ISSN:
1089-7550
Source:
AIP Digital Archive
Topics:
Physics
Notes:
We have calculated the 2-point correlation functions ωil(N)=(4/3)〈Si ⋅ Si+l〉 and their averages over i, ωl(N), in the ground state of the 1-dimensional antiferromagnetic Heisenberg model for N=4(2)16 spins. Both periodic (rings) and free-ends (chains) boundary conditions are considered. Surprisingly tight lower and upper bounds have been obtained for ωl(∞) under reasonable assumptions. In addition to showing the rather strong even-l-odd-l alternation in ||ωl(N)||, already known, our bounds indicate a smooth behavior in l||ωl(∞)|| for l odd and for l even, with, surprisingly, a broad maximum attained within the odd-l values at l(approximately-equal-to)6 to 8. The bounds obtained from the chain results were essential to seeing this maximum (because the l-values available for given N are larger than for rings). The quantity l||ωl(N)|| for chains with fixed N also shows such a maximum, and in addition shows a similar maximum for even l's. If the trends for large l and N which we have found continue in ωl(∞) and in SN, the structure factor at wave vector π, then finite-size contributions to ωl(N) will have to contribute to the (seemingly) logarithmic divergence of SN as N→∞. We are not aware of any models where a similarly weak divergence shows such a finite-size contribution. Earlier results, including ||ωl(∞)||≈A/l for l→∞, gave no hint of the decrease in l||ωl(∞)|| described above. Recently "logarithmic corrections'' have been mentioned, wherein ||ωl(∞)||≈(A/l) (ln l+B)−1. This might be related to the decrease in l||ωl(∞)|| which we found. If finite-size corrections are neglected, then this 1/l ln l behavior would predict SN≈ln ln N for N→∞, as opposed to the trend SN∼ln N that we found; continuation of the latter trend would then have to be due entirely to the finite-size contributions. Some insight into various surprising aspects of ωil(N) is gained by considering a single-band model of noninteracting electrons, which is a special case of the Hubbard model, as is the Heisenberg model.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.335098
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