Thermodynamics of a Fermi Liquid beyond the Low-Energy Limit (original) (raw)
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Physical Review B, 2006
We revisit the issue of the leading nonanalytic corrections to the temperature dependence of the specific heat coefficient, γ(T ) = C(T )/T, for a system of interacting fermions in three dimensions. We show that the leading temperature dependence of the specific heat coefficient γ(T ) − γ(0) ∝ T 3 ln T comes from two physically distinct processes. The first process involves a thermal excitation of a single particle-hole pair, whose components interact via a nonanalytic dynamic vertex. The second process involves an excitation of three particle-hole pairs which interact via the analytic static fixed-point vertex. We show that the single-pair contribution is expressed via the backscattering amplitude of quasiparticles at the Fermi surface. The three-pair contribution does not have a simple expression in terms of scattering in particular directions. We clarify the relation between these results and previous literature on both 3D and 2D systems, and discuss the relation between the nonanalyticities in γ and those in spin susceptibilities.
Marginal Fermi liquid behavior from 2d Coulomb interaction
A full, nonperturbative renormalization group analysis of interacting electrons in a graphite layer is performed, in order to investigate the deviations from Fermi liquid theory that have been observed in the experimental measures of a linear quasiparticle decay rate in graphite. The electrons are coupled through Coulomb interactions, which remain unscreened due to the semimetallic character of the layer. We show that the model flows towards the noninteracting fixed-point for the whole range of couplings, with logarithmic corrections which signal the marginal character of the interaction separating Fermi liquid and non-Fermi liquid regimes. 71.27.+a, 73.20.Dx, 05.30.Fk During recent years there has been important progress in understanding the properties of quantum electron liquids in dimension D < 3. One of the most fruitful approaches in this respect springs from the use of renormalization group (RG) methods, in which the different liquids are characterized by several fixed-points controlling the low-energy properties. The Landau theory of the Fermi liquid in dimension D > 1 can be taken as a paradigm of the success of this program. It has been shown that, at least in the continuum limit, a system with isotropic Fermi surface and regular interactions is susceptible of developing a fixed-point in which the interaction remains stable in the infrared 1 .
Marginal-Fermi-liquid behavior from two-dimensional Coulomb interaction
Physical Review B, 1999
A full, nonperturbative renormalization group analysis of interacting electrons in a graphite layer is performed, in order to investigate the deviations from Fermi liquid theory that have been observed in the experimental measures of a linear quasiparticle decay rate in graphite. The electrons are coupled through Coulomb interactions, which remain unscreened due to the semimetallic character of the layer. We show that the model flows towards the noninteracting fixed-point for the whole range of couplings, with logarithmic corrections which signal the marginal character of the interaction separating Fermi liquid and non-Fermi liquid regimes. 71.27.+a, 73.20.Dx, 05.30.Fk During recent years there has been important progress in understanding the properties of quantum electron liquids in dimension D < 3. One of the most fruitful approaches in this respect springs from the use of renormalization group (RG) methods, in which the different liquids are characterized by several fixed-points controlling the low-energy properties. The Landau theory of the Fermi liquid in dimension D > 1 can be taken as a paradigm of the success of this program. It has been shown that, at least in the continuum limit, a system with isotropic Fermi surface and regular interactions is susceptible of developing a fixed-point in which the interaction remains stable in the infrared 1 .
Lack of thermalisation in a Fermi liquid
We study an interaction quench in a three-dimensional Fermi gas. We first show that the perturbative expansion of the long-wavelength structure factor S(q) is not compatible with the hypothesis that steady-state averages correspond to thermal ones. In particular, S(q) remains non-analytic at q → 0, signaling a power-law decay of correlation functions in real space instead of the finitetemperature exponential one. We next consider the case of a dilute gas, where one can obtain non-perturbative results in the interaction strength but at lowest order in the density. We find that in the steady-state the momentum distribution jump at the Fermi surface remains finite, though smaller than in equilibrium, up to second order in kF f0, where f0 is the scattering length of two particles in the vacuum. Both results question the emergence of a finite length scale in the unitary quench-dynamics as expected by thermalisation. PACS numbers: 71.10.-w, 05.30.Fk, 05.70.Ln
Absence of thermalization in a Fermi liquid
Physical Review B, 2014
We study an interaction quench in a three-dimensional Fermi gas. We first show that the perturbative expansion of the long-wavelength structure factor S(q) is not compatible with the hypothesis that steady-state averages correspond to thermal ones. In particular, S(q) remains non-analytic at q → 0, signaling a power-law decay of correlation functions in real space instead of the finitetemperature exponential one. We next consider the case of a dilute gas, where one can obtain non-perturbative results in the interaction strength but at lowest order in the density. We find that in the steady-state the momentum distribution jump at the Fermi surface remains finite, though smaller than in equilibrium, up to second order in kF f0, where f0 is the scattering length of two particles in the vacuum. Both results question the emergence of a finite length scale in the unitary quench-dynamics as expected by thermalisation. PACS numbers: 71.10.-w, 05.30.Fk, 05.70.Ln
Journal of Superconductivity and Novel Magnetism
We investigate the effects of exchange and correlation on the quasiparticle properties such as the self-energy, the manybody effective mass and the renormalization constant in a two-dimensional system of ultracold dipolar fermions with dipole moments aligned in the perpendicular direction to the plane. We use the G 0 W approximation along with the generalized random phase approximation, where the many-body effects have been incorporated in the effective interaction W through the Hubbard local-field factor. The many-body effective mass and the renormalization constant are reduced with the increase of coupling strength. We also study the effect of dipole-dipole interaction on the single-particle spectral function of the two dimensional dipolar Fermi liquid. We observe composite hole-zero sound excitation which is a bound state of quasiparticles with the collective mode (i.e. zero-sound) at intermediate and high coupling constants. These composite excitations are undamped at small wave vectors. Due to repulsion between quasiparticle and composite excitation resonances, we find a gap-like feature between quasiparticle and composite excitation dispersions at long wavelengths. Keywords Dipolar Fermi liquid • G 0 W • Effective mass • Renormalization constant • Spectral function • Composite quasiparticles 1 Introduction Ultracold atomic gases are classified as a member of relatively strongly correlated systems due to their longrange and anisotropic interactions [1, 2]. They have many interesting applications in chemical reactions, quantum information and novel quantum phase transitions [3-6]. Instabilities occur in dipolar quantum gases when interactions are sufficiently strong and attractive [7-9]. The long-range interaction leads to the emergence of a variety of quantum phases [2, 10, 11]. The many-body B.
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1995
Proceeding from the simplest field theoretical model of 2D metal, the normal phase Green functions of the weakly interacting fermions and the order parameter fluctuations (responsible for the attraction between fermions) are obtained. It is shown that taking into consideration the fluctuations mentioned leads to a considerable reduction of the fermion wave function renormalization constant (quasiparticle weight) as well as to a linear dependence of the quasiparticle damping on the temperature. A general dependence of 2D Fermi liquid properties on the fermion density is discussed. The relevance of the proposed model to the marginal behavior of the Fermi liquid of high-T c superconductors, in particular, to their linear temperature dependence of the resistivity is indicated.
A theory of marginal fermi-liquids
Physica C: Superconductivity, 1991
We propose a microscopic justification for the recently proposed "marginal Fermi-liquid" (MFL) phenomenology of the high Te materials. In some models, and for sufficiently strong interactions, excitonic charge and spin modes between quasi-coherent one-particle states at the chemical potential and high-energy incoherent one-particle states which are the residual of the Hubbard bands of the insulating phase gives rise to singularities in certain low energy scattering amplitudes. The resulting new phase has the MFL polarizabilities. The one-particle spectrum near the chemical potential is predicted to be the sum of the quasi-coherent MFL spectrum and of an incoherent contribution.