DMRG study of ferromagnetism in a one-dimensional Hubbard model

Daul, S.; Noack, R. M.

doi:10.1007/s002570050376

Cited by 37 publications

(43 citation statements)

References 9 publications

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“…A stabilization of this phase at intermediate U values requires a sufficiently large spectral weight near one of the band edges as is typical for frustrated (e.g., fcc-type) lattices which optimize the kinetic energy of the polarized state and, at the same time, frustrate the parasitic antiferromagnetic order. This finding, together with the results obtained for dimension d = 1 [32,15,14,19], finally establishes the stability of band ferromagnetism in the one-band Hubbard model on regular lattices and at intermediate values of the interaction U and density n. Thereby one of the prominent questions of many-body theory in this field is finally answered. By contrast, the origin of metallic ferromagnetism in the band-degenerate Hubbard model at intermediate U values is not primarily a spectral weight effect but is already caused by moderately strong Hund's rule couplings .…”

Section: Discussionmentioning

confidence: 78%

“…In this situation the development of new numerical techniques during the last few years was of crucial importance for progress in this field. In particular, for one-dimensional systems the DMRG [19], and for highdimensional systems the DMFT have led to important insights. Here we restrict ourselves to results obtained by DMFT.…”

Section: Frustrated Latticesmentioning

confidence: 99%

“…They were made possible mainly by the development (i) of new analytic approaches, such as the mathematical methods used to investigate flat-band ferromagnetism [6] and its extensions [14,15] as well as dynamical mean-field theory (DMFT) [16,17,18], (ii) of new numerical techniques, such as the density matrix renormalization group (DMRG) which yields precise results in d = 1 [19], and (iii) of new comprehensive approximation schemes such as the multiband Gutzwiller wave function [20], or the new ab initio computational scheme LDA+DMFT [21,22,23] which merges conventional band structure theory (LDA) with a comprehensive many-body technique (DMFT).…”

Section: Introductionmentioning

confidence: 99%

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Metallic Ferromagnetism — An Electronic Correlation Phenomenon

Vollhardt

Blümer

Held

et al. 2001

Band-Ferromagnetism

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Abstract. New insights into the microscopic origin of itinerant ferromagnetism were recently gained from investigations of electronic lattice models within dynamical meanfield theory (DMFT). In particular, it is now established that even in the one-band Hubbard model metallic ferromagnetism is stable at intermediate values of the interaction U and density n on regular, frustrated lattices. Furthermore, band degeneracy along with Hund's rule couplings is very effective in stabilizing metallic ferromagnetism in a broad range of electron fillings. DMFT also permits one to investigate more complicated correlation models, e.g., the ferromagnetic Kondo lattice model with Coulomb interaction, describing electrons in manganites with perovskite structure. Here we review recent results obtained with DMFT which help to clarify the origin of band-ferromagnetism as a correlation phenomenon.

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Section: Discussionmentioning

confidence: 78%

Section: Frustrated Latticesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Metallic Ferromagnetism — An Electronic Correlation Phenomenon

Vollhardt

Blümer

Held

et al. 2001

Band-Ferromagnetism

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“…As mentioned above, the fully polarized ferromagnetic state is the ground state for the open-boundary t-t ′ Hubbard model 4,5 . This is also the case with the open-boundary Hubbard ladders 14,15 .…”

mentioning

confidence: 99%

“…The reason we have chosen the Hubbard model is that the magnetic phase diagram on the n − U plane has been obtained for the t-t ′ Hubbard model by Daul and Noack (inset of Fig.2), 4,5 so that we can identify the region on which we work. For the Hubbard model we find the same curious behavior of the spectral function.…”

mentioning

confidence: 99%

Spectral function of the spiral spin state in the trestle and ladder Hubbard model

et al. 1998

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Eder and Ohta have found a violation of the Luttinger rule in the spectral function for the t-t ′ -J model, which was interpreted as a possible breakdown of the Tomonaga-Luttinger(TL) description in models where electrons can pass each other. Here we have computed the spin correlation along with the spectral function for the one-dimensional t-t ′ Hubbard model and two-leg Hubbard ladder. By varying the Hubbard U we have identified that such a phenomenon is in fact a spinless-fermionlike behavior of holes moving in a spiral spin configuration that has a spin correlation length of the system size.PACS numbers: 71.10.Fd It is widely believed that the low-energy physics of a wide class of one-dimensional (1D) systems can be described as a Tomonaga-Luttinger(TL) liquid 1,2 , which is an effective theory for electrons interacting in 1D. The ansatz has indeed been shown to be valid for exactly solvable 1D models such as the Hubbard model or the supersymmetric t-J model, and also for some other models numerically. However, recently, Eder and Ohta 3 looked into the spectral function in 1D t-J model that has t ′ (t-t ′ -J model), and made a very interesting observation that the density of electrons n and Fermi momentum k F are related with k F = πn in a certain parameter regime, which is incompatible with the Luttinger relation, k F = πn/2, expected for a TL liquid, which they suggest to be an indication for a breakdown of the TL description.In order to clarify the origin of such an curious behavior, here we study the t-t ′ Hubbard model with finite values of U . The reason we have chosen the Hubbard model is that the magnetic phase diagram on the n − U plane has been obtained for the t-t ′ Hubbard model by Daul and Noack (inset of Fig.2), 4,5 so that we can identify the region on which we work. For the Hubbard model we find the same curious behavior of the spectral function. We further find that the state in question is a spiral spin state, in which the spin correlation has a wave length of the system size and thus has a local ferromagnetic nature. The curious behavior of the spectral function can be understood by a picture in which holes can hop almost freely in such a spin background as originally proposed by Doucot and Wen 7 as a trial state for finite systems to prove the instability of Nagaoka's ferromagnetism 8 . The ferromagnetic-like state naturally explains the doubling of k F into πn as a spinless-fermion-like behavior. The region over which the spiral behavior appears is indeed consistent with the phase diagram for the t-t ′ Hubbard model. In order to see if the appearance of the spiral state extends to other quasi-1D systems, we have also studied the 2-leg Hubbard ladder with U = ∞, and have found similar features as in the t-t ′ Hubbard model. The t-t ′ Hubbard Hamiltonian is given byin standard notations. Hereafter we set t = 1. First we numerically calculate, with the continued fraction expansion, the single-particle spectral function given bywhere A + (A − ) denote the electron addition (removal) spect...

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Frustration of antiferromagnetism in the t‐t′‐Hubbard model at weak coupling

Hofstetter

Vollhardt

1998

Annalen der Physik

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The perfect-nesting instability towards antiferromagnetism of the Hubbard model is suppressed by next-nearest neighbor hopping t'. The asymptotic behavior of the critical coupling Uc(t') at small t' is calculated in dimensions d = 2,3,00 using Hartree theory; this yields the exact result at least in d > 2. The order of the transition is also determined. A region of stability of a metallic antiferromagnetic phase in d = 3 is identified.

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DMRG study of ferromagnetism in a one-dimensional Hubbard model

Abstract: The one dimensional Hubbard model with nearest and (negative) next-nearest neighbour hopping has been studied with the densitymatrix renormalization group (DMRG) method. A large region of ferromagnetism has been found for finite density and finite on-site interaction.

Cited by 37 publications

References 9 publications

Metallic Ferromagnetism — An Electronic Correlation Phenomenon

Metallic Ferromagnetism — An Electronic Correlation Phenomenon

Spectral function of the spiral spin state in the trestle and ladder Hubbard model

Frustration of antiferromagnetism in the t‐t′‐Hubbard model at weak coupling

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