Materials with thickness ranging from a few nanometers to a single atomic layer present unprecedented opportunities to investigate new phases of matter constrained to the two-dimensional plane. Particle–particle Coulomb interaction is dramatically affected and shaped by the dimensionality reduction, driving well-established solid state theoretical approaches to their limit of applicability. Methodological developments in theoretical modelling and computational algorithms, in close interaction with experiments, led to the discovery of the extraordinary properties of two-dimensional materials, such as high carrier mobility, Dirac cone dispersion and bright exciton luminescence, and inspired new device designparadigms. This review aims to describe the computational techniques used to simulate and predict the optical, electronic and mechanical properties of two-dimensional materials, and to interpret experimental observations. In particular, we discuss in detail the particular challenges arising in the simulation of two-dimensional constrained fermions and quasiparticles, and we offer our perspective on the future directions in this field.

厚度范围从几纳米到单个原子层的材料为研究受限于二维平面的新物质相提供了前所未有的机会。粒子-粒子库仑相互作用受到维数降低的显着影响和塑造，推动了完善的固态理论方法达到其适用性的极限。理论建模和计算算法的方法论发展与实验密切交互，导致发现了二维材料的非凡特性，例如高载流子迁移率、狄拉克锥色散和明亮的激子发光，并激发了新的器件设计范式。本综述旨在描述用于模拟和预测光学、二维材料的电子和机械特性，并解释实验观察。特别是，我们详细讨论了二维约束费米子和准粒子模拟中出现的特殊挑战，并提供了对该领域未来方向的看法。