The Short Range RVB State of Even Spin Ladders: A Recurrent Variational Approach

TL;DR

This paper introduces a recursive variational approach to analyze the ground state of two-legged spin ladders, calculating dimer coverings, energy, and correlations, with potential applications to other short-range quantum systems.

Contribution

It develops a recurrent relations method for constructing variational ansatzs and analyzing short-range quantum systems, providing new insights into the RVB state of spin ladders.

Findings

Number of dimer coverings follows Fibonacci sequence

Derived energy density and spin correlations for the ladder

Conjecture on bond amplitudes based on results

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-RVB state and their generalization for the nondimer ones. 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 2-leg ladder.