周期势场中的任意子晶体和霍尔晶体
Anyon Crystals and Hall Crystals in a Periodic Potential
AI总结：
研究在强垂直磁场和周期势场下二维电子系统的基态，通过对附着奇数个磁通量子的玻色子有效晶格模型平均场分析，得到整数和分数量子霍尔晶体等态，发现特定条件下任意子晶体可稳定，强相互作用下实现任意子晶体态。
AI中文摘要：
我们将整数和分数量子霍尔晶体作为二维电子系统在强垂直磁场和周期势场下的基态获得。对于某些分数态，我们表明霍尔晶体可构成任意子晶体，具有明确任意子的周期性排序。我们发现当朗道能级混合足够弱且在底层晶格接近半填充时，后一种态可在奇分母朗道能级填充分数下稳定。这些相通过对附着奇数个磁通量子的玻色子有效晶格模型的平均场分析得到，该模型将其统计特性转变为电子的统计特性。在玻色子坐标中，霍尔晶体是一种超固体：具有电荷序的超流体。在强相互作用下，涡旋 - 反涡旋对在超固体中自发成核，实现任意子的晶体态。
英文摘要：
We obtain integer and fractional quantum Hall crystals as ground states of a two-dimensional electron system subject to a strong perpendicular magnetic field and a periodic potential. For certain fractional states, we show that the Hall crystal can constitute an anyon crystal, with a periodic ordering of well-defined anyons. We find that the latter states can be stabilized at odd denominator Landau level filling fractions when Landau level mixing is sufficiently weak, and near half-filling of the underlying lattice. These phases are obtained from a mean-field analysis of an effective lattice model of bosons attached to an odd number of flux quanta, which transmutes their statistics to that of electrons. In boson coordinates, the Hall crystal is a supersolid: a superfluid with charge order. Under strong interactions, vortex-anti-vortex pairs spontaneously nucleate in the supersolid, realizing a crystalline state of anyons.
