Non-Analytic Crossover Behavior of SU(${\mathcal{N}}_c$) Fermi Liquid

Abstract

We consider the thermodynamic potential of a dilute Fermi gas with a contact interaction, at both finite temperature $T$ and non-zero effective magnetic fields $\mathbf{H}$, and derive the equation of state analytically using second order perturbation theory. Special attention is paid to the non-analytic dependence of $\Omega$ on temperature $T$ and (effective) magnetic field $\mathbf{H}$, which exhibits a crossover behavior as the ratio of the two is continuously varied. This non-analyticity is due to the particle-hole pair excitation being always gapless and long-ranged. The non-analytic crossover found in this paper can therefore be understood as an analog of the Ginzberg-Landau critical scaling, albeit only at the sub-leading order. We extend our results to an ${\mathcal{N}}_c$- component Fermi gas with an $\mathrm{SU}({\mathcal{N}}_c)$-symmetric interaction, and point out possible enhancement of the crossover behavior by a large ${\mathcal{N}}_c$.

References in corpus (24)

• Feshbach Resonances in Ultracold Gases
• Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas
• The Equation of State of a Low-Temperature Fermi Gas with Tunable Interactions
• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Degenerate Fermi Gases of Ytterbium
• Ultracold Gases of Ytterbium: Ferromagnetism and Mott States in an SU(6) Fermi System
• Influence of Generic Scale Invariance on Classical and Quantum Phase Transitions
• Anisotropy in the electrical resistivity and susceptibility of superconducting BaFe${}_2$As${}_2$ single crystals
• First order transitions and multicritical points in weak itinerant ferromagnets
• Feynman diagrams versus Fermi-gas Feynman emulator
• Degenerate Fermi Gas of ${}^{87}$Sr
• Nonanalytic behavior of the spin susceptibility in clean Fermi systems
• Non-analytic corrections to the Fermi-liquid behavior
• Universal linear-temperature dependence of static magnetic susceptibility in iron-pnictides
• Nonanalytic paramagnetic response of itinerant fermions away and near a ferromagnetic quantum phase transition
• Nonanalytic corrections to the specific heat of a three-dimensional Fermi liquid
• Quantum critical behavior of clean itinerant ferromagnets
• Fit-free determination of scale invariant equations of state: application to the 2D Bose gas across the Berezinksii-Kosterlitz-Thouless transition
• The First Temperature Corrections to the Fermi Liquid Fixed Point in Two Dimensions
• Non-analytic spin susceptibility of a nested Fermi liquid: the case of Fe-based pnictides
• Thermodynamics of a Fermi liquid in a magnetic field
• Thermodynamics of a Fermi liquid beyond the low-energy limit
• Trapped Resonant Fermions above Superfluid Transition Temperature
• SU(N) Fermi liquid at finite temperature

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• Collective modes of ultracold fermionic alkaline-earth gases with SU(N) symmetry
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• Superfluidity in multicomponent fermions via the functional renormalization group