Faculty of Physics, Adam Mickiewicz University in Poznań, Umultowska 85, 61-614 Poznań, Poland.
National Quantum Information Centre of Gdańsk, 81-824 Sopot, Poland.
Phys Rev E. 2016 Jun;93(6):061301. doi: 10.1103/PhysRevE.93.061301. Epub 2016 Jun 20.
Models of noninteracting fermions coupled to auxiliary classical fields are relevant to the understanding of a wide variety of problems in many-body physics, e.g., the description of manganites, diluted magnetic semiconductors, or strongly interacting electrons on lattices. We present a flat-histogram Monte Carlo algorithm that simulates a statistical ensemble that allows one to directly acquire the partition function at all temperatures for such systems. The defining feature of the algorithm is that it utilizes the complete thermodynamic information from the full energy spectrum of noninteracting fermions available during sampling of the configuration space of the classical fields. We benchmark the method for the classical Ising and Potts models in two dimensions, as well as the Falicov-Kimball model describing itinerant electrons interacting with heavy ions.
与辅助经典场耦合的非相互作用费米子模型与多体物理中各种各样的问题的理解有关，例如，锰氧化物、稀磁半导体或晶格上强相互作用电子的描述。我们提出了一种平面直方图蒙特卡罗算法，该算法模拟了一个统计集合，允许直接在所有温度下获取此类系统的配分函数。该算法的定义特征是，它利用了在经典场构型空间采样过程中，非相互作用费米子的全能谱中提供的完整热力学信息。我们在二维上对经典的伊辛和玻尔兹曼模型以及描述巡游电子与重离子相互作用的法利科夫-金博尔模型对该方法进行了基准测试。
