New method for the Anderson model

Barnes, S. E.

doi:10.1088/0305-4608/6/7/018

Cited by 517 publications

(342 citation statements)

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“…23 One of the most powerful techniques in this context is the auxiliary boson technique [24][25][26] . It has two major advantages: (i) In its lowest order self-consistent approximation, the non-crossing approximation (NCA) [27][28][29] , it yields an accurate quantitative description of the single-channel Anderson model in equilibrium [29][30][31] down to low temperatures, although it does not capture correctly the Fermi liquid regime.…”

Section: In the 1980's Zawadowski And Vladarmentioning

confidence: 99%

Nonequilibrium dynamics of the Anderson impurity model

1998

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The M -channel Anderson impurity model (M = 1, 2) is studied in the Kondo limit with a finite voltage bias applied to the conduction electron reservoirs. Using the Non-Crossing Approximation (NCA), we calculate the local spectral functions, the differential conductance, and susceptibility at non-zero bias for symmetric as well as asymmetric coupling of the impurity to the leads. We describe an effective procedure to solve the NCA integral equations which enables us to reach temperatures far below the Kondo scale. This allows us to study the scaling regime where the conductance depends on the bias only via a scaling function. Our results are applicable to both tunnel junctions and to point contacts. We present a general formula which allows one to go between the two cases of tunnel junctions and point contacts. Comparison is also made between the conformal field theory and the NCA conduction electron self-energies in the two channel case.

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Section: In the 1980's Zawadowski And Vladarmentioning

confidence: 99%

Nonequilibrium dynamics of the Anderson impurity model

1998

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“…Current proposals for the low-energy physics of doped Mott insulators are based either on perturbation theory [7] followed by projecting out the high-energy sector or slaved [8] operators designed to exclude double occupancy. As projection is not integration, neither permits an explicit integration of the high-energy scale, and both miss relevant physical aspects.…”

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confidence: 99%

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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“…Within the slave-boson representation Barnes (1976);Coleman (1984), Eq. (4) is rewritten in terms of the projected fermion operators f † imσ and f imσ , as well as the slave boson operators at each site, which rule out the double and multiple fermion occupancies.…”

Section: Strong Correlation Regimementioning

confidence: 99%

“…The present constrained spin-orbital formulation resembles to the 4-fold degenerate state of pseudo-angular momentum j=3/2 proposed by Barnes Barnes (1976) and Coleman Coleman (1984), if we define…”

Section: Strong Correlation Regimementioning

confidence: 99%