Fermi Liquid Parameters Research Articles

Few cycle pulses in semi-holographic Fermi liquid with impurities

Special aspects of few cycle pulses propagation in semi-holographic Fermi liquid with impurities are considered in this paper. Green’s function poles which are in charge of excitation states dispersion law of the liquid under consideration were given according to the ADS/CFT correspondence. The impact of both Fermi liquid parameters and its impurities on the few cycle pulse shape was defined.

Propagation of few cycle optical pulses in marginal Fermi liquid and ADS/CFT correspondence

Absract The paper considers features of few cycle optical pulse propagation in marginal Fermi liquid. The Green functions whose poles are responsible for the dispersion law excitation states of the liquid have been derived within the framework of ADS/CFT correspondence. Marginal Fermi liquid parameters influence on the pulse shape was defined.

Skyrme interaction to second order in nuclear matter

Based on the phenomenological Skyrme interaction various density-dependent nuclear matter quantities are calculated up to second order in many-body perturbation theory. The spin–orbit term as well as two tensor terms contribute at second order to the energy per particle. The simultaneous calculation of the isotropic Fermi-liquid parameters provides a rigorous check through the validity of the Landau relations. It is found that published results for these second order contributions are incorrect in most cases. In particular, interference terms between s-wave and p-wave components of the interaction can contribute only to (isospin or spin) asymmetry energies. Even with nine adjustable parameters, one does not obtain a good description of the empirical nuclear matter saturation curve in the low density region . The reason for this feature is the too strong density-dependence of several second-order contributions. The inclusion of the density-dependent term is therefore indispensable for a realistic description of nuclear matter in the Skyrme framework.

Fermi-liquid theory for the single-impurity Anderson model

We generalize Nozi\`eres' Fermi-liquid theory for the low-energy behavior of the Kondo model to that of the single-impurity Anderson model. In addition to the electrons' phase shift at the Fermi energy, the low-energy Fermi-liquid theory is characterized by four Fermi-liquid parameters: the two given by Nozi\`eres that enter to first order in the excitation energy, and two additional ones that enter to second order and are needed away from particle-hole symmetry. We express all four parameters in terms of zero-temperature physical observables, namely the local charge and spin susceptibilities and their derivatives with respect to the local level position. We determine these in terms of the bare parameters of the Anderson model using Bethe Ansatz and Numerical Renormalization Group (NRG) calculations. Our low-energy Fermi-liquid theory applies throughout the crossover from the strong-coupling Kondo regime via the mixed-valence regime to the empty-orbital regime. From the Fermi-liquid theory, we determine the conductance through a quantum dot symmetrically coupled to two leads in the regime of small magnetic field, low temperature and small bias voltage, and compute the coefficients of the $\sim B^2$, $\sim T^2$, and $\sim V^2$ terms \textit{exactly} in terms of the Fermi-liquid parameters. The coefficients of $T^2$, $V^2$ and $B^2$ are found to change sign during the Kondo to empty-orbital crossover. The crossover becomes universal in the limit that the local interaction is much larger than the level width. For completeness, we also compute the shot noise and discuss the resulting Fano factor.

Measurements of the anisotropic mass of magnons confined in a harmonic trap in superfluid 3He-B

We can pump magnons to a nearly harmonic magneto-textural trap in superfluid $^3$He-B. Using the NMR spectroscopy of levels in the trap we have measured the anisotropic magnon mass and related values of the spin-wave velocities. Based on our measurements we provide values of the Fermi-liquid parameter $F^a_1$.

Physics input for modelling superfluid neutron stars with hyperon cores

Observations of massive ($M \approx 2.0~M_\odot$) neutron stars (NSs), PSRs J1614-2230 and J0348+0432, rule out most of the models of nucleon-hyperon matter employed in NS simulations. Here we construct three possible models of nucleon-hyperon matter consistent with the existence of $2~M_\odot$ pulsars as well as with semi-empirical nuclear matter parameters at saturation, and semi-empirical hypernuclear data. Our aim is to calculate for these models all the parameters necessary for modelling dynamics of hyperon stars (such as equation of state, adiabatic indices, thermodynamic derivatives, relativistic entrainment matrix, etc.), making them available for a potential user. To this aim a general non-linear hadronic Lagrangian involving $\sigma\omega\rho\phi\sigma^\ast$ meson fields, as well as quartic terms in vector-meson fields, is considered. A universal scheme for calculation of the $\ell=0,1$ Landau Fermi-liquid parameters and relativistic entrainment matrix is formulated in the mean-field approximation. Use of this scheme allow us to obtain numerical tables with the equation of state, Landau quasiparticle effective masses, adiabatic indices, the $\ell=0,1$ Landau Fermi-liquid parameters, and the relativistic entrainment matrix for the selected models of nucleon-hyperon matter. These data are available on-line and suitable for numerical implementation in computer codes modelling various dynamical processes in NSs, in particular, oscillations of superfluid NSs and their cooling.

Quantum Monte Carlo calculation of the Fermi liquid parameters of the two-dimensional homogeneous electron gas

Fermi liquid theory is the basic paradigm within which we understand the normal behavior of interacting electron systems, but quantitative values for the parameters that occur in this theory are currently unknown in many important cases. One such case is the two-dimensional homogeneous electron gas (2D HEG), which is realized in a wide variety of semiconductor devices. We have used quantum Monte Carlo (QMC) methods to calculate the Landau interaction functions between pairs of quasiparticles. We use these to study the Fermi liquid parameters, finding that finite-size effects represent a serious obstacle to the direct determination of Fermi liquid parameters in QMC calculations. We have used QMC data in the literature for other properties of the 2D HEG to assemble a set of "best available" values for the Fermi liquid parameters.

AN EXPLANATION OF SUPERFLUIDITY OF LIQUID 3He

In this paper, we will apply the derived equation of interaction for two quasiparticles in the other paper of ours (J. D. Fan and Y. M. Malozovsky, Int. J. Mod. Phys. B, Vol. 27 No. 15, 2013)1 to the model of a Fermi liquid with a weak contact attractive interaction between 3 He particles. We will show that in terms of the perturbative approach and the random phase approximation (RPA), the evaluated Fermi-liquid interaction parameters are in remarkably good agreement with experimental data on liquid 3 He . Thus, our simple model, in contrast to very complicated and numerically correlated basis function model exploited by Finberg and co-authors [E. Finberg, Theory of Quantum Fluids (Academic Press, New York, 1969)], enables to reproduce the Fermi liquid parameters for liquid 3 He . In addition, using the result we obtained in Ref. 1, we have qualitatively explained superfluidity of 3 He under pressure.

Normal-state properties of spin-orbit-coupled Fermi gases in the upper branch of the energy spectrum

We investigate normal state properties of spin-orbit coupled Fermi gases with repulsive s-wave interaction, in the absence of molecule formation, i.e., in the so-called "upper branch". Within the framework of random phase approximation, we derive analytical expressions for the quasi-particle lifetime $\tau_s$, the effective mass $m_s^*$, and the Green's function renormalization factor $Z_s$ in the presence of Rashba spin-orbit coupling. In contrast to spin-orbit coupled electron gas with Coulomb interaction, we show that the modifications are dependent on the Rashba band index s, and occur in the first order of the spin-orbit coupling strength. We also calculate experimental observable such as spectral weight, density of state and specific heat, which exhibit significant differences from their counterparts without spin-orbit coupling. We expect our microscopic calculations of these Fermi liquid parameters would have the immediate applications to the spin-orbit coupled Fermi gases in the upper branch of the energy spectrum.

Chiral Fermi liquid approach to neutron matter

We present a microscopic calculation of the complete quasiparticle interaction, including central as well as noncentral components, in neutron matter from high-precision two- and three-body forces derived within the framework of chiral effective-field theory. The contributions from two-nucleon forces are computed in many-body perturbation theory to first and second order (without any simplifying approximations). In addition we include the leading-order one-loop diagrams from the next-to next-to leading order (N${}^{2}$LO) chiral three-nucleon force, which contribute to all Fermi liquid parameters except those associated with the center-of-mass tensor interaction. The relative-momentum dependence of the quasiparticle interaction is expanded in Legendre polynomials up to $L=2$. Second-order Pauli blocking and medium polarization effects act coherently in specific channels; namely, for the Landau parameters ${f}_{1}$, ${h}_{0}$, and ${g}_{0}$, which results in a dramatic increase in the quasiparticle effective mass as well as a decrease in both the effective tensor force and the neutron matter spin susceptibility. For densities greater than about half the nuclear matter saturation density ${\ensuremath{\rho}}_{0}$, the contributions to the Fermi liquid parameters from the leading-order chiral three-nucleon force scale in all cases approximately linearly with the nucleon density. The largest effect of the three-nucleon force is to generate a strongly repulsive effective interaction in the isotropic spin-independent channel. We show that the leading-order chiral three-nucleon force leads to an increase in the spin susceptibility of neutron matter, but we observe no evidence for a ferromagnetic spin instability in the vicinity of the saturation density ${\ensuremath{\rho}}_{0}$. This work sets the foundation for future studies of neutron matter response to weak and electromagnetic probes with applications to neutron star structure and evolution.

Benchmark of a modified iterated perturbation theory approach on the fcc lattice at strong coupling

The Dynamical Mean-Field theory (DMFT) approach to the Hubbard model requires a method to solve the problem of a quantum impurity in a bath of non-interacting electrons. Iterated Perturbation Theory (IPT) has proven its effectiveness as a solver in many cases of interest. Based on general principles and on comparisons with an essentially exact Continuous-Time Quantum Monte Carlo (CTQMC) solver, here we show that the standard implementation of IPT fails away from half-filling when the interaction strength is much larger than the bandwidth. We propose a slight modification to the IPT algorithm that replaces one of the equations by the requirement that double occupancy calculated with IPT gives the correct value. We call this method IPT-$D$. We recover the Fermi liquid ground state away from half-filling. The Fermi liquid parameters, density of states, chemical potential, energy and specific heat on the FCC lattice are calculated with both IPT-$D$ and CTQMC as benchmark examples. We also calculated the resistivity and the optical conductivity within IPT-$D$. Particle-hole asymmetry persists even at coupling twice the bandwidth. Several algorithms that speed up the calculations are described in appendices.

Fermi-liquid theory for thin arbitrarily polarized3He films

We study the thermodynamic response, effective masses, and collective excitations for thin (submonolayer) ${}^{3}$He films as a function of density and polarization using Fermi liquid theory. The Landau parameters ${f}^{\ensuremath{\uparrow}\ensuremath{\uparrow}},{f}^{\ensuremath{\uparrow}\ensuremath{\downarrow}},{f}^{\ensuremath{\downarrow}\ensuremath{\downarrow}}$ are obtained to quadratic order in the low-density $s$-wave and $p$-wave $T$-matrix interaction parameters. Values for the effective interaction components are determined by fitting zero-polarization experimental data for the cases of thin ${}^{3}$He films on graphite and also thin ${}^{3}$He films in surface states of thin superfluid ${}^{4}$He films. By fitting the interaction parameters, we can calculate the Landau parameters to all orders, and we show results for the behavior of ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{F}}_{\ensuremath{\ell}}^{\ensuremath{\uparrow}\ensuremath{\uparrow}}\phantom{\rule{4.pt}{0ex}}\text{for}\phantom{\rule{4.pt}{0ex}}\ensuremath{\ell}\ensuremath{\leqslant}30$. With knowledge of the Landau parameters we calculate the polarization dependence of the state-dependent effective masses, compressibility, spin susceptibility, and zero-sound spectra for the mobile submonolayer range of areal densities. Our results predict a dramatic decrease in the effective masses for ${}^{3}$He on graphite as a function of polarization at higher coverages. At fixed density, the compressibility is shown to decrease monotonically with increasing polarization. At small polarization the inverse spin susceptibility is largest for small density whereas at large polarization it is largest for large density. We show that zero sound will propagate at all densities and polarizations whereas spin zero sound does not propagate in these systems. The condition for thermodynamic stability in an arbitrarily polarized Fermi liquid film is derived and discussed. We show explicitly the Fermi surface distortion due to the presence of a zero-sound mode. A table of predicted values for the zero polarization Fermi liquid parameters ${F}_{0}^{\text{s}}\phantom{\rule{4.pt}{0ex}}\text{and}\phantom{\rule{4.pt}{0ex}}{F}_{1}^{\text{a}}$ is provided.

D-wave superfluid with gapless edges in a cold-atom trap

We consider a strongly repulsive fermionic gas in a two-dimensional optical lattice confined by a harmonic trapping potential. To address the strongly repulsive regime, we consider the $t\ensuremath{-}J$ Hamiltonian. The presence of the harmonic trapping potential enables the stabilization of coexisting and competing phases. In particular, at low temperatures, this allows the realization of a $d$-wave superfluid region surrounded by purely (gapless) normal edges. Solving the Bogoliubov--de Gennes equations and comparing them with the local density approximation, we show that the proximity to the Mott insulator is revealed by a downturn of the Fermi liquid order parameter at the center of the trap where the $d$-wave gap has a maximum. The density profile evolves linearly with distance.

1/(N-1) expansion for a finite-UAnderson model away from half-filling

We apply recently developed $1/(N\ensuremath{-}1)$ expansion to a particle-hole asymmetric SU($N$) Anderson model with finite Coulomb interaction $U$. To leading order in $1/(N\ensuremath{-}1)$ it describes the Hartree-Fock random-phase approximation (HF-RPA), and the higher-order corrections describe systematically the fluctuations beyond the HF-RPA. We show that the next-leading-order results of the renormalized parameters for the local Fermi-liquid state agree closely with the numerical renormalization group results at $N=4$. This ensures the reliability of the next-leading-order results for $N\ensuremath{\geqslant}4$, and we examine the $N$ dependence of the local Fermi-liquid parameters. Our expansion scheme uses the standard Feynman diagrams and has wide potential applications.

Landau parameters for asymmetric nuclear matter with a strong magnetic field

The Landau Fermi-liquid parameters are calculated for charge-neutral asymmetric nuclear matter in beta equilibrium at zero temperature in the presence of a very strong magnetic field with relativistic mean-field models. Due to the isospin structure of the system, with different populations of protons and neutrons and spin alignment to the field, we find nonvanishing Landau mixing parameters. The existence of quantized Landau levels for the charged sector has some impact on the Landau parameters with the presence of discretized features in those involving the proton sector. Using the Fermi-liquid formalism singlet and triplet excited quasiparticle states are analyzed, and we find that in-medium effects and magnetic fields are competing; however, the former are more important in the interaction energy range considered. It is found that for magnetic field strengths ${\mathrm{log}}_{10}B(G)\ensuremath{\le}17$ the relatively low polarization of the system produces mild changes in the generalized Landau parameters with respect to the unmagnetized case, while for larger strengths there is a resolution of the degeneracy of the interaction energies of quasiparticles in the system. As an application we calculate the incompressibility and first sound velocities to illustrate how this formalism can be used to obtain physical information from the system.

Second-order quasiparticle interaction in nuclear matter with chiral two-nucleon interactions

We employ Landau's theory of normal Fermi liquids to study the quasiparticle interaction in nuclear matter in the vicinity of saturation density. Realistic low-momentum nucleon-nucleon interactions evolved from the Idaho N3LO chiral two-body potential are used as input potentials. We derive for the first time exact results for the central part of the quasiparticle interaction computed to second order in perturbation theory, from which we extract the L=0 and L=1 Landau parameters as well as some relevant bulk equilibrium properties of nuclear matter. The accuracy of the intricate numerical calculations is tested with analytical results derived for scalar-isoscalar boson exchange and (modified) pion exchange at second order. The explicit dependence of the Fermi liquid parameters on the low-momentum cutoff scale is studied, which provides important insight into the scale variation of phase-shift equivalent two-body potentials. This leads naturally to explore the role that three-nucleon forces must play in the effective interaction between two quasiparticles.

Fermi liquid description of relativistic high density matter

We calculate pionic contribution to the relativistic Fermi Liquid parameters (RFLPs) using Chiral Effective Lagrangian. The RFLPs so determined are then used to calculate chemical potential, exchange energy due to πN interaction. We also compare the results of exchange energy from two loop ring diagrams involving σ, ω and π meson with what one obtains from the relativistic Fermi Liquid theory (RFLT).

Thermodynamics of the unitary Fermi gas

The understanding of quantum many-body systems is one of the most daunting challenges of modern physics. Thanks to recent progress in cooling and trapping techniques, it is now possible to investigate their properties in the well controlled environment of ultra-cold gas systems. In this article, we present experimental results on the thermodynamics of strongly correlated Fermi gases and we provide a reinterpretation of the equation of state of a strongly polarized Fermi gas in terms of Fermi liquid parameters

Extended Hubbard model: Charge ordering and Wigner-Mott transition

Strong correlation effects, which are often associated to the approach to a Mott insulating state, in some cases may be observed even far from half-filling. This typically happens whenever the inter-site Coulomb repulsion induces a tendency towards charge ordering, an effect that confines the electrons, and in turn favors local moment formation, i.e. Mott localization. A distinct intermediate regime then emerges as a precursor of such a Wigner-Mott transition, which is characterized by both charge and spin correlations, displaying large mass enhancements and strong renormalizations of other Fermi liquid parameters. Here we present a careful study of a quarter filled extended Hubbard model - a simple example where such physics can be studied in detail, and discuss its relevance for the understanding of the phenomenology of low-density two dimensional electron gases.

Pionic contribution to relativistic Fermi liquid parameters

We calculate pionic contribution to the relativistic Fermi liquid parameters (RFLPs) using a chiral effective Lagrangian. The RFLPs so determined are then used to calculate chemical potential, exchange and nuclear symmetry energies due to πN interaction. We also evaluate two loop ring diagrams involving σ, ω, and π meson exchanges and compare results with what one obtains from the relativistic Fermi liquid theory (RFLT).