Pair Excitations and Vertex Corrections in Fermi Fluids

Based on an equations--of--motion approach for time--dependent pair correlations in strongly interacting Fermi liquids, we have developed a theory for describing the excitation spectrum of these systems. Compared to the known ``correlated'' random--phase approximation (CRPA), our approach has the following properties: i) The CRPA is reproduced when pair fluctuations are neglected. ii) The first two energy--weighted sumrules are fulfilled implying a correct static structure. iii) No ad--hoc assumptions for the effective mass are needed to reproduce the experimental dispersion of the roton in 3He. iv) The density response function displays a novel form, arising from vertex corrections in the proper polarisation. Our theory is presented here with special emphasis on this latter point. We have also extended the approach to the single particle self-energy and included pair fluctuations in the same way. The theory provides a diagrammatic superset of the familiar GW approximation. It aims at a consistent calculation of single particle excitations with an accuracy that has previously only been achieved for impurities in Bose liquids.Comment: to be published in: JLTP (2007) Proc. Int. Symp. QFS2006, 1-6 Aug. 2006, Kyoto, Japa

Two-Dimensional 3He: A Crucial System for Understanding Fermion Dynamics

International audienceNeutron scattering measurements at the Institut Laue-Langevin off quasi-twodimensional 3He have shown, for the first time, a situation where the collective mode crosses the particle-hole continuum and reappears, at a momentum transfer of q≈ 1.55 ˚A−1 as a well-defined collective excitation. The effect is well described by the Fermion generalization of multi-particle fluctuation theory of Jackson, Feenberg, and Campbell that has been so successful for bosonic quantum fluids. We describe the theory briefly and state that it can be mapped onto the form of time dépendent Hartree-Fock theory (TDHF)containing energy dépendent effective interactions; these are obtained from microscopic ground state theory. Our theoretical result has far-reaching consequences: a popular paradigm in discussing the density-density response function of Fermi systems is the "random phase approximation" (RPA), most frequently applied with some static interaction and, perhaps, some effective mass. Such a "phenomenologically modified" RPA can be justified only under severe simplifying approximations and is unable to describe the experimental situation consistently. As soon as one goes beyond the RPA, intermediate states which cannot be described in terms of the quantum numbers of a single (quasi-)particle become essential for capturing the correct physics. In oder to understand the above mentioned experiment, their appropriate inclusion, as presented in this work, is essential

Observation of zero-sound at atomic wave-vectors in a monolayer of liquid 3He

International audienceThe elementary excitations of a strongly interacting two-dimensional Fermi liquid have been investigated by inelastic neutron scattering in an experimental model system: a monolayer of liquid3He adsorbed on graphite preplated by a monolayer of solid 4He. We observed for the first time the particle-hole excitations characterizing the Fermi liquid state of two-dimensional liquid 3He, and we were also able to identify the highly interesting zero-sound collective mode above a particle-hole band. Contrarily to bulk 3He, at low wave-vectors this mode lies very close to the particle-hole band. At intermediate wave-vectors, the collective mode enters the particle-hole band, where it is strongly broadened by Landau damping. At high wave-vectors, where the Landau theory is not applicable, the zero-sound collective mode reappears beyond the particle hole band as a well defined excitation, with a dispersion relation quite similar to that of superfluid 4He. This spectacular effect is observed for the first time in a Fermi liquid (including plasmons excitations in electronic systems)

Pair excitations and vertex corrections in Fermi fluids and the dynamic structure function of two-dimensional 3He

International audienceWe use the equations-of-motion approach for time-dependent pair correlations in strongly interacting Fermiliquidsto develop a theory of the excitation spectrum and the single-particle self energy in such systems. We present here the fully correlated équations and their approximate solutions for3He. Our theory has the following properties: It reduces to both, i) the "correlated" random-phase approximation (RPA) for strongly interacting fermions if the two-particle-two-hole correlations are ignored, and, ii) to the correlated Brillouin-Wigner perturbation theory for boson quantum fluids in the appropriate limit. iii) It preserves the two firstenergy-weighted sum rules,and systematically improves upon higher ones. iv) A familiar problem of the standard RPA is that it predicts a roton energy that lies more than a factor of two higher than what is found in experiments. A popular cure for this is to introduce an effective mass in the Lindhard function. No such ad-hoc assumption is invoked in our work. We demonstrate that the inclusion of correlated pair-excitations improves the dispersion relation significantly. Finally, a novel form of the density response function is derived that arises from vertex corrections in the proper polarization

Reemergence of the collective mode in 3He and electron layers

International audienceNeutron scattering experiments on a3Helayer ongraphite show an unexpected behavior of the collective mode. After having been broadened by Landau damping at intermediate wave vectors, the phonon-roton mode resharpens at large wave vectors and even emerges from the particle-hole continuum at low energies. The measured spectra cannot be explained by a random phase approximation with any static interaction. We show here that the data are well described if dynamic two-pair fluctuations are accounted for. We predict similar effects for electron layers

Roton collective mode observed in a two-dimensional Fermi liquid

International audienceUnderstanding the dynamics of correlated many-body quantum systems has been a challenge for modern physics. Due to the simplicity of their Hamiltonian, 4He (bosons) and 3He (fermions) have served as paradigm for strongly interacting quantum fluids. For this reason, substantial efforts have been devoted to their understanding. An important milestone was the direct observation of the collective "phonon-roton" mode in liquid 4He by neutron scattering, verifying Landau's prediction and his fruitful concept of elementary excitations. In a Fermi system, collective density fluctuations ("zero-sound" in 3He, "plasmons" in charged systems) as well as incoherent particle-hole (PH) excitations are observed. At small wave-vectors and energies, both types of excitations are described by Landau's theory of Fermi liquids. At higher wavevectors, the collective mode enters the PH band, where it is strongly damped. The dynamics of Fermi liquids at high wave-vectors was thus believed to be essentially incoherent. We report here the first observation of a roton-like excitation in a Fermi liquid, obtained in a monolayer of liquid 3He, studied by inelastic neutron scattering. We find that the collective density mode reappears as a well-defined excitation at momentum transfers larger than twice the Fermi momentum. We thus observe unexpected collective behaviour of a Fermi many-body system in the region outside the scope of Landau's theory. A satisfactory interpretation of the measured spectra is obtained within a novel dynamic many-body theory

Dynamic Many-Body Theory. II. Dynamics of Strongly Correlated Fermi Fluids

We develop a systematic theory of multi-particle excitations in strongly interacting Fermi systems. Our work is the generalization of the time-honored work by Jackson, Feenberg, and Campbell for bosons, that provides, in its most advanced implementation, quantitative predictions for the dynamic structure function in the whole experimentally accessible energy/momentum regime. Our view is that the same physical effects -- namely fluctuations of the wave function at an atomic length scale -- are responsible for the correct energetics of the excitations in both Bose and Fermi fluids. Besides a comprehensive derivation of the fermion version of the theory and discussion of the approximations made, we present results for homogeneous He-3 and electrons in three dimensions. We find indeed a significant lowering of the zero sound mode in He-3 and a broadening of the collective mode due to the coupling to particle-hole excitations in good agreement with experiments. The most visible effect in electronic systems is the appearance of a ``double-plasmon'' excitation.Comment: submitted to Phys. Rev.

Cutting edges at random in large recursive trees

We comment on old and new results related to the destruction of a random recursive tree (RRT), in which its edges are cut one after the other in a uniform random order. In particular, we study the number of steps needed to isolate or disconnect certain distinguished vertices when the size of the tree tends to infinity. New probabilistic explanations are given in terms of the so-called cut-tree and the tree of component sizes, which both encode different aspects of the destruction process. Finally, we establish the connection to Bernoulli bond percolation on large RRT's and present recent results on the cluster sizes in the supercritical regime.Comment: 29 pages, 3 figure