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Register a new userEnhancement of diamagnetism by momentum-momentum interaction: application to benzene
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Thais Victa Trevisan
Publication date
2020
fields
Physics
and research's language is
English
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A well-known property of aromatic molecules is their highly anisotropic response to the presence of an external magnetic field: the component of their magnetic susceptibility parallel to the field is generally much larger than the remaining in-plane components. This intriguing phenomenon is rationalized as a consequence of the delocalization of the itinerant electrons that populate the aromatic ring. In this work, we revisit the magnetism of aromatic molecules and propose an extended Hubbard model for the electrons in the aromatic ring that takes into account the interaction between them and the bonding electrons. We show that the bonding electrons play an important and overlooked role: they mediate an effective, attractive momentum-momentum interaction between the itinerant electrons, which promotes a strong enhancement in the magnetic response of the aromatic ring. For the particular case of benzene, we show that the experimentally observed magnetic anisotropy is recovered with realistic values of the coupling constants.
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We investigate the application of the Density Matrix Renormalization Group (DMRG) to the Hubbard model in momentum-space. We treat the one-dimensional models with dispersion relations corresponding to nearest-neighbor hopping and $1/r$ 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.
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