2 research outputs found
A Plaquette Basis for the Study of Heisenberg Ladders
We employ a plaquette basis-generated by coupling the four spins in a
lattice to a well-defined total angular momentum-for the study of
Heisenberg ladders with antiferromagnetic coupling. Matrix elements of the
Hamiltonian in this basis are evaluated using standard techniques in
angular-momentum (Racah) algebra. We show by exact diagonalization of small
( and ) systems that in excess of 90% of the ground-state
probability is contained in a very small number of basis states. These few
basis states can be used to define a severely truncated basis which we use to
approximate low-lying exact eigenstates. We show how, in this low-energy basis,
the isotropic spin-1/2 Heisenberg ladder can be mapped onto an anisotropic
spin-1 ladder for which the coupling along the rungs is much stronger than the
coupling between the rungs. The mapping thereby generates two distinct energy
scales which greatly facilitates understanding the dynamics of the original
spin-1/2 ladder. Moreover, we use these insights to define an effective
low-energy Hamiltonian in accordance to the newly developed COntractor
REnormalization group (CORE) method. We show how a simple range-2 CORE
approximation to the effective Hamiltonian to be used with our truncated basis
reproduces the low-energy spectrum of the exact theory at the \alt
1% level.Comment: 12 pages with two postscript figure