论文标题
迈向分数量子厅效应的新理论
Toward a new theory of the fractional quantum Hall effect
论文作者
论文摘要
1982年实验发现了分数量子大厅的效应。据观察，在二维电子系统的霍尔电导率$σ_{yx} $中进行了量化，$σ_{yx} = e^2/3H $，在Landau级别的附近填充因子$ν= 1/3 $。 1983年，劳林（Laughlin）提出了一个试验多体波功能，他声称这是``新物质状态'' - 一种均质不可压缩的液体，带有分裂的准粒子。在这里，我开发了一个精确的对角线理论，该理论允许计算$ n $二维库仑相互作用的$ n $ n $二维库仑相互作用电子的能量和其他物理特性。我用$ n \ le 7 $电子的系统的能量，电子密度和其他物理性能分析，连续地作为磁场的函数$ 1/4 \lisesimν<1 $。结果表明，系统的地面和激发态都类似于滑动的Wigner晶体，其参数受磁场的影响。随着磁场的变化，许多粒子光谱中的能量隙会出现并消失。我还计算出$ n \ le 8 $的$ν= 1/3 $ lughlin State的物理属性，并表明该状态和其分数的激发都没有描述物理现实。结果为分数量子霍尔效应中的地面和激发态的性质开辟了新的灯光。
The fractional quantum Hall effect was experimentally discovered in 1982. It was observed that the Hall conductivity $σ_{yx}$ of a two-dimensional electron system is quantized, $σ_{yx}=e^2/3h$, in the vicinity of the Landau level filling factor $ν=1/3$. In 1983, Laughlin proposed a trial many-body wave function, which he claimed described a ``new state of matter'' -- a homogeneous incompressible liquid with fractionally charged quasiparticles. Here I develop an exact diagonalization theory that allows calculation of the energy and other physical properties of the ground and excited states of a system of $N$ two-dimensional Coulomb interacting electrons in a strong magnetic field. I analyze the energies, electron densities, and other physical properties of the systems with $N\le 7$ electrons, continuously as a function of magnetic field in the range $1/4\lesssimν<1$. The results show that both the ground and excited states of the system resemble a sliding Wigner crystal, whose parameters are influenced by the magnetic field. Energy gaps in the many-particle spectra appear and disappear as the magnetic field changes. I also calculate the physical properties of the $ν=1/3$ Laughlin state for $N\le 8$ and show that neither this state nor its fractionally charged excitations describe the physical reality. The results obtained shed new light on the nature of the ground and excited states in the fractional quantum Hall effect.
