No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
Compression of Hamiltonian matrix: Application to spin-1/2 Heisenberg square lattice
Y. Saad, Numerical Methods for Large Eigenvalue Problems: Revised Edition (SIAM, 2011) p. 26.
F. Harary, “A graph theoretic method for the complete reduction of a matrix with a view toward finding its eigenvalues,” J. of Mathematics and Physics 38, 104–111 (1956).
G. H. Golub and C. F. V. Loan, Matrix Computations, 4th ed. (The Johns Hopkins University Press, 2013).
G. Diercksen, B. Sutcliffe, and A. Veillard, “Computational techniques in quantum chemistry and molecular physics,” In Proceedings of the NATO Advanced Study Institute held at Ramsau 280 (1974).
S. Capponi and A. M. Läuchli, “Phase diagram of interacting spinless fermions on the honeycomb lattice: A comprehensive exact diagonalization study,” Phys. Rev. B 92, 085146 (2015).
L. Wang, D. Poilblanc, Z.-C. Gu, X.-G. Wen, and F. Verstraete, “Constructing a gapless spin-liquid state for the spin-1/2 J1J2 heisenberg model on a square lattice,” Phys. Rev. Lett. 111, 037202 (2013).
G. Evenbly and G. Vidal, “Frustrated Antiferromagnets with Entanglement Renormalization: Ground State of the Spin– Heisenberg Model on a Kagome Lattice,” Phys. Rev. Lett. 104, 187203 (2010).
C. Lanczos, “An iteration method for the solution of the eigenvalue problem of linear differential and integral operators,” Journal of Research of the National Bureau of Standards 45, 255–282 (1950).
C. Lanczos, “Chebyshev polynomials in the solution of large-scale linear systems,” In Proceedings of the ACM 45, 124–133 (1952).
R. Diestel, Graph Theory, 3rd ed. (Springer, 2006) p. 3.
G. Chartrand, L. Lesniak, and P. Zhang, Graphs and Digraphs, 5th ed. (Chapman and Hall/CRC, 2011) p. 201.
C. Godsil and G. F. Royle, Algebraic Graph Theory (Springer, 2001) p. 22.
Article metrics loading...
We introduce a simple algorithm providing a compressed representation () of an irreducible Hamiltonian matrix (number of magnons
M constrained, dimension: ) of the spin-1/2 Heisenberg antiferromagnet on the non-periodic lattice, not looking for a good basis. As L increases, the ratio of the matrix dimension to N
orbits converges to 8 (order of the symmetry group of square) for the exact ground state computation. The sparsity of the Hamiltonian is retained in the compressed representation. Thus, the computational time and memory consumptions are reduced in proportion to the ratio.
Full text loading...
Most read this month