Ferromagnetism in the Infinite-
                    <i>U</i>
                    Hubbard Model

Liang, Shoudan; Pang, Hanbin

doi:10.1209/0295-5075/32/2/014

Cited by 41 publications

(50 citation statements)

References 20 publications

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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 . Then, in the thermodynamic limit, the spiral ground state (in PBC) can either give way to the ferromagnetic state, remain the ground state, or become degenerate with the ferromagnetic one.…”

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confidence: 72%

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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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“…Ferromagnetic behavior is also found in the ladders where U is infinite 14,15 , so it is intriguing to study whether a spiral state appears in this system as well, and if so, whether A(k, ω) exhibits a DW-like behavior. The Hamiltonian is given by…”

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confidence: 99%

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

et al. 1998

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“…In practice, this leads to a large entanglement between the system and environment blocks and therefore a slower fall-off of the eigenvalues of the density matrix, requiring many more states to be kept to attain a given accuracy. This scaling of the required number of states has been studied systematically for the case of two-dimensional noninteracting spinless fermions, where it is found that the number scales exponentially with the linear dimension of the lattice [90,95]. It is not completely clear that this exponential scaling is fundamental for system block environment block all systems; in fact, noninteracting particles are probably the worst case because of the absence of length scales in the wave functions and because of the highly degenerate gapless excitation spectrum.…”

Section: Real-space Algorithm In Two Dimensionsmentioning

confidence: 99%

Diagonalization- and Numerical Renormalization-Group-Based Methods for Interacting Quantum Systems

Noack¹,

Manmana²

2005

AIP Conference Proceedings

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Abstract. In these lecture notes, we present a pedagogical review of a number of related numerically exact approaches to quantum many-body problems. In particular, we focus on methods based on the exact diagonalization of the Hamiltonian matrix and on methods extending exact diagonalization using renormalization group ideas, i.e., Wilson's Numerical Renormalization Group (NRG) and White's Density Matrix Renormalization Group (DMRG). These methods are standard tools for the investigation of a variety of interacting quantum systems, especially low-dimensional quantum lattice models. We also survey extensions to the methods to calculate properties such as dynamical quantities and behavior at finite temperature, and discuss generalizations of the DMRG method to a wider variety of systems, such as classical models and quantum chemical problems. Finally, we briefly review some recent developments for obtaining a more general formulation of the DMRG in the context of matrix product states as well as recent progress in calculating the time evolution of quantum systems using the DMRG and the relationship of the foundations of the method with quantum information theory.

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“…It is well known that the ferromagnetic Nagaoka [16] state is stabilized when one electron is added to the half filled system. Different works [18][19][20] indicate that a partially polarized FM state is favored for a finite range of concentrations away from half filling. In addition, we have recently found numerical evidence of itinerant ferromagnetism in the PAM for the mixed valence regime and |V | < ∼ |t| [5,6].…”

Section: B) Virtual States Lowest Energymentioning

confidence: 99%

Ferromagnetism in the strong hybridization regime of the periodic Anderson model

2003

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We determine exactly the ground state of the one-dimensional periodic Anderson model (PAM) in the strong hybridization regime. In this regime, the low energy sector of the PAM maps into an effective Hamiltonian that has a ferromagnetic ground state for any electron density between half and three quarters filling. This rigorous result proves the existence of a new magnetic state that was excluded in the previous analysis of the mixed valence systems.Rigorous results, numerical and analytic, have greatly aided the study of strongly correlated electrons systems. Unfortunately, few such results exist. The numerical renormalization group and Bethe ansatz solutions of the single impurity Anderson and Kondo models are perhaps the best examples of a solid numerical approach and exact solution of simple models that changed and solidified the thinking in what was a highly controversial and puzzling problem area. Another important result was the rigorous connection between the two models established by Schrieffer and Wolff [1]. Their work showed that the low lying energy spectrum of the Anderson model in the strong coupling and weak hybridization limit (U/t ≫ 1 and V ≪ |E F −ǫ f |) can be mapped into the Kondo model in the weak coupling regime (J/t ≪ 1).For dense systems, the natural extensions of the impurity models are the periodic Anderson (PAM) and Kondo lattice (KLM) models. For these, numerical renormalization group and Bethe Ansatz solutions are lacking even in one-dimension. In addition, very few rigorous results are available for the PAM [2,3]. What remains true however is the connection between the strong and weak coupling limits via a natural extension of the Schrieffer-Wolff transformation.There are two basic questions one can ask about these lattice models: what is their relevance to real materials and in what other parameter regimes might their physics be connected? In several well known papers, Doniach [4], at least implicitly, made several assumptions about the answers to both questions and proposed the now standard picture of the magnetic properties of f-electron materials that portrays a competition between the RKKY magnetic interaction which is obtained from a fourth order expansion in the hybridization and the Kondo exchange.The reasoning behind this intuitively appealing picture is something like the following: From the Schrieffer-Wolff perturbation theory, the Kondo exchange coupling is related to the parameters in the PAM via J ≈ |V | 2 /|E F − ǫ f |. In the PAM, a mixed valence regime corresponds to positioning the f-electron orbitals in the conduction band near the Fermi energy, i.e., |E F − ǫ f | ≈ 0. In this regime, the Schrieffer-Wolff result suggests the Kondo exchange is strong and thus can lead to a complete compensation of the f-moments by one or more of the conduction band electrons. Implied in this line of reasoning there are two important assumptions [4]: I) The strong coupling limit of the KLM is connected to the mixed valence regime (for weak hybridzation |V | ≪ |t|) of the PAM, and II)...

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Ferromagnetism in the Infinite- U Hubbard Model

Abstract: PACS. 75.10-b -General theory and models of magnetic ordering. PACS. 71.27 + a -Strongly correlated electron systems.

Cited by 41 publications

References 20 publications

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

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

Diagonalization- and Numerical Renormalization-Group-Based Methods for Interacting Quantum Systems

Ferromagnetism in the strong hybridization regime of the periodic Anderson model

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