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arXiv:1312.6765 · Physical Review A

Theory of SU(N) Fermi liquids

Sungkit Yip, Bor-Luen Huang, Jung-Shen Kao

Published Apr 15, 2014• 26 citations
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Abstract

We generalize the Fermi-liquid theory to $N$ component systems with $\mathrm{SU}(N)$ symmetry. We evaluate the Fermi-liquid parameters, effective mass, compressibility, and spin susceptibilities for a repulsive gas. We emphasize the important role of induced density fluctuations when $N$ is large. These fluctuations dramatically modify the properties of the gas, in particular the spin susceptibilities, from mean-field predictions.

DOI
10.1103/physreva.89.043610

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1. Introduce density distribution and momentum distribution of non-interacting Fermi gas. 2. Discuss the transport property of a Fermi gas through a quantum point contact. 3. Discuss Fermi surface as a key of a non-interacting Fermi gas and its generalization to a Fermi liquid. 4. Introduce the effective mass and the quasi-particle residue as two key parameters of the Fermi liquid. 5. Introduce the self-energy and the universal relations between the effective mass, the quasi-particle residue and the self-energy. 6. Discuss Fermi polaron as an example of the Fermi liquid, and show these universal relations with this example. 7. Discuss the divergence of the effective mass and vanishing of quasi-particle residue when Fermi liquid description fails. 8. Introduce the radio-frequency spectroscopy and how it measures the polaron energy and the quasi-particle residue. 9. Summarize different spectroscopy measurements in ultracold atomic systems.
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We study the thermodynamic response, effective masses, and collective excitations for thin (submonolayer) 3{}^{3}3He 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 sss-wave and ppp-wave TTT-matrix interaction parameters. Values for the effective interaction components are determined by fitting zero-polarization experimental data for the cases of thin 3{}^{3}3He films on graphite and also thin 3{}^{3}3He films in surface states of thin superfluid 4{}^{4}4He 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{}^{3}3He 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 F0sandF1a{F}_{0}^{\text{s}}\phantom{\rule{4.pt}{0ex}}\text{and}\phantom{\rule{4.pt}{0ex}}{F}_{1}^{\text{a}}F0s​andF1a​ is provided.