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arXiv:cond-mat/9902267 · Physical Review Letters

Absence of Hysteresis at the Mott-Hubbard Metal-Insulator Transition in Infinite Dimensions

J. Schlipf, Mark Jarrell, P. G. J. van Dongen, Nils Blümer, Stefan K. Kehrein, Thomas Pruschke, D. Vollhardt

Published Jun 14, 1999• 51 citations
arXivHTMLPDF

Abstract

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 $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}W/140$ ( $W\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\mathrm{bandwidth}$). 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 ${T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.325T}_{\mathrm{IPT}}$. 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.

DOI
10.1103/physrevlett.82.4890

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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 TIPT\ensuremath≃0.022W{T}_{\mathrm{IPT}}\ensuremath{\simeq}0.022WTIPT​\ensuremath≃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 consider a Mott transition of the Hubbard model in infinite dimensions. The dynamical meanfield theory is employed in combination with a continuous-time quantum Monte Carlo (CTQMC) method for an accurate description at low temperatures. From the double occupancy and the energy density, which are directly measured from the CTQMC method, we construct the phase diagram. We pay particular attention to the construction of the first-order phase transition line (PTL) in the coexistence region of metallic and insulating phases. The resulting PTL is found to exhibit reasonable agreement with earlier finite-temperature results. We also show by a systematic inclusion of low-temperature data that the PTL, which is achieved independently of the previous zero-temperature results, approaches monotonically the transition point from earlier zerotemperature studies.
The Quantum Monte Carlo simulations of the ionic Hubbard model on a two-dimensional square lattice at half filling were performed. The method based on the direct-space, proposed by Suzuki and al., Hirsch and al., was used. Cycles of increasing and decreasing values of the Coulomb interaction $ U $ were performed for fixed temperature ($ kT=0.01 $). Results indicate that, at low temperature, the two insulator phases are separated by a metallic phase for weak to intermediate values of the staggered potential $ Δ$. For large Coulomb repulsion the system is in a Mott insulator with an antiferromagnetism order. On increasing and decreasing the Coulomb interaction $ U $ the metal-Mott insulator transition shows an hysteresis phenomenon while the metal-band insulator transition is continue. For large $ Δ$ it seems that the metallic region shrinks to a single metallic point. However, the band insulator to the Mott insulator transition is not direct for the studied model. A phase diagram is drawn for the temperature $ kT=0.01 $. For $ Δ=0.5 $ cycles of increasing and decreasing temperature were programmed for different values of the Coulomb interaction $ U $ . A behaviour change appears for $ U\simeq 1.75 $. This suggests that a crossover line divides the metallic region of the phase diagram.
We study the Hubbard model in dimension d= infinity , within an approximation that simultaneously reproduces the atomic limit and the weak-coupling limit up to second order in the interaction strength U. This method, which is a slightly modified version of an approximation suggested by Edwards and Hertz, is applied to the calculation of the self-energy and of the spectral function in the paramagnetic regime for different U, band fillings n, and temperatures T. We find Fermi-liquid behaviour for small U and (for half-filling n=0.5) a metal-insulator (Mott) transition at a critical value U cr , but also a metallic non-Fermi-liquid phase for intermediate values U<U cr . We compare our results with results obtained within the second-order perturbation theory in U and (at finite temperature) with the (essentially exact) quantum Monte Carlo (QMC) results. Qualitatively, the approximation reproduces the correct tendencies obtained by QMC, but in detail there are still discrepancies, in particular for intermediate values of U.
We study the transition from paramagnetic metal to paramagnetic insulator by finite temperature Quantum Monte-Carlo simulations for the 2D Hubbard model at half-filling. Working at the moderately high temperature T=0.33*t where the spin correlation length has dropped to 1.5 lattice spacings, and scanning the interaction strength U, we observe an unambiguous metal-insulator transition with onset at U_c=4t. In the metallic phase there are no indications of any `correlation narrowing' of the band width, nor for any decrease of spectral weight at the Fermi energy. The Mott-Hubbard gap opens gradually with increasing U and is accompanied by the formation of side bands near the Fermi energy. In the first stages of gap formation the gap opens at (pi,0), reminiscent of the `pseudogap' phenomenology in cuprate superconductors.
The Hubbard model in the strong-coupling regime is mainly studied by Kondo-lattice theory or 1/d expansion theory, with d the spatial dimensionality. In two dimensions and higher, the ground state within the Hilbert subspace with no order parameter is a normal Fermi liquid except for n=1 and U/W=+infinity, with n the electron density per unit cell, U the on-site repulsion, and W the bandwidth; the cooperation between the Kondo effect, which favors a local singlet on each unit cell, and a resonating-valence-bond effect, which favors a local singlet on each pair of nearest-neighbor unit cells, stabilizes the Fermi liquid, whose ground state is a singlet as a whole, in the strong-coupling regime. In the whole Hilbert space with no restriction, the normal Fermi liquid is unstable at least against a magnetic or superconducting state. This analysis confirms an early Fermi-liquid theory of high-temperature superconductivity, F. J. Ohkawa, Jpn. J. Appl. Phys. 26, L652 (1987). The ground state for n=1 and U/W=+infinity is a Mott insulator. Actual metal-insulator transitions cannot be explained within the Hubbard model. In order to explain them, the electron-phonon interaction, multi-band or multi-orbital effects, and effects of disorder should be considered beyond the Hubbard model. The crossover between local-moment magnetism and itinerant-electron magnetism corresponds to that between a localized spin and a normal Fermi liquid in the Kondo effect and it is simply a Mott metal-insulator crossover.