Construction of size-consistent effective Hamiltonians for systems with arbitrary Hilbert space

Abstract

Effective Hamiltonians are usually constructed by using canonical transformations or projection techniques. In contrast to this, we present a method for systems with arbitrary Hilbert space based on the introduction of cumulants. Cumulants guarantee size consistency, a property that is not always evident in other treatments. As a nontrivial example of use the derived method is applied to the strong-coupling limit of the half-filled Hubbard model on a general lattice in arbitrary spatial dimension for which the fourth-order expansion in t/U of the effective Hamiltonian is derived.

Charge ordering in quarter-filled ladder systems coupled to the lattice

“…28 However, a quantitative comparison cannot be made since in the experiment the ordering and, correspondingly, J eff , are traced as a function of temperature for given other system parameters while we investigate the ordering at T = 0 as a function of the extended Hubbard repulsion V. Our calculation also agrees well with the analytical results of Refs. 16 and 29, where it was shown that the exchange rapidly decreases with increasing V. Quantitatively, at V =3, C = 0 our results give J eff Ϸ 0.06 while perturbation theory 16,29 predicts J eff Ϸ 0.04. Moreover, for V = 1.3, C = 0.35, which give a lattice distortion close to the value observed experimentally (see Fig.…”

Computer-aided perturbation theory by cumulants: Dimerized and frustrated spin-12chain

“…An example for a degenerate unperturbed groundstate was discussed in Ref. 9. Note that the cumulant expression (4) is also closely related to an effective Hamiltonian which was derived by Takahashi.…”

“…9 This method is a projection approach and is based on the construction of effective Hamiltonians for low-energy properties. Besides the automatically preserved size consistency of extensive variables, this cumulant method offers compact expressions for the different orders of the perturbation theory.…”

“…Recently, a systematic perturbation expansion for many-particle systems in terms of cumulants has been proposed by two of us [9]. This method is an projection approach and is based on the construction of effective Hamiltonians for low-energy properties.…”

“…The paper is organized as follows. In the next section the cumulant approach [9] is formulated. In particular, the perturbation expansion of the resulting effective Hamiltonian is given in terms of cumulant expressions.…”