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Register a new userPacifying the Fermi-liquid: battling the devious fermion signs
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The fermion sign problem is studied in the path integral formalism. The standard picture of Fermi liquids is first critically analyzed, pointing out some of its rather peculiar properties. The insightful work of Ceperley in constructing fermionic path integrals in terms of constrained world-lines is then reviewed. In this representation, the minus signs associated with Fermi-Dirac statistics are self consistently translated into a geometrical constraint structure (the {em nodal hypersurface}) acting on an effective bosonic dynamics. As an illustrative example we use this formalism to study 1+1-dimensional systems, where statistics are irrelevant, and hence the sign problem can be circumvented. In this low-dimensional example, the structure of the nodal constraints leads to a lucid picture of the entropic interaction essential to one-dimensional physics. Working with the path integral in momentum space, we then show that the Fermi gas can be understood by analogy to a Mott insulator in a harmonic trap. Going back to real space, we discuss the topological properties of the nodal cells, and suggest a new holographic conjecture relating Fermi liquids in higher dimensions to soft-core bosons in one dimension. We also discuss some possible connections between mixed Bose/Fermi systems and supersymmetry.
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We study the acoustic attenuation rate in the Fermi-Bose model describing a mixtures of bosonic and fermionic atom gases. We demonstrate the dramatic change of the acoustic attenuation rate as the fermionic component is evolved through the BEC-BCS crossover, in the context of a mean-field model applied to a finite-range fermion-fermion interaction at zero temperature, such as discussed previously by M.M. Parish et al. [Phys. Rev. B 71, 064513 (2005)] and B. Mihaila et al. [Phys. Rev. Lett. 95, 090402 (2005)]. The shape of the acoustic attenuation rate as a function of the boson energy represents a signature for superfluidity in the fermionic component.
We calculate expressions for the state-dependent quasiparticle lifetime, the thermal conductivity $kappa$, the shear viscosity $eta$, and discuss the spin diffusion coefficient $D$ for Fermi-liquid films in two dimensions. The expressions are valid for low temperatures and arbitrary polarization. The low-temperature expressions for the transport coefficients are essentially exact. We find that $kappa^{-1} sim T ln{T}$, and $eta^{-1} sim T^{2}$ for arbitrary polarizations $0 le {mathcal{P}} le 1$. We note that the shear viscosity requires a unique analysis. We utilize previously determined values for the density and polarization dependent Landau parameters to calculate the transition probabilities in the lowest order $ell = 0$ approximation, and thus we obtain predictions for the density, temperature and polarization dependence of the thermal conductivity, shear viscosity, and spin diffusion coefficient for thin he3 films. Results are shown for second layer he3 films on graphite, and thin he3-he4 superfluid mixtures. The density dependence is discussed in detail. For $kappa$ and $eta$ we find roughly an order of magnitude increase in magnitude from zero to full polarization. For $D$ a simialr large increase is predicted from zero polarization to the polarization where $D$ is a maximum ($sim 0.74$). We discuss the applicability of he3 thin films to the question of the existence of a universal lower bound for the ratio of the shear viscosity to the entropy density.
The fermion sign problem is often viewed as a sheer inconvenience that plagues numerical studies of strongly interacting electron systems. Only recently, it has been suggested that fermion signs are fundamental for the universal behavior of critical metallic systems and crucially enhance their degree of quantum entanglement. In this work we explore potential connections between emergent scale invariance of fermion sign structures and scaling properties of bipartite entanglement entropies. Our analysis is based on a wavefunction ansatz that incorporates collective, long-range backflow correlations into fermionic Slater determinants. Such wavefunctions mimic the collapse of a Fermi liquid at a quantum critical point. Their nodal surfaces -- a representation of the fermion sign structure in many-particle configurations space -- show fractal behavior up to a length scale $xi$ that diverges at a critical backflow strength. We show that the Hausdorff dimension of the fractal nodal surface depends on $xi$, the number of fermions and the exponent of the backflow. For the same wavefunctions we numerically calculate the second Renyi entanglement entropy $S_2$. Our results show a cross-over from volume scaling, $S_2sim ell^theta$ ($theta=2$ in $d=2$ dimensions), to the characteristic Fermi-liquid behavior $S_2sim ellln ell$ on scales larger than $xi$. We find that volume scaling of the entanglement entropy is a robust feature of critical backflow fermions, independent of the backflow exponent and hence the fractal dimension of the scale invariant sign structure.
Heavy electron metals on the verge of a quantum phase transition to magnetism show a number of unusual non-fermi liquid properties which are poorly understood. This article discusses in a general way various theoretical aspects of this phase transition with an eye toward understanding the non-fermi liquid phenomena. We suggest that the non-Fermi liquid quantum critical state may have a sharp Fermi surface with power law quasiparticles but with a volume not set by the usual Luttinger rule. We also discuss the possibility that the electronic structure change associated with the possible Fermi surface reconstruction may diverge at a different time/length scale from that associated with magnetic phenomena.
Strong electron correlations can give rise to extraordinary properties of metals with renormalized quasiparticles which are at the basis of Landaus Fermi liquid theory. Near a quantum critical point, these quasiparticles can be destroyed and non-Fermi liquid behavior ensues. YbRh$_2$Si$_2$ is a prototypical correlated metal as it exhibits quasiparticles formation, formation of Kondo lattice coherence and quasiparticle destruction at a field-induced quantum critical point. Here we show how, upon lowering the temperature, the Kondo lattice coherence develops and finally gives way to non-Fermi liquid electronic excitations. By measuring the single-particle excitations through scanning tunneling spectroscopy down to 0.3 K, we find the Kondo lattice peak emerging below the Kondo temperature $T_{rm K} sim$ 25 K, yet this peak displays a non-trivial temperature dependence with a strong increase around 3.3 K. At the lowest temperature and as a function of an external magnetic field, the width of this peak is minimized in the quantum critical regime. Our results provide a striking demonstration of the non-Fermi liquid electronic excitations in quantum critical metals, thereby elucidating the strange-metal phenomena that have been ubiquitously observed in strongly correlated electron materials.
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