He 3 -He 4 solutions and other low-density Fermi liquids in a magnetic field

Subhro Bhattacharjee, Sung-Sik Lee, Yong Baek Kim

V. M. Pudalov, A. Yu. Kuntsevich, M. E. Gershenson +2 more

We report temperature and density dependences of the spin susceptibility of strongly interacting electrons in Si inversion layers. We measured (i) the itinerant electron susceptibility ${\ensuremath{\chi}}^{*}$ from the Shubnikov-de Haas oscillations in crossed magnetic fields and (ii) thermodynamic susceptibility ${\ensuremath{\chi}}_{\mathrm{T}}$ sensitive to all the electrons in the layer. Both ${\ensuremath{\chi}}^{*}$ and ${\ensuremath{\chi}}_{\mathrm{T}}$ are strongly enhanced with lowering the electron density in the metallic phase. However, there is no sign of divergency of either quantity at the density of the metal-insulator transition ${n}_{c}$. Moreover, the value of ${\ensuremath{\chi}}_{\mathrm{T}}$, which can be measured across the transition down to very low densities deep in the insulating phase, increases with density at $n<{n}_{c}$, as expected. In the absence of magnetic field, we found the temperature dependence of ${\ensuremath{\chi}}^{*}$ to be consistent with Fermi-liquid-based predictions, and to be much weaker than the power law predicted by non-Fermi-liquid models. We attribute a much stronger temperature dependence of ${\ensuremath{\chi}}_{\mathrm{T}}$ to localized spin droplets. In strong enough in-plane magnetic field, we found the temperature dependence of ${\ensuremath{\chi}}^{*}$ to be stronger than that expected for the Fermi liquid interaction corrections.

Stanislav Z. Dunin, E. P. Fetisov

Xiao-Gang Wen

In this paper, we study gapless fermionic and bosonic systems in $d$-dimensional continuum space with $U(1)$ particle-number-conservation and ${\mathbb{R}}^{d}$ translation symmetry. We present low-energy effective field theories for several gapless phases with the $U(1)\ifmmode\times\else\texttimes\fi{}{\mathbb{R}}^{d}$ symmetry. The $U(1)\ifmmode\times\else\texttimes\fi{}{\mathbb{R}}^{d}$ symmetry has a property that a $U(1)$ symmetry twist will induce a nonzero momentum proportional to the $U(1)$ charge density $\overline{\ensuremath{\rho}}$, which will be referred to as a mixed anomaly. The different effective field theories for different phases of the same system must have the same mixed anomaly. As a result, all the low-energy effective field theories must have fields with nonzero momenta of the order of ${\overline{\ensuremath{\rho}}}^{1/d}$. In particular, we present a low-energy effective field theory with infinite number of fields for Fermi liquid. We also present the Fermi-liquid effective field theory in the presence of a real space magnetic field and $\mathbit{k}$-space ``magnetic'' field, as well as in the presence of interaction described by Landau parameters. Our effective field theory correctly captures the mixed anomaly, which constrains the low-energy dynamics, such as determines the volume of the Fermi surface in terms of the mixed anomaly [i.e., in terms of the $U(1)$ charge density]. This is another formulation of the Luttinger-Ward-Oshikawa theorem.

Michele Filippone, Cătălin Paşcu Moca, Andreas Weichselbaum +2 more

This paper is a corrected version of Phys. Rev. B 95, 165404 (2017), which we have retracted because it contained a trivial but fatal sign error that lead to incorrect conclusions. We extend a recently developed Fermi liquid (FL) theory for the asymmetric single-impurity Anderson model [C. Mora et al., Phys. Rev. B 92, 075120 (2015)] to the case of an arbitrary local magnetic field. To describe the system's low-lying quasiparticle excitations for arbitrary values of the bare Hamiltonian's model parameters, we construct an effective low-energy FL Hamiltonian whose FL parameters are expressed in terms of the local level's spin-dependent ground-state occupations and their derivatives with respect to level energy and local magnetic field. These quantities are calculable with excellent accuracy from the Bethe ansatz solution of the Anderson model. Applying this effective model to a quantum dot in a nonequilibrium setting, we obtain exact results for the curvature of the spectral function, ${c}_{A}$, describing its leading $\ensuremath{\sim}{\ensuremath{\varepsilon}}^{2}$ term, and the transport coefficients ${c}_{V}$ and ${c}_{T}$, describing the leading $\ensuremath{\sim}{V}^{2}$ and $\ensuremath{\sim}{T}^{2}$ terms in the nonlinear differential conductance. A sign change in ${c}_{A}$ or ${c}_{V}$ is indicative of a change from a local maximum to a local minimum in the spectral function or nonlinear conductance, respectively, as is expected to occur when an increasing magnetic field causes the Kondo resonance to split into two subpeaks. We find that the fields ${B}_{A}$, ${B}_{T}$, and ${B}_{V}$ at which ${c}_{A}$, ${c}_{T}$, and ${c}_{V}$ change sign, respectively, are all of order ${T}_{K}$, as expected, with ${B}_{A}={B}_{T}={B}_{V}=0.75073{T}_{K}$ in the Kondo limit.

D. ter Haar