Spectral properties of the Hubbard bands

Eskes, Henk; Olés, A.M.; Meinders, M.B.J.; Stephan, W.

doi:10.1103/physrevb.50.17980

Cited by 161 publications

(174 citation statements)

References 92 publications

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“…Similarly, physical quantities in the effective theory are not the expectation values for operators calculated with the projection of the vectors into the subspace. Since |0 H = e −iS |0 s , the expectation value of an operator O H in the original Hubbard model can be computed in the state |0 s as long as the transformed operator O s = e iS O H e −iS is used 1,3,10,11,12,13,14 . In other words, …”

Section: B Staggered Magnetization Operatormentioning

confidence: 99%

Néel order, ring exchange, and charge fluctuations in the half-filled Hubbard model

et al. 2005

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We investigate the ground state properties of the two dimensional half-filled one band Hubbard model in the strong (large-U ) to intermediate coupling limit (i.e. away from the strict Heisenberg limit) using an effective spin-only low-energy theory that includes nearest-neighbor exchange, ring exchange, and all other spin interactions to order t(t/U ) 3 . We show that the operator for the staggered magnetization, transformed for use in the effective theory, differs from that for the order parameter of the spin model by a renormalization factor accounting for the increased charge fluctuations as t/U is increased from the t/U → 0 Heisenberg limit. These charge fluctuations lead to an increase of the quantum fluctuations over and above those for an S = 1/2 antiferromagnet. The renormalization factor ensures that the zero temperature staggered moment for the Hubbard model is a monotonously decreasing function of t/U , despite the fact that the moment of the spin Hamiltonien, which depends on transverse spin fluctuations only, in an increasing function of t/U . We also comment on quantitative aspects of the t/U and 1/S expansions.

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Section: B Staggered Magnetization Operatormentioning

confidence: 99%

Néel order, ring exchange, and charge fluctuations in the half-filled Hubbard model

et al. 2005

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“…As the x empty sites can be occupied by either spin up or spin down electrons, the 2x sum rule is exact [1] in the atomic limit. Further, in the presence of hybridization (with matrix element t), virtual excitations between the LHB and UHB increase the loss of spectral weight at high energy thereby leading to a faster than 2x growth [1][2][3] of the low-energy spectral weight, a phenomenon confirmed [4 -6] widely in the high-temperature copper-oxide superconductors.…”

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confidence: 92%

Hidden Charge2eBoson in Doped Mott Insulators

2007

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We construct the low-energy theory of a doped Mott insulator, such as the high-temperature superconductors, by explicitly integrating over the degrees of freedom far away from the chemical potential. For either hole or electron doping, a charge 2e bosonic field emerges at low energy. The charge 2e boson mediates dynamical spectral weight transfer across the Mott gap and creates a new charge e excitation by binding a hole. The result is a bifurcation of the electron dispersion below the chemical potential as observed recently in angle-resolved photoemission on Pb-doped Bi 2 Sr 2 CaCu 2 O 8 (Pb2212). DOI: 10.1103/PhysRevLett.99.046404 PACS numbers: 71.27.+a Two problems beset the construction of a proper lowenergy theory (explicit integration of the high-energy scale) of doped Mott insulators. First, the high-energy degrees of freedom are neither fermionic nor bosonic. To illustrate, in a Mott insulator, the chemical potential lies in a charge gap between two bands that represent electron motion on empty (lower Hubbard band, LHB for short) and singly occupied sites (upper Hubbard band, hereafter UHB). Since the latter involves double occupancy, the gap between the bands is set by the on-site repulsion energy U. Nonetheless, both double occupancy and double holes represent high-energy excitations in the half-filled insulating state as each is equally far from the chemical potential. As neither of these is fermionic, standard fermionic path integral procedures are of no use.Second, unlike the static bands in band insulators, the UHB and LHB are not rigid, thereby permitting spectral weight transfer. When x holes are placed in a Mott insulator, at least 2x [1] single particle addition states are created just above the chemical potential. The deviation from x, as would be the case in a band insulator, is intrinsic to the strong correlations that mediate the Mott insulating state in a half-filled band, thereby distinguishing Mottness from ordering. The states in excess of x arise from two distinct effects. Each hole reduces the number of ways of creating a doubly occupied site by one, thereby reducing the spectral weight at high energy. As the x empty sites can be occupied by either spin up or spin down electrons, the 2x sum rule is exact [1] in the atomic limit. Further, in the presence of hybridization (with matrix element t), virtual excitations between the LHB and UHB increase the loss of spectral weight at high energy thereby leading to a faster than 2x growth [1-3] of the low-energy spectral weight, a phenomenon confirmed [4 -6] widely in the high-temperature copper-oxide superconductors.Because some of the low-energy degrees of freedom of doped Mott insulators derive from the high-energy scale, low-energy descriptions must either (C1) abandon Fermi statistics or (C2) generate new degrees of freedom [1] which ultimately leads to electron number nonconservation. Current proposals for the low-energy physics of doped Mott insulators are based either on perturbation theory [7] followed by projecting out the high...

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“…20-23 Also, while a t − J model is enough to explain the observed dispersion in photoemission measurements in Sr 2 CuO 2 Cl 2 , the mapping of the operators 24,25 is crucial to explain the observed intensities.…”

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confidence: 99%

“…The expression of the transformed original fermions for ∆ = 0 and any filling to lowest order in t/U can be found in Refs. 24,25 . The first two terms of the last member of Eq.…”

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Charge dynamics in the Mott insulating phase of the ionic Hubbard model

Aligia

2004

Phys. Rev. B

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I extend to charge and bond operators the transformation that maps the ionic Hubbard model at half filling onto an effective spin Hamiltonian. Using the transformed operators I calculate the amplitude of the charge density wave in different dimensions D. In 1D, the charge-charge correlations at large distance d decay as d −3 ln −3/2 d, in spite of the finite charge gap, due to remaining charge-spin coupling. Bond-bond correlations decay as (−1) d d −1 ln −3/2 d as in the usual Hubbard model.

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Spectral properties of the Hubbard bands

Cited by 161 publications

References 92 publications

Néel order, ring exchange, and charge fluctuations in the half-filled Hubbard model

Néel order, ring exchange, and charge fluctuations in the half-filled Hubbard model

Hidden Charge2eBoson in Doped Mott Insulators

Charge dynamics in the Mott insulating phase of the ionic Hubbard model

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