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DIAMAGNETIC SUSCEPTIBILITY OF THE INFINITY-U HUBBARD-MODEL

A. J. Schofield, Jm Wheatley, T. Xiang

Published Jan 1, 1991• 0 citations
OpenAlex

Abstract

The diamagnetic susceptibility of the infinity-U Hubbard model is investigated in one and two dimensions. In one dimension, it is shown that the charge current flowing in the ground state of a ring threaded by a flux tube vanishes in the thermodynamic lim

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Diamagnetic susceptibility of the ∞-UHubbard model

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Persistent currents flowing through disordered mesoscopic rings threaded by a magnetic flux are investigated. Models of fermions with on-site interactions (Hubbard model) or models of spinless fermions with nearest neighbor interactions are considered on 2D cylinders with twisted boundary conditions in one direction to account for a magnetic flux. Self-consistent Hartree-Fock methods are used to treat the electron-electron interaction beyond first order. We show that the second harmonic of the current (which is relevant in the diffusive regime) is strongly suppressed by the interaction in the case of spinless fermions while it is significantly enhanced in the Hubbard model. Our data also strongly suggest that the reduction (increase) of this harmonic is related to a strong increase (reduction) of the spatial fluctuations of the charge density.

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The diamagnetic susceptibility of the \ensuremath{\infty}-U Hubbard model is investigated in one and two dimensions. In one dimension, it is shown that the change current flowing in the ground state of a ring threaded by a flux tube vanishes in the thermodynamic limit. Similar behavior is inferred for the single-hole problem on a two-dimensional square lattice, from exact-diagonalization results on small clusters. Effectively the applied field is cancelled by an induced fictitious field and the susceptibility vanishes. Our results suggest that the Nagaoka ferromagnet is unstable with respect to a low-spin state level crossing to a chiral spin state occurring at infinitesimally small diamagnetic coupling.
In this work we obtain the magnetic and thermodynamic properties of the classical Hubbard model. This one is easier to handle than the original Hubbard model, and it maintains fundamental aspects like charge and particle-hole symmetry. We find the relationship between this and the Ising model. For square and simple cubic lattices, the thermodynamic properties and phase diagrams were calculated by Monte Carlo method. We show the behavior of internal energy, specific heat, and magnetic susceptibility as a function of the temperature. For the considered lattices, the ground state is anti-ferromagnetic. The Néel temperatures were found as a function of the electronic interaction in the case of half-filled band. In the limit of vanishing of diverging interaction, our results agree with the Ising model.
We investigated the fidelity susceptibility in the one-dimension (1D) Hubbard model and the extended Hubbard model at half-filling via the density matrix renormalization group. From the numerical results, we argue that in the 1D Hubbard model, the fidelity susceptibility shows a divergence at two points which is infinitesimally close to the critical point while it is always extensive exactly at the critical point. For the extended Hubbard model, we found that for a properly chosen driving parameter, the fidelity susceptibility is able to reveal the quantum phase transitions between the PS (phase separation)-superconducting, superconducting-CDW (charge-density wave), CDW-SDW(spin-density wave), SDW-PS, CDW-BOW (bond-order wave), and the BOW-SDW phases.
To gain insight into the behavior of the Hubbard model, we define a SU(n)\mathrm{SU}(n)SU(n) invariant generalization of the Hubbard-Heisenberg model and, in the large-nnn limit, solve it in one dimension and in two dimensions on a square lattice. In one dimension the ground state is completely dimerized near half filling. We show that this behavior agrees with a renormalization-group solution of the one-dimensional SU(n)\mathrm{SU}(n)SU(n) Hubbard model. In two spatial dimensions we find several different ground states depending on the size of the hopping term ttt, the doping $\ensuremath{\delta}$, and the biquadratic spin interaction $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}$. In particular, the undimerized "flux" or "s+ids+ids+id" phase is the ground state at half filling for sufficiently large ttt or $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}$. We study the electronic and spin excitations of the various phases and comment on the relevance of the large-nnn problem to the high-Tc{T}_{c}Tc​ superconductors.
The magnetic susceptibility of the one-dimensional Hubbard model with open boundary conditions at arbitrary filling is obtained from field theory at low temperatures and small magnetic fields, including leading and next-leading orders. Logarithmic contributions to the bulk part are identified as well as algebraic-logarithmic divergences in the boundary contribution. As a manifestation of spin-charge separation, the result for the boundary part at low energies turns out to be independent of filling and interaction strength and identical to the result for the Heisenberg model. For the bulk part at zero temperature, the scale in the logarithms is determined exactly from the Bethe ansatz. At finite temperature, the susceptibility profile as well as the Friedel oscillations in the magnetisation are obtained numerically from the density-matrix renormalisation group applied to transfer matrices. Agreement is found with an exact asymptotic expansion of the relevant correlation function.
Persistent currents flowing through disordered mesoscopic rings threaded by a magnetic flux are investigated. Models of fermions with on-site interactions (Hubbard model) or models of spinless fermions with nearest neighbor interactions are considered on 2D cylinders with twisted boundary conditions in one direction to account for a magnetic flux. Self-consistent Hartree-Fock methods are used to treat the electron-electron interaction beyond first order. We show that the second harmonic of the current (which is relevant in the diffusive regime) is strongly suppressed by the interaction in the case of spinless fermions while it is significantly enhanced in the Hubbard model. Our data also strongly suggest that the reduction (increase) of this harmonic is related to a strong increase (reduction) of the spatial fluctuations of the charge density.