A Convergent Method for Calculating the Properties of Many Interacting Electrons

A method is presented for calculating binding energies and other properties of extended interacting systems using the projected density of transitions (PDoT) which is the probability distribution for transitions of different energies induced by a given localized operator, the operator on which the transitions are projected. It is shown that the transition contributing to the PDoT at each energy is the one which disturbs the system least, and so, by projecting on appropriate operators, the binding energies of equilibrium electronic states and the energies of their elementary excitations can be calculated. The PDoT may be expanded as a continued fraction by the recursion method, and as in other cases the continued fraction converges exponentially with the number of arithmetic operations, independent of the size of the system, in contrast to other numerical methods for which the number of operations increases with system size to maintain a given accuracy. These properties are illustrated with a calculation of the binding energies and zone-boundary spin- wave energies for an infinite spin-1/2 Heisenberg chain, which is compared with analytic results for this system and extrapolations from finite rings of spins.Comment: 30 pages, 4 figures, corrected pd

Roger Haydock, Phineas Pemberton, July 1, 1682

Letter dated July 1, 1682 (June 21, 1682 Old Style) from Roger Haydock to Phineas Pemberton

Roger Haydock and Elinor Haydock, Phineas Pemberton, June 17, 1684; June 26, 1684

Two letters from Roger and Elinor Haydock to Phineas Pemberton. The first letter, sent from Warrington, is dated June 17, 1684 (June 7, 1684 Old Style). The second, sent from Liverpool, is dated June 26, 1684 (June 16, 1684 Old Style)

Roger Haydock, Phineas Pemberton, July 5 1683

Letter dated July 5, 1683 (June 25, 1683 Old Style) from Roger Haydock to Phineas Pemberton