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Solid State Communications

Comparison between Lanczos and linked cluster methods for the Heisenberg antiferromagnet on a square lattice

Jay D. Mancini, William J. Massano, Robert K. Murawski

Published Dec 1, 1997• 7 citations
Publisher
DOI
10.1016/s0038-1098(97)00347-5

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Comparisons are made between the results of three different linked cluster expansion methods, as applied to the S=1/2 Heisenberg antiferromagnet on a square lattice at zero temperature. Connected moments of the Hamiltonian are calculated up to 15th order, extending previous results of Lee and Lo, and are used to form a t expansion. The t expansion is found to be less accurate than the coupled cluster expansion, which in turn is less accurate than the standard perturbation expansion for this system.
Numerical linked-cluster expansions allow one to calculate finite-temperature properties of quantum lattice models directly in the thermodynamic limit through exact solutions of small clusters. However, full diagonalization is often the limiting factor for these calculations. Here we show that a partial diagonalization of the largest clusters in the expansion using the Lanczos algorithm can be as useful as full diagonalization for the method while mitigating some of the time and memory issues. As test cases, we consider the frustrated Heisenberg model on the checkerboard lattice and the Fermi-Hubbard model on the square lattice. We find that our approach can surpass state of the art in performance in a parallel environment.