Action-based quantum Monte Carlo approach to fermion-boson lattice models

基于动作的费米子-玻色子晶格模型的量子蒙特卡罗方法

• 批准号: 299340206
• 负责人: Dr. Martin Hohenadler
• 金额: --
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/299340206?language=en
• 关键词: Action; based; quantum; Monte; Carlo

The interaction between fermionic and bosonic degrees of freedom plays animportant role in many areas of condensed matter physics. A key example isthe coupling of electrons to lattice vibrations (phonons) in a solid, whichunderlies phenomena such as superconductivity or the Peierls instability.In this project, we will apply exact numerical methods to improve ourunderstanding of different fermion-boson models. We will, for example,investigate the role of an unscreened electron-phonon interaction forsuperconductivity, or the effect of phonons on the temperature dependence ofthe specific heat and heat transport. Moreover, we will study the crossoverfrom one-dimensional chains, which are dominated by the Peierls instability,to two dimensions. Finally, we will investigate a recently proposed model forhigh-temperature superconductivity mediated by spin fluctuations.The unbound number of bosonic excitations, and the different time scales ofthe fermion and boson dynamics pose a challenge even for modern numericalmethods. We will use a continuous-time quantum Monte Carlo method that isparticularly suited to investigate complex fermion-boson problems. Thebosonic degrees of freedom can be integrated out to obtain a purely fermionicproblem that can be simulated very efficiently, and without systematicerrors.Our results are expected to be relevant for low-dimensional materials such aspolymers, dichalcogenides, or cuprate superconductors. Moreover, themethodological developments are expected to enable investigations of othercomplex fermion-boson problems in the future.

费米子自由度和玻色子自由度之间的相互作用在凝聚态物理的许多领域中起着重要的作用。一个关键的例子是电子与固体中晶格振动（声子）的耦合，这是超导或Peierls不稳定性等现象的基础。在这个项目中，我们将应用精确的数值方法来提高我们对不同费米子-玻色子模型的理解。例如，我们将研究未屏蔽的电子-声子相互作用对超导性的作用，或者声子对比热和热输运的温度依赖性的影响。此外，我们还将研究由Peierls不稳定性控制的一维链到二维链的交叉。最后，我们将研究一个最近提出的由自旋涨落介导的高温超导模型，玻色子激发的非束缚数，以及费米子和玻色子动力学的不同时间尺度，即使对现代数值方法也是一个挑战。我们将使用连续时间量子蒙特卡罗方法，特别适合于研究复杂的费米子玻色子问题。玻色子自由度可以积分出来，得到一个可以非常有效地模拟的纯费米子问题，并且没有系统误差。我们的结果有望与低维材料如聚合物、二硫属化物或铜酸盐超导体有关。此外，方法学的发展有望使未来对其他复杂费米子-玻色子问题的研究成为可能。