2013/10/14 by Edward Perepelitsky, Perepelitsky, Edward
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Strongly Correlated Electrons (cond-mat.str-el) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1310.3797
openalex publication_date 2013/10/14 · openalex created_date 2022/08/30 · openalex updated_date 2026/07/28
We develop a diagrammatic approach for calculating the high temperature\nexpansion of dynamic correlation functions, such as the electron Green's\nfunction and the time-dependent density-density and spin-spin correlation\nfunctions, for the infinite-U Hubbard Model with any number of spin species.\nThe formalism relies on the use of restricted lattice sums, in which distinct\nvertices of the diagram represent distinct sites on the lattice. We derive a\nnew formula for the restricted lattice sum of a disconnected diagram consisting\nof several connected components, and use it to prove the linked cluster theorem\nwith respect to "generalized connected diagrams", formed by overlapping the\noriginal connected components on the lattice. This enables us to express all\nquantities as a sum over these generalized connected diagrams. We compute the\nGreen's function to 4th order in \β t for the case of m spin species on a\nd-dimensional hypercube by hand. We take the m\→\∞ limit, enabling us to\nobtain expressions for the Dyson-Mori self-energy to 4th order in \β t for\nthe case of an infinite number of spin species. This may have connections to\nslave boson techniques used for the study of this model. Our approach is\ncomputationally more efficient than any used previously for the calculation of\nthe high temperature expansion of dynamic correlation functions, and high order\nresults for both the Green's function and the time-dependent density-density\nand spin-spin correlation functions shall be presented in a separate paper\n[25].\n