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arXiv:1909.07349 · Physical review. B./Physical review. B

Onset of ferromagnetism for strongly correlated electrons in one-dimensional chains

Hernan B. Xavier, E. A. Kochetov, Álvaro Antônio Bandeira Ferraz

Published Jan 13, 2020• 6 citations
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Abstract

The existence of the Nagaoka ferromagnetism is examined in the context of the one-dimensional $U=\ensuremath{\infty}$ Hubbard model. We construct the exact quantum partition function to describe the physics of such a regime. Our calculation reveals that, while the ground state in an open chain is always spin degenerate, in a finite size closed chain with at least one vacancy, the ground state can only be ferromagnetic when the number of electrons is less than or equal to three. Our results shed more light on a very recent experimental verification of Nagaoka ferromagnetism in a quantum dot setup.

DOI
10.1103/physrevb.101.045112

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The existence of the Nagaoka ferromagnetism is examined in the context of the one-dimensional U=\ensuremath∞U=\ensuremath{\infty}U=\ensuremath∞ Hubbard model. We construct the exact quantum partition function to describe the physics of such a regime. Our calculation reveals that, while the ground state in an open chain is always spin degenerate, in a finite size closed chain with at least one vacancy, the ground state can only be ferromagnetic when the number of electrons is less than or equal to three. Our results shed more light on a very recent experimental verification of Nagaoka ferromagnetism in a quantum dot setup.
Two-dimensional Hubbard lattices with two or three holes are investigated as a function of UUU in the large-UUU limit. In the so-called Nagaoka limit (one-hole system at infinite UUU), it is known that the Hubbard model exhibits a ferromagnetic ground state. Here, by means of exact full configuration interaction quantum Monte Carlo simulations applied to periodic lattices up to 24 sites, we compute spin-spin correlation functions as a function of increasing UUU. The correlation functions clearly demonstrate the onset of ferromagnetic domains, centered on individual holes. The overall total spin of the wave functions remains the lowest possible (0 or 12\frac{1}{2}21​, depending on the number of holes). The ferromagnetic domains appear at interaction strengths comparable to the critical interaction strengths of the Nagaoka transition in finite systems with strictly one hole. The existence of such ferromagnetic domains is the signature of Nagaoka physics in Hubbard systems with a small (but greater than 1) number of holes.
Abstract. We study the influence of on-site disorder on the magnetic properties of the ground state of the infinite-U one-dimensional (1D) Hubbard model. We find that the ground state is not ferromagnetic. This is analysed in terms of the algebraic structure of the spin dependence of the Hamiltonian. A simple explanation is derived for the 1=N periodicity in the persistent current for this model. The Hubbard model is the simplest model one can study to examine the effects of correlations between electrons in narrow energy bands. The Hamiltonian consists of a nearest neighbour hopping term and an electron–electron repulsion, U, which acts only when two electrons are on the same site. The Hubbard model is also the canonical model for the study of itinerant ferromagnetism. The strong coupling regime is of special importance for the study of ferromagnetism, since a theorem by Nagaoka [1] states that in theU D 1 limit, the ground state (GS) is ferromagnetic given some connectivity property of the lattice (which holds in most cases for d> 1). The model is solvable in one dimension and it was shown [2] that for open boundary conditions (BCs) the GS for finiteU is a singlet, i.e. there can be no ferromagnetism unless one postulates explicitly spin- or velocity-dependent forces. For infinite U, the GS of
Ferromagnetic domains in the large-UUU Hubbard model with a few holes: an FCIQMC study
Two-dimensional Hubbard lattices with two or three holes are investigated as a function of UUU in the large-UUU limit. In the so-called Nagaoka limit (one-hole system at infinite UUU), it is known that the Hubbard model exhibits a ferromagnetic ground-state. Here, by means of exact FCIQMC simulations applied to periodic lattices up to 24 sites, we compute spin-spin correlation functions as a function of increasing UUU. The correlation functions clearly demonstrate the onset of ferromagnetic domains, centred on individual holes. The overall total spin of the wavefunctions remain the lowest possible (0, or 12\frac{1}{2}21​, depending on the number of holes). The ferromagnetic domains appear at interaction strengths comparable to the critical interaction strengths of the Nagaoka transition in finite systems with strictly one hole. The existence of such ferromagnetic domains is the signature of Nagaoka physics in Hubbard systems with a small (but greater than one) number of holes.
Correlations of a one-dimensional doubly degenerate Hubbard model are studied for the one-quarter-filled case. Exact calculations on a four-site lattice show that a ferromagnetic state exists in the strong-coupling regime. For a one-dimensional chain, a strong-coupling effective Hamiltonian was studied using a self-consistent calculation, a high-temperature expansion, and quantum Monte Carlo simulations. The results provide information on the parameters needed for ferromagnetic correlations, and the temperature dependence of the spin and orbital correlations.
We investigate the magnetization of the ground state of the one-dimensional flat-band Hubbard model as a function of the electron filling, using exact diagonalization techniques. Our calculation shows that the systems with odd n holes added to half-filling bands for a sufficiently large U (the on-site Coulomb repulsion energy) have a saturated ferromagnetic ground state, which is nondegenerate except for the trivial spin degeneracy. Dependences of the critical value of U on the size and on λ (a parameter of the system) are also investigated. For all values of λ, it is found that the ground state is a saturated ferromagnetic state if U is sufficiently large. Moreover, we find that the critical U for the saturated ferromagnetic ground state is almost independent on the system size, at least, for the system near quarter-filling. These facts indicate that even if the system size go to infinity, the ferromagnetic ground state can be exist for a finite U .
Nagaoka showed that ferromagnetism can arise from a basic Hubbard model of certain lattices under special conditions. Motivated by recent experimental advances in simulating such systems using small plaquettes of a few quantum dots, this work investigates what geometrical arrangement of these dots and what number of electrons are necessary to lead to nontrivial ferromagnetic ground states. This includes many situations not covered by Nagaoka's theorem, which is only valid under specific constraints.