Ground-State Phase Diagram of 2D Electrons in a High Landau Level: A Density-Matrix Renormalization Group Study

The ground-state phase diagram of 2D electrons in a high Landau level (index $N=2\mathrm{}$) is studied by the density-matrix renormalization group method. Pair correlation functions are systematically calculated for various filling factors from $\nu =1/8\mathrm{}$ to $1/2$. It is shown that the ground-state phase diagram consists of three different charge density wave states called stripe phase, bubble phase, and Wigner crystal. The boundary between the stripe and the bubble phases is determined to be ${\nu }_c^{\mathrm{s}\mathrm{-}\mathrm{b}}\sim 0.38$, and that for the bubble phase and Wigner crystal is ${\nu }_c^{\mathrm{b}\mathrm{-}\mathrm{W}}\sim 0.24$. Each transition is of first order.