Density Matrix Renormalization Group study of rapidly-rotating two-dimensional bosons

Takanori Sugihara

Dmitry L. Kovrizhin

We developed a density matrix renormalization group technique to study quantum Hall fractions of fast rotating bosons. In this paper, we present a discussion of the method together with the results which we obtain in three distinct cases of the narrow-channel, cylinder, and spherical geometries. In the narrow-channel case, which is relevant to anisotropic confining traps in the limit of extremely fast rotation, we find a series of zero-temperature phase transitions in the strongly interacting regime as a function of the interaction strength between bosons. We compute energies and density profiles for different filling fractions on a cylinder and compare the convergence rates of the method in the cylinder and a sphere geometries.

Leslie O. Baksmaty, Constantine Yannouleas, Uzi Landman

Satoshi Nishimoto, M. ARIKAWA

Eric Jeckelmann, Steven R. White

We propose a density-matrix renormalization-group (DMRG) approach to study lattices including bosons. The key to the approach is an exact mapping of a boson site containing ${2}^{N}$ states to $N$ pseudosites, each with 2 states. The pseudosites can be viewed as the binary digits of a boson level. We apply the pseudosite DMRG method to the polaron problem in the one- and two-dimensional Holstein models. Ground-state results are presented for a wide range of electron-phonon coupling strengths and phonon frequencies on lattices large enough (up to 80 sites in one dimension and up to $20\ifmmode\times\else\texttimes\fi{}20$ sites in two dimensions) to eliminate finite-size effects, with up to 128 phonon states per phonon mode. We find a smooth but quite abrupt crossover from a quasi-free-electron ground state with a slightly renormalized mass at weak electron-phonon coupling to a polaronic ground state with a large effective mass at strong coupling, in agreement with previous studies.

Gaetano Busiello, L. De Cesare