Conductivity in a symmetry-broken phase: Spinless fermions with 1/<i>d</i>corrections

Uhrig, Götz S.

doi:10.1103/physrevb.54.10436

Cited by 9 publications

(7 citation statements)

References 27 publications

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“…It is not possible to compute R for the whole Hilbert space except under simplifying conditions like infinite coordination number 32 . Hence we will restrict the inversion to certain subspaces which still allow an analytical treatment.…”

Section: Resolvent Approachmentioning

confidence: 99%

Lattice dependence of saturated ferromagnetism in the Hubbard model

1997

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We investigate the instability of the saturated ferromagnetic ground state (Nagaoka state) in the Hubbard model on various lattices in dimensions d = 2 and d = 3. A variational resolvent approach is developed for the Nagaoka instability both for U = ∞ and for U < ∞ which can easily be evaluated in the thermodynamic limit on all common lattices. Our results significantly improve former variational bounds for a possible Nagaoka regime in the ground state phase diagram of the Hubbard model. We show that a pronounced particle-hole asymmetry in the density of states and a diverging density of states at the lower band edge are the most important features in order to stabilize Nagaoka ferromagnetism, particularly in the low density limit.75.10. Lp, 75.30.Kz, 71.27.+a

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Section: Resolvent Approachmentioning

confidence: 99%

Lattice dependence of saturated ferromagnetism in the Hubbard model

1997

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“…where ρ (0) (ǫ) is the approximate form for the non-interacting electron density of states on a 3D cubic lattice as shown in Figure 1, given by Uhrig 23 , and…”

Section: Formalismmentioning

confidence: 99%

Possible experimentally observable effects of vertex corrections in superconductors

1998

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We calculate the effects of vertex corrections, of nonconstant density of states and of a ͑self-consistently determined͒ phonon self-energy for the Holstein model on a three-dimensional cubic lattice. We replace vertex corrections with a Coulomb pseudopotential C * adjusted to give the same T c , and repeat the calculations, to see which effects are a distinct feature of vertex corrections. This allows us to determine directly observable effects of vertex corrections on a variety of thermodynamic properties of superconductors. To this end, we employ conserving approximations ͑in the local approximation͒ to calculate the superconducting critical temperatures, isotope coefficients, superconducting gaps, free-energy differences, and thermodynamic critical fields for a range of parameters. We find that the dressed value of is significantly larger than the bare value. While vertex corrections can cause significant changes in all the above quantities ͑even when the bare electronphonon coupling is small͒, the changes can usually be well modeled by an appropriate Coulomb pseudopotential. The isotope coefficient proves to be the quantity that most clearly shows effects of vertex corrections that can not be mimicked by a C * .

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“…Each discrete wave vector sums is assumed normalized so that it becomes dk/(2π) in the continuum. Φ xx (ε) can be evaluated by first computing its Fourier transform 31 , that we call X(w). where J 0 (s) and J 1 (s) are Bessel functions.…”

Section: Discussionmentioning

confidence: 99%

“…which allows us to find an expression for the derivative of Φ xy , Eq. (31), that follows from the sum rule 1 2…”

Section: Hall Transport Function From Sum Rulementioning

confidence: 99%

Transport functions for hypercubic and Bethe lattices

Arsenault

Tremblay

2013

Phys. Rev. B

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In calculations of transport quantities, such as the electrical conductivity, thermal conductivity, Seebeck, Peltier, Nernst, Ettingshausen, Righi-Leduc, or Hall coefficients, sums over the Brillouin zone of wave-vector derivatives of the dispersion relation commonly appear. When the self-energy depends only on frequency, as in single-site dynamical mean-field theory, it is advantageous to perform these sums once and for all. We show here that in the case of a hypercubic lattice in d dimensions, the sums needed for any of the transport coefficients can be expressed as integrals over powers of the energy weighted by the energy-dependent non-interacting density of states. It is also shown that our exact expressions for the transport functions can be obtained from differential equations that follow from sum rules. By substituting the Bethe lattice density of states, one can obtain the previously unknown transport function for the electrical or thermal Hall coefficients and for the Nernst coefficient of the Bethe lattice.Comment: 12 pages, 3 figures. Final version. Section III.D and Appendix B have been adde

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Conductivity in a symmetry-broken phase: Spinless fermions with 1/dcorrections

Cited by 9 publications

References 27 publications

Lattice dependence of saturated ferromagnetism in the Hubbard model

Lattice dependence of saturated ferromagnetism in the Hubbard model

Possible experimentally observable effects of vertex corrections in superconductors

Transport functions for hypercubic and Bethe lattices

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