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Journal of Physics Condensed Matter

The failure of Fermi-liquid theory at strong coupling

V. Janiš

Published Mar 11, 1996• 1 citation
Publisher

Abstract

We investigate quantitatively the effects of strong electron - electron coupling on the dynamics of lattice electrons. For this purpose the self-consistent version of the bubble-chain approximation at zero temperature and half filling of the Anderson (Hubbard) model is used. Special attention is paid to a critical region of an electron - hole correlation function shaping the transition from weak to strong interaction. We find an analytic solution with Fermi-liquid properties on the weak-coupling side of the critical region around the two-particle pole. It is shown that Fermi-liquid theory does not lead to a consistent behaviour of the self-consistent solution on the strong-coupling side of the critical region.

DOI
10.1088/0953-8984/8/11/003

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We investigate quantitatively the effects of strong electron - electron coupling on the dynamics of lattice electrons. For this purpose the self-consistent version of the bubble-chain approximation at zero temperature and half filling of the Anderson (Hubbard) model is used. Special attention is paid to a critical region of an electron - hole correlation function shaping the transition from weak to strong interaction. We find an analytic solution with Fermi-liquid properties on the weak-coupling side of the critical region around the two-particle pole. It is shown that Fermi-liquid theory does not lead to a consistent behaviour of the self-consistent solution on the strong-coupling side of the critical region.
We investigate quantitatively the effects of strong electron-electron coupling onto the dynamics of lattice electrons. To that purpose the self-consistent version of the bubble-chain approximation at zero temperature and half filling of the Anderson (Hubbard) model is used. Special attention is paid to a critical region of an electron-hole correlation function shaping the transition from weak to strong interaction. We find an analytic solution with Fermi-liquid properties on the weak-coupling side of the critical region around the two-particle pole. It is shown that Fermi-liquid theory does not lead to a consistent behavior of the self-consistent solution on the strong-coupling side of the critical region.
It has become easy to calculate numerically self-energy corrections in second-order perturbation theory. In order to find out its capabilities and limitations, we analyse the weak-coupling approach for a system of one-dimensional correlated fermions. We compare the self-energy contributions due to different scattering processes of left- and right-moving particles which can be treated analytically. We find that for Tomonaga-Luttinger processes second-order perturbation theory gives reliable results and show how deviations from Fermi-liquid behaviour and the separation of spin- and charge-density excitations can be detected from the numerical data. Choosing the Hubbard model as a typical example we present numerical results for the self-energy and the spectral density. Special attention is paid to the case without particle-hole symmetry. The insulating behaviour at half filling is outside the scope of the weak-coupling method applied.
We present a numerical study on the non-Fermi liquid behavior of a three-dimensional strongly correlated system. The Hubbard model in a simple cubic lattice is simulated by the dynamical cluster approximation; in particular, the quasi-particle weight is calculated at finite dopings for a range of temperatures. By fitting the quasi-particle weight to the marginal Fermi liquid form at finite doping near the putative quantum critical point, we find evidence of a separatrix between Fermi liquid and non-Fermi liquid regions. Our results suggest that a marginal Fermi liquid and possibly a quantum critical point exist in the non-symmetry broken solution of the three-dimensional interacting electron systems. We also calculate the spectral function, close to the half-filling, and we obtain evidence of pseudogap.
The physical properties of two-dimensional interacting electron systems are of great current interest. An open question in the physics of low-dimensional fermionic models is whether their properties are described by standard Fermi-liquid theory or whether instead they show unconventional behaviour in strongly correlated electron systems. As the two-dimensional Hubbard model is the typical example of a strongly correlated electron system, we solve for this model the two-body problem in the vicinity of a half-filled Fermi sea. The results obtained show that for a low hole concentration the well known Fermi-liquid picture fails.
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.
For pt.I see Physics B, vol.163, p.527 (1990). An exact diagrammatic analysis of the electron self-energy in the Hubbard and related models is given within the local approximation. Contact is made with recent work for dimension d= infinity where the local approximation becomes exact. It is shown that the approximate method of paper I of the series may be fitted into the new framework and yields sensible results for the Anderson impurity model. This lends weight to the prediction of I that for paramagnetic solutions of the Hubbard model Fermi liquid behaviour breaks down in a whole region of the T=0 phase diagram, not just for a half-filled band where the Mott transition occurs.