2013/07/29 by Medha Sharma, Sharma, Medha, M. A. H. Ahsan +1 · 1 citation
Physics and Astronomy · #FOS: Physical sciences #Magnetic properties of thin films #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.1307.7542
openalex publication_date 2013/07/29 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
We present an alternative scheme to the widely used method of representing\nthe basis of one-band Hubbard model through the relation\nI=I uparrow+2MI downarrow given by H. Q. Lin and J. E. Gubernatis\n[Comput. Phys. 7, 400 (1993)], where I uparrow, I downarrow and I\nare the integer equivalents of binary representations of occupation patterns of\nspin up, spin down and both spin up and spin down electrons respectively, with\nM being the number of sites. We compute and store only I uparrow or\nI downarrow at a time to generate the full Hamiltonian matrix. The\nnon-diagonal part of the Hamiltonian matrix given as\n calI downarrow\⊗ bfH uparrow \⊕\n bfH downarrow\⊗ calI uparrow is generated using a\nbottom-up approach by computing the small matrices bfH uparrow(spin\nup hopping Hamiltonian) and bfH downarrow(spin down hopping\nHamiltonian) and then forming the tensor product with respective identity\nmatrices calI downarrow and calI uparrow, thereby saving\nsignificant computation time and memory. We find that the total CPU time to\ngenerate the non-diagonal part of the Hamiltonian matrix using the new one spin\nconfiguration basis scheme is reduced by about an order of magnitude as\ncompared to the two spin configuration basis scheme. The present scheme is\nshown to be inherently parallelizable. Its application to translationally\ninvariant systems, computation of Green's functions and in impurity solver part\nof DMFT procedure is discussed and its extention to other models is also\npointed out.\n