标题： 平方格子上的 Hubbard-Holstein 模型中的纠缠涨落和同位素效应的功能性重整化 显示英文标题

标题： Intertwined fluctuations and isotope effects in the Hubbard-Holstein model on the square lattice from functional renormalization

摘要： 电子-电子和电子-声子相互作用导致了层状量子材料中自旋、电荷和超导关联的形成。 一种能够同时捕捉这两种相互作用的典型模型是具有非色散爱因斯坦声子的二维Hubbard-Holstein模型。 在本工作中，我们对半满和非半满情况下的磁性、电荷和超导涨落进行了详细分析。 为此，我们采用了功能重正化群方法，并使用了最近引入的单玻色子交换形式的扩展方法。 更准确地说，我们超越了该模型之前的处理方法，通过解析两粒子顶点的完整频率依赖性并考虑电子自能的反馈作用。 我们在Hubbard排斥能、电子-声子耦合强度和声子频率的空间内进行广泛的参数扫描，以从绝热到反绝热区域探索主导的磁性、电荷和超导灵敏度。 我们的数值数据表明，自能效应导致$d$波超导灵敏度随着声子频率的增加而增强，这与早期的同位素效应研究相反。 在低声子频率下，$s$波超导灵敏度的大电荷贡献会改变符号，并最终随着电子-声子耦合的增加而导致$s$波超导性的降低，这标志着Migdal-Eliashberg理论的失效。 我们系统地分析了这些发现，采用对纠缠涨落的详细诊断，并确定了物理灵敏度的各种正负同位素效应。 显示英文摘要

摘要： Electron-electron and electron-phonon interactions are responsible for the formation of spin, charge, and superconducting correlations in layered quantum materials. A paradigmatic model for such materials that captures both kinds of interactions is the two-dimensional Hubbard-Holstein model with a dispersionless Einstein phonon. In this work, we provide a detailed analysis of the magnetic, density, and superconducting fluctuations at and away from half-filling. To that end, we employ the functional renormalization group using the recently introduced extension of the single-boson exchange formulation. More precisely, we go beyond previous approaches to the model by resolving the full frequency dependence of the two-particle vertex and taking into account the feedback from the electronic self-energy. We perform broad parameter scans in the space of Hubbard repulsion, electron-phonon coupling strength, and phonon frequency to explore the leading magnetic, density, and superconducting susceptibilities from the adiabatic to the anti-adiabatic regime. Our numerical data reveal that self-energy effects lead to an enhancement of the $d$-wave superconducting susceptibility towards larger phonon frequencies, in contrast to earlier isotope-effect studies. At small phonon frequencies, large density contributions to the $s$-wave superconducting susceptibility change sign and eventually lead to a reduction of $s$-wave superconductivity with increasing electron-phonon coupling, signaling the breakdown of Migdal-Eliashberg theory. We analyze our findings systematically, employing detailed diagnostics of the intertwined fluctuations and pinning down the various positive and negative isotope effects of the physical susceptibilities.