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arXiv:cond-mat/9908062

The Recurrent Variational Approach applied to the Electronic Structure of Conjugated Polymers

S. Pleutin, Eric Jeckelmann, Miguel Angel Martin-Delgado, Germán Sierra

Published Aug 4, 1999• 0 citations
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Abstract

In this note, first the Recurrent Variational Approach (RVA) is introduced by using as example a non-trivial spin-model, the spin-1/2 antiferromagnetic two-leg-ladder. Then, a first application of this scheme to the electronic structure of conjugated polymers is proposed. An analogy between the two-leg ladder and the dimerized chain described by the Extended Peierls-Hubbard Hamiltonian is underlined and comparisons are made with DMRG calculations. The proposed ansatz is useful to get some analytical insight and it is a good starting point for further improvements using the RVA.

DOI
10.48550/arxiv.cond-mat/9908062

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In this note, first the Recurrent Variational Approach (RVA) is introduced by using as example a non-trivial spin-model, the spin-1/2 antiferromagnetic two-leg-ladder. Then, a first application of this scheme to the electronic structure of conjugated polymers is proposed. An analogy between the two-leg ladder and the dimerized chain described by the Extended Peierls-Hubbard Hamiltonian is underlined and comparisons are made with DMRG calculations. The proposed ansatz is useful to get some analytical insight and it is a good starting point for further improvements using the RVA.
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Using a recursive method we construct dimer and nondimer variational ansatzs of the ground state for the two-legged ladder, and compute the number of dimer coverings, the energy density, and the spin-correlation functions. The number of dimer coverings are given by the Fibonacci numbers for the dimer-resonating-valence-bond state and their generalization for the nondimer states. Our method relies on the recurrent relations satisfied by the overlaps of the states with different lengths, which can be solved using generating functions. The recurrent-relation method is applicable to other short-range systems. Based on our results we make a conjecture about the bond amplitudes of the two-legged ladder.
We present a variational treatment of the ground state of the two-leg $t\ensuremath{-}J$ ladder, which combines the dimer and the hard-core boson models into one effective model. This model allows us to study the local structure of the hole pairs as a function of doping. A second-order recursion relation is used to generate the variational wave function, which substantially simplifies the computations. We obtain good agreement with numerical density matrix renormalization group results for the ground state energy in the strong-coupling regime. We find that the local structure of the pairs depends upon whether the ladder is slightly or strongly dopped.
We present a variational treatment of the ground state of the 2-leg t-J ladder, which combines the dimer and the hard-core boson models into one effective model. This model allows us to study the local structure of the hole pairs as a function of doping. A second order recursion relation is used to generate the variational wave function, which substantially simplifies the computations. We obtain good agreement with numerical density matrix renormalization group results for the ground state energy in the strong coupling regime. We find that the local structure of the pairs depends upon whether the ladder is slightly or strongly dopped.
A fully variational resonance-valence-bond (RVB) study is performed for two-, three- and four-legged isotropic spin-1/2 Heisenberg ladders under periodic boundary conditions along the rungs and periodic/twisted boundary conditions along the chains. By using the full lattice groups of these systems very accurate results have been obtained for the ground-state bulk limit properties in the case of the dimer RVB basis. The results reported here represent the best one can do within the dimer RVB ansatz and should be useful when comparing with results obtained from an a priori fixed structure of the wavefunction. Further results are presented for some finite-sized systems, extending beyond the dimer RVB approach by including RVB functions containing spin pairings between non-nearest-neighbour sites. These results indicate that the three-legged ladder with periodic boundary conditions along the rungs falls into the same universality class of ladders possessing short-range RVB wavefunctions as the two- and four-legged ladders.