521 research outputs found
Effective Theory of Magnetization Plateaux in the Shastry-Sutherland Lattice
We use the non-perturbative Contractor-Renormalization method (CORE) in order
to derive an effective model for triplet excitations on the Shastry-Sutherland
lattice. For strong enough magnetic fields, various magnetization plateaux are
observed, e.g. at 1/8, 1/4, 1/3 of the saturation, as found experimentally in a
related compound. Moreover, other stable plateaux are found at 1/9, 1/6 or 2/9.
We give a critical review of previous works and try to resolve some apparent
inconsistencies between various theoretical approaches.Comment: published version with minor change
Numerical Contractor Renormalization Method for Quantum Spin Models
We demonstrate the utility of the numerical Contractor Renormalization (CORE)
method for quantum spin systems by studying one and two dimensional model
cases. Our approach consists of two steps: (i) building an effective
Hamiltonian with longer ranged interactions using the CORE algorithm and (ii)
solving this new model numerically on finite clusters by exact diagonalization.
This approach, giving complementary information to analytical treatments of the
CORE Hamiltonian, can be used as a semi-quantitative numerical method. For
ladder type geometries, we explicitely check the accuracy of the effective
models by increasing the range of the effective interactions. In two dimensions
we consider the plaquette lattice and the kagome lattice as non-trivial test
cases for the numerical CORE method. On the plaquette lattice we have an
excellent description of the system in both the disordered and the ordered
phases, thereby showing that the CORE method is able to resolve quantum phase
transitions. On the kagome lattice we find that the previously proposed twofold
degenerate S=1/2 basis can account for a large number of phenomena of the spin
1/2 kagome system. For spin 3/2 however this basis does not seem to be
sufficient anymore. In general we are able to simulate system sizes which
correspond to an 8x8 lattice for the plaquette lattice or a 48-site kagome
lattice, which are beyond the possibilities of a standard exact diagonalization
approach.Comment: 15 page
Recent progress in the truncated Lanczos method : application to hole-doped spin ladders
The truncated Lanczos method using a variational scheme based on Hilbert
space reduction as well as a local basis change is re-examined. The energy is
extrapolated as a power law function of the Hamiltonian variance. This
systematic extrapolation procedure is tested quantitatively on the two-leg t-J
ladder with two holes. For this purpose, we have carried out calculations of
the spin gap and of the pair dispersion up to size 2x15.Comment: 5 pages, 4 included eps figures, submitted to Phys. Rev. B; revised
versio
Local renormalization method for random systems
In this paper, we introduce a real-space renormalization transformation for
random spin systems on 2D lattices. The general method is formulated for random
systems and results from merging two well known real space renormalization
techniques, namely the strong disorder renormalization technique (SDRT) and the
contractor renormalization (CORE). We analyze the performance of the method on
the 2D random transverse field Ising model (RTFIM).Comment: 12 pages, 13 figures. Submitted to the Special Issue on "Quantum
Information and Many-Body Theory", New Journal of Physics. Editors: M.B.
Plenio, J. Eiser
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