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arXiv:cond-mat/9602154 · Physical review. B, Condensed matter

Fermi-liquid-to-polaron crossover. I. General results

Andrew J. Millis, R. Mueller, Boris I. Shraiman

Published Aug 15, 1996• 239 citations
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Abstract

We use analytic techniques and the dynamical mean-field method to study the crossover from Fermi liquid to polaron behavior in models of electrons interacting with dispersionless classical phonons. \textcopyright{} 1996 The American Physical Society.
DOI
10.1103/physrevb.54.5389

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We study theoretically the lifetimes of attractive and repulsive Fermi polarons, as well as the molecule at finite momentum in three dimensions. To this end, we develop a technique that allows for the computation of Green's functions in the whole complex frequency plane using exact analytical continuation within the functional renormalization group. The improved numerical stability and reduced computational cost of this method yield access to previously inaccessible momentum-dependent quasiparticle properties of low-lying excited states. While conventional approaches like the non-self-consistent T -matrix approximation method cannot determine these lifetimes, we are able to find the momentum-dependent lifetime at different interaction strengths of both the attractive and repulsive polaron as well as the molecule. At weak coupling our results confirm predictions made from effective Fermi liquid theory regarding the decay of the attractive polaron, and we demonstrate that Fermi liquidlike behavior extends far into the strong-coupling regime where the attractive polaron and molecule exhibit a p 4 momentum scaling in their decay widths. Our results offer an intriguing insight into the momentum-dependent quasiparticle properties of the Fermi polaron problem, which can be measured using techniques such as Raman transfer and Ramsey interferometry. Published by the American Physical Society 2024
It has been claimed that an impurity hopping between two sites in a metal can lead to non-Fermi-liquid behavior if the bias between the two sites is tuned to zero. Here it is shown that several extra tunneling processes are allowed; those involving bare impurity tunneling as well as two-electron-assisted tunneling play important roles. These terms generally drive the system away from the intermediate-coupling non-Fermi-liquid fixed point, which has the character of the two-channel Kondo problem. In order to find the non-Fermi-liquid behavior a combination of these terms must be small over a range of energy scales. The prospects for obtaining these conditions are studied by analyzing both the weak-coupling and the intermediate-coupling behavior, together with the connecting crossover region. Unfortunately, the conclusions are rather pessimistic. The phase diagram and the important crossover are analyzed via bosonization and refermionization and some of the results compared to those obtained from conformal field theory. Finally, an additional non-Fermi-liquid fixed point is found, a multicritical point with two relevant directions even in the unbiased case. \textcopyright{} 1996 The American Physical Society.