A path-sum Monte Carlo approach for many-electron systems within a tight-binding basis

作者：David J K^*; Register L F; Banerjee S K

来源：Journal of Computational Electronics, 2012, 11(2): 172-181.

DOI：10.1007/s10825-012-0393-z

• Tight binding path integral Monte Carlo
• Fixed node approximation
• Graphene bilayers
• Excitons

We present a Path-Sum Monte Carlo method, a tight-biding approach to Path Integral Monte Carlo, as an alternative to mean-field theory for analyzing exchange-correlation effects in many-electrons systems. To test the algorithm we apply it to a small trial system of either four or six electrons confined to two parallel six single-orbital-atom rings (12 atoms and orbitals total) for which exact results are available for comparison. We observe the phase diagram for exciton formation as a function of interlayer separation and temperature, showing good agreement between the Monte Carlo and exact calculations. Moreover, although the Monte Carlo algorithm employs a fixed node approximation to avoid the Fermion sign problem and, therefore, is inexact, we consider two different limits to the fixed node approximation which provide upper and lower bounds on the total energy. While a simple system is considered here to allow the comparison with exact results, the algorithm should extend the reach of computational analysis to larger many-electrons systems such as, e.g., paired graphene layers for which room-temperature superfluidity has been predicted elsewhere.

• 出版日期2012-6