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arXiv:cond-mat/9803149 · Physical Review Letters

Density of States near the Mott-Hubbard Transition in the Limit of Large Dimensions

Stefan K. Kehrein

Published Nov 2, 1998• 31 citations
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Abstract

The zero temperature Mott-Hubbard transition as a function of the Coulomb repulsion $U$ is investigated in the limit of large dimensions. The behavior of the density of states near the transition at ${U\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}U}_{c}$ is analyzed in all orders of the skeleton expansion. It is shown that only two transition scenarios are consistent with the skeleton expansion for $U<{U}_{c}$: (i) The Mott-Hubbard transition is ``discontinuous'' in the sense that in the density of states finite spectral weight is redistributed at ${U}_{c}$. (ii) The transition occurs via a point at ${U\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}U}_{c}$ where the system is neither a Fermi liquid nor an insulator.

DOI
10.1103/physrevlett.81.3912

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The zero temperature Mott-Hubbard transition as a function of the Coulomb repulsion UUU is investigated in the limit of large dimensions. The behavior of the density of states near the transition at U=Uc{U\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}U}_{c}U=Uc​ is analyzed in all orders of the skeleton expansion. It is shown that only two transition scenarios are consistent with the skeleton expansion for U<UcU<{U}_{c}U<Uc​: (i) The Mott-Hubbard transition is ``discontinuous'' in the sense that in the density of states finite spectral weight is redistributed at Uc{U}_{c}Uc​. (ii) The transition occurs via a point at U=Uc{U\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}U}_{c}U=Uc​ where the system is neither a Fermi liquid nor an insulator.
The unanalytical feature of the Mott–Hubbard metal-insulator transition in infinite dimensions is studied by using a modified self-consistency scheme in the framework of dynamical mean-field theory. For a specific low temperature T=0.0025W (W: half bandwidth), the "Z"-shaped or "S"-shaped curves for double occupancy D, energy per lattice site E, and the quasi-particle weight Z are obtained as functions of U. Direct observation shows that the Fermi-liquid phase changes to the insulating phase through a non-Fermi-liquid phase at the unstable level. Based on our results, a scenario of zero temperature MIT is proposed. The phase diagram for MIT on the T–D plane is also presented.
The nature of the Mott-Hubbard metal-insulator transition in the infinite-dimensional Hubbard model is investigated by quantum Monte Carlo simulations down to temperature T=W/140T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}W/140T=W/140 ( W=bandwidthW\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\mathrm{bandwidth}W=bandwidth). Calculating with significantly higher precision than in previous work, we show that the hysteresis below ${T}_{\mathrm{IPT}}\ensuremath{\simeq}0.022W$, reported in earlier studies, disappears. Hence the transition is found to be continuous rather than discontinuous down to at least T=0.325TIPT{T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.325T}_{\mathrm{IPT}}T=0.325TIPT​. We also study the changes in the density of states across the transition, which illustrate that the Fermi liquid breaks down before the gap opens.
We study the nature of metal-insulator transition in the paramagnetic state for the Hubbard model on the Bethe lattice. The single-particle density of states is calculated via the operator Lanczos method. Our study shows that the metal-insulator transition is continuous and there is no preformed gap. The quasiparticle weight vanishes linearly with the distance from the transition point (Uc){(U}_{c})(Uc​) in agreement with results of iterative perturbation theory and exact diagonalization method. Our Uc{U}_{c}Uc​ is comparable to that by the random dispersion approximation. Our result indicates non-Fermi-liquid feature at the transition point.
One of the fundamental questions about high-temperature cuprate superconductors is the size of the Fermi surface underlying the superconducting state. By analyzing the single-particle spectral function for the Fermi-Hubbard model as a function of repulsion UUU and chemical potential $\ensuremath{\mu}$, we find that the Fermi surface in the normal state undergoes a transition from a large Fermi surface matching the Luttinger volume as expected in a Fermi liquid, to a Fermi surface that encloses fewer electrons that we dub the ``Luttinger breaking'' phase, as the Mott insulator is approached. This transition into a non-Fermi-liquid phase that violates the Luttinger count occurs at a critical density in the absence of any other broken symmetry. We obtain the Fermi-surface contour from the spectral weight ${A}_{\mathbf{k}}(\ensuremath{\omega}=0)$ and from an analysis of the singularities of the Green's function ReGk(E=0)\mathrm{Re}\phantom{\rule{0.16em}{0ex}}{G}_{\mathbf{k}}(E=0)ReGk​(E=0), calculated using determinantal quantum Monte Carlo and analytic continuation methods. We discuss our numerical results in connection with experiments on Hall measurements, scanning tunneling spectroscopy, and angle-resolved photoemission spectroscopy.