjugate zeros of ${\cal Z}_{gauge}(z)$ move to the real axis located at the famous forbidden singularity. Passing through the singularity the system transits from the low- to high-fugacity phase, accompanied by dramatic changes in scaling behaviors of the free energy and dominant microscopic configurations. Our findings indicate that physics of phase transitions from eigenstate thermalization is very rich.
Comments6 pages, 2 figures
