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arXiv:cond-mat/9704212 · Physical review. B, Condensed matter

Short-range resonating-valence-bond state of even-spin ladders: A recurrent variational approach

Germán Sierra, Miguel Angel Martin-Delgado

Published Oct 1, 1997• 26 citations

Abstract

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.

DOI: 10.1103/physrevb.56.8774

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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.

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An interesting aspect of antiferromagnetic quantum spin ladders, with complete dimer coverings, is that the wave function can be recursively generated by estimating the number of coverings in the valence bond basis, which follow the fabled Fibonacci sequence. In this work, we show that generalized forms of such sequences can also be derived for multi-legged and doped quantum spin ladders, which allows the corresponding dimer covered state to be recursively generated. This simplifies the investigation and estimation of several important quantities in these many-body quantum systems. In particular, we show that the valence bond entanglement entropy, which is a substantial figure of merit for understanding critical behavior, can be conveniently derived for large spin ladders.

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.