arXiv:cond-mat/9809124

Momentum Distribution of the Hubbard Model

Girish S. Setlur

Published Sep 8, 1998• 1 citation

Abstract

Using the recently perfected sea-boson method, we compute the momentum distribution of the one-band Hubbard model in one and two spatial dimensions. We compute the asymptotic features of the momentum distribution explicitly away from half filling for weak coupling in one and two dimensions. While the results are not exact by any means, they provide the exact asymptotics, namely they are able to reproduce the exponents obtained by Shulz in one dimension obtained using Bethe ansatz. The corresponding results in more than one dimension are therefore as believeable.

DOI: 10.48550/arxiv.cond-mat/9809124

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arXiv:cond-mat/9809124

Momentum Distribution of the Hubbard Model

Girish S. Setlur

Published Sep 8, 1998• 1 citation

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.cond-mat/9809124

Related papers

Bethe-ansatz wave function, momentum distribution, and spin correlation in the one-dimensional strongly correlated Hubbard model

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{k}_{F}

is analyzed from the system size dependence. In addition to the

{k}_{F}

singularity, n(k) has a weak singularity at k=3

{k}_{F}

; however, no detectable singularity is present at 2

{k}_{F}

, which one might expect from the spinless fermion wave function. The singularity of S(k) at 2

{k}_{F}

is also examined in detail. It is concluded from the size dependence that, when the system is away from half-filling, the nature of the singularity at 2

{k}_{F}

is different from that in the Heisenberg model. The results are compared with the behavior in the weak-correlation regime examined with the perturbation calculation, the prediction of g-ology, and recent Monte Carlo calculations.

1/r

hopping and the two-dimensional model with isotropic nearest-neighbor hopping. By comparing with the exact solutions for both one-dimensional models and with exact diagonalization in two dimensions, we first investigate the convergence of the ground-state energy. We find variational convergence of the energy with the number of states kept for all models and parameter sets. In contrast to the real-space algorithm, the accuracy becomes rapidly worse with increasing interaction and is not significantly better at half filling. We compare the results for different dispersion relations at fixed interaction strength over bandwidth and find that extending the range of the hopping in one dimension has little effect, but that changing the dimensionality from one to two leads to lower accuracy at weak-to-moderate interaction strength. In the one-dimensional models at half filling, we also investigate the behavior of the single-particle gap, the dispersion of spinon excitations, and the momentum distribution function. For the single-particle gap, we find that proper extrapolation in the number of states kept is important. For the spinon dispersion, we find that good agreement with the exact forms can be achieved at weak coupling if the large momentum-dependent finite-size effects are taken into account for nearest-neighbor hopping. For the momentum distribution, we compare with various weak-coupling and strong-coupling approximations and discuss the importance of finite-size effects as well as the accuracy of the DMRG.