We present the Millennium-II Simulation (MS-II), a very large N-body simulation of dark matter evolution in the concordance LCDM cosmology. The MS-II assumes the same cosmological parameters and uses the same particle number and output data structure as the original Millennium Simulation (MS), but was carried out in a periodic cube one-fifth the size (100 Mpc/h) with 5 times better spatial resolution (a Plummer equivalent softening of 1.0 kpc/h) and with 125 times better mass resolution (a particle mass of 6.9 times 10^6 Msun/h). By comparing results at MS and MS-II resolution, we demonstrate excellent convergence in dark matter statistics such as the halo mass function, the subhalo abundance distribution, the mass dependence of halo formation times, the linear and nonlinear autocorrelations and power spectra, and halo assembly bias. Together, the two simulations provide precise results for such statistics over an unprecedented range of scales, from halos similar to those hosting Local Group dwarf spheroidal galaxies to halos corresponding to the richest galaxy clusters. The Milky Way halos of the Aquarius Project were selected from a lower resolution version of the MS-II and were then resimulated at much higher resolution. As a result, they are present in the MS-II along with thousands of other similar mass halos. A comparison of their assembly histories in the MS-II and in resimulations of 1000 times better resolution shows detailed agreement over a factor of 100 in mass growth. We publicly release halo catalogs and assembly trees for the MS-II in the same format within the same archive as those already released for the MS.
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