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Journal de Physique I

Screening of an external magnetic field by spin currents: the infinite U Hubbard model

J C Anglès d'Auriac, Benoît Douçot

Published Feb 1, 1993• 0 citations
Publisher

Abstract

The infinite U Hubbard model with a single hole in the presence of an external orbital magnetic field is studied on a finite cluster for several geometries. Exact diagonalization results for the energy, total spin and several spin correlation functions are presented. They strongly support the idea of the compensation of the applied flux by a flictitious flux induced by a non-coplanar spin background. A variational study also shows evidence of this phenomenon.

DOI
10.1051/jp1:1993146

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The infinite U Hubbard model with a single hole in the presence of an external orbital magnetic field is studied on a finite cluster for several geometries. Exact diagonalization results for the energy, total spin and several spin correlation functions are presented. They strongly support the idea of the compensation of the applied flux by a flictitious flux induced by a non-coplanar spin background. A variational study also shows evidence of this phenomenon.
Using an original Quantum Monte Carlo algorithm, we study the thermodynamical properties of a single hole in the two-dimensional infinite-U Hubbard model at finite temperature. We investigate the energy and the spin correlators as a function of an external orbital magnetic field. This field is found to destroy the Nagaoka ferromagnetism and to induce chirality in the spin background. The applied field is partially screened by a fictitious magnetic field coming from the chirality. Our algorithm allows us to reach a temperature low enough to discuss the ground state properties of the model.
We present different numerical calculations based on variational quantum Monte Carlo simulations supporting a ferromagnetic ground state for finite and small hole densities in the two-dimensional infinite-U Hubbard model. Moreover, by studying the energies of different total spin sectors, these calculations strongly suggest that the paramagnetic phase is unstable against a phase with a partial polarization for large hole densities delta approximately 0.40 with evidence for a second-order transition to the paramagnetic large doping phase.
We calculate the dynamical behavior of a hole in various spin backgrounds in infinite dimensions, where it can be determined exactly. We consider hypercubic lattices with two different types of spin backgrounds. On one hand we study an ensemble of spin configurations with an arbitrary spin probability on each sublattice. This model corresponds to a thermal average over all spin configurations in the presence of staggered or uniform magnetic fields. On the other hand we consider a definite spin state characterized by the angle between the spins on different sublattices, i.e., a classical spin system in an external magnetic field. When spin fluctuations are considered, this model describes the physics of unpaired particles in strong-coupling superconductors.
We studied the Kane-Mele-Hubbard model at half filling with Zeeman magnetic field using rotationally invariant slave boson method. The competition between external magnetic field and spin orbital coupling at large Hubbard U is explored. It is found that different canted antiferromagnetic phases exist in the presence of longitudinal and transverse magnetic fields. With longitudinal external magnetic field and strong electron correlation, the z component of the local moment is preferred by the finite spin-orbital coupling.
The infinite-U Hubbard model on finite two-dimensional square lattices is investigated by the use of exact numerical diagonalization. Configurations with one spin flip away from the ferromagnetic state and up to three holes are studied for lattice sizes ranging from 4*4 to 12*12. For all these situations, the state with one spin flip is found to be more stable than the Nagaoka ferromagnetic state. The crystal momentum of the ground state in this spin sector depends on the system size. Systematic comparison with the Gutzwiller wavefunction shows that it reproduces qualitatively the crystal momentum dependence of the energy, but not the exact correlation between the spin flip and the holes.
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.