Theory of the Fractional Quantum Hall Effect

9615005目前的拨款是为了支持PI关于复合费米子描述分数量子霍尔效应的早期工作的扩展。更具体地说，PI设计了一种形式，利用蒙特卡罗技术计算大系统的基态和激发态的波函数。热力学极限计算的可能性保证了对各种悬而未决的实验问题的定量理解。特别是，这项拨款计划计算一般分数下的能隙和集体模色散，包括塞曼能量在内的偏振度，分数量子霍尔态和维格纳晶体之间的跃迁，以及介观量子点对外加强磁场的响应。分数量子霍尔效应的研究近年来一直是一个活跃的领域，这在很大程度上是因为这个PI发现了复合费米子的描述。到目前为止，一个严重的限制是理论计算仅限于较小尺寸的系统，而不是通常针对较大尺寸的实验。PI最近的一项重大发展表明，这一限制可能会被取消。这项拨款是为了支持在大系统极限下各种实验观察值的计算。***

9615005 Jain The present grant is to support the extension of earlier work by the PI on composite fermion description of the fractional quantum Hall effect. More specifically, the PI has devised a formalism to calculate the wave functions of the ground as well as the excited states for large systems using Monte Carlo techniques. The possibility of calculations in thermodynamic limit promises a quantitative understanding of various outstanding experimental issues. In particular the grant plans to calculate the energy gaps and collective mode dispersions at general fractions, degree of polarization including the Zeeman energy, transitions between the fractional quantum Hall states and a Wigner crystal and finally the response of a mesoscopic quantum dot to applied high magnetic fields. %%% The subject of fractional quantum Hall effect has been an active area in recent years, in significant part due to this PI's discovery of the composite fermion description. A serious limitation so far has been that the theoretical calculations are limited to system of smaller sizes, as opposed to the experiments which are generally for larger sizes. A significant development recently by the PI suggests possible removal of this limitation. This grant is to support calculations of various experimental observable in the large system limit. ***