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/content/aip/journal/adva/6/9/10.1063/1.4963834
1.
Y. Saad, Numerical Methods for Large Eigenvalue Problems: Revised Edition (SIAM, 2011) p. 26.
2.
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, 104111 (1956).
http://dx.doi.org/10.1002/sapm1959381104
3.
G. H. Golub and C. F. V. Loan, Matrix Computations, 4th ed. (The Johns Hopkins University Press, 2013).
4.
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).
5.
P. Moustanis and S. Thanos, “The antiferromagnetic heisenberg cube,” Physica B: Condensed Matter 202, 6574 (1994).
http://dx.doi.org/10.1016/0921-4526(94)90182-1
6.
E. Manousakis, “The spin-1/2 Heisenberg antiferromagnet on a square lattice and its application to the cuprous oxides,” Rev. Mod. Phys. 63, 162 (1991).
http://dx.doi.org/10.1103/RevModPhys.63.1
7.
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).
http://dx.doi.org/10.1103/PhysRevB.92.085146
8.
K. Pakrouski, M. Troyer, Y.-L. Wu, S. Das Sarma, and M. R. Peterson, “Enigmatic 12/5 fractional quantum hall effect,” Phys. Rev. B 94, 075108 (2016).
http://dx.doi.org/10.1103/PhysRevB.94.075108
9.
H. J. Schulz and T. A. L. Ziman, “Finite-size scaling for the two-dimensional frustrated quantum heisenberg antiferromagnet,” EPL (Europhysics Letters) 18, 355 (1992).
http://dx.doi.org/10.1209/0295-5075/18/4/013
10.
P. W. Leung and V. Elser, “Numerical studies of a 36-site kagome antiferromagnet,” Phys. Rev. B 47, 54595462 (1993).
http://dx.doi.org/10.1103/PhysRevB.47.5459
11.
R. Orús, “A practical introduction to tensor networks: Matrix product states and projected entangled pair states,” Annals of Physics 349, 117158 (2014).
http://dx.doi.org/10.1016/j.aop.2014.06.013
12.
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).
http://dx.doi.org/10.1103/PhysRevLett.111.037202
13.
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).
http://dx.doi.org/10.1103/PhysRevLett.104.187203
14.
U. Schollwöck, “The density-matrix renormalization group in the age of matrix product states,” Annals of Physics 326, 96192 (2011), january 2011 Special Issue.
http://dx.doi.org/10.1016/j.aop.2010.09.012
15.
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, 255282 (1950).
http://dx.doi.org/10.6028/jres.045.026
16.
C. Lanczos, “Chebyshev polynomials in the solution of large-scale linear systems,” In Proceedings of the ACM 45, 124133 (1952).
17.
J. Schulenburg, “SPINPACK, http://www-e.uni-magdeburg.de/jschulen/spin/index.html,” (2003).
18.
R. Diestel, Graph Theory, 3rd ed. (Springer, 2006) p. 3.
19.
G. Chartrand, L. Lesniak, and P. Zhang, Graphs and Digraphs, 5th ed. (Chapman and Hall/CRC, 2011) p. 201.
20.
C. Godsil and G. F. Royle, Algebraic Graph Theory (Springer, 2001) p. 22.
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/content/aip/journal/adva/6/9/10.1063/1.4963834
2016-09-26
2016-12-08

Abstract

We introduce a simple algorithm providing a compressed representation () of an irreducible Hamiltonian matrix (number of magnons constrained, dimension: ) of the spin-1/2 Heisenberg antiferromagnet on the non-periodic lattice, not looking for a good basis. As increases, the ratio of the matrix dimension to 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.

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