Consequences of Fermi liquid theory close to a divergings-wave scattering length

We derive the thermodynamic properties of a Fermi gas, deep into the quantum degenerate regime. We show that, if Luttinger's theorem holds, a first-order phase transition occurs in the normal phase as a function of the interaction strength. We also show that a volume change occurs at finite temperatures as we go through a divergence in the s-wave scattering length, in the normal phase. The first-order transition has a critical temperature, T *, above the BCS transition temperature. Also, we show that a paramagnetic system in equilibrium, close to the divergence of the scattering length, on the negative side, screens out any applied magnetic field.We derive the thermodynamic properties of a Fermi gas, deep into the quantum degenerate regime. We show that, if Luttinger's theorem holds, a first-order phase transition occurs in the normal phase as a function of the interaction strength. We also show that a volume change occurs at finite temperatures as we go through a divergence in the s-wave scattering length, in the normal phase. The first-order transition has a critical temperature, T *, above the BCS transition temperature. Also, we show that a paramagnetic system in equilibrium, close to the divergence of the scattering length, on the negative side, screens out any applied magnetic field.

arXiv:cond-mat/0703722The Philosophical Magazine A Journal of Theoretical Experimental and Applied PhysicsJun 20, 20092 citations

Light scattering from a fermi liquid

Aurea Rosas Vasconcellos, Roberto Luzzi

Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento BOct 1, 19749 citations

Correlation functions of higher-dimensional Luttinger liquids

Lorenz Bartosch, Peter Kopietz

Using higher-dimensional bosonization we study correlation functions of fermions with singular forward scattering. Following Bares and Wen [Phys. Rev. B 48, 8636 (1993)] we consider density-density interactions in $d$ dimensions that diverge in Fourier space for small momentum transfers |q| as $|\mathbf{q}{|}^{\ensuremath{-}\ensuremath{\eta}}$ with $\ensuremath{\eta}=2(d\ensuremath{-}1).$ In this case the single-particle Green's function shows Luttinger-liquid behavior. However, in contrast to $d=1,$ in higher dimensions the singularity of the momentum distribution ${n}_{\mathbf{k}}$ for wave vectors k close to the Fermi wave vector ${k}_{F}$ is characterized by a different exponent than the singularity of the density of states \ensuremath{\rho}(\ensuremath{\omega}) for frequencies \ensuremath{\omega} close to zero. We also calculate the irreducible polarization ${\ensuremath{\Pi}}_{\ensuremath{\star}}(\mathbf{q},\ensuremath{\omega})$ for $|\mathbf{q}|\ensuremath{\approx}{2k}_{F}.$ Whereas in the one-dimensional Tomonaga-Luttinger model ${\ensuremath{\Pi}}_{\ensuremath{\star}}(\ifmmode\pm\else\textpm\fi{}{2k}_{F}+q,\ensuremath{\omega})$ exhibits anomalous scaling, we show that in $d>1$ the leading singular corrections cancel. Thus, even though singular density-density interactions in $d>1$ lead to Luttinger liquid behavior of the single-particle Green's function, gauge invariant correlation functions such as the polarization or the conductivity show conventional Fermi-liquid behavior. We discuss consequences for the effect of disorder on higher-dimensional Luttinger liquids.Using higher-dimensional bosonization we study correlation functions of fermions with singular forward scattering. Following Bares and Wen [Phys. Rev. B 48, 8636 (1993)] we consider density-density interactions in $d$ dimensions that diverge in Fourier space for small momentum transfers |q| as $|\mathbf{q}{|}^{\ensuremath{-}\ensuremath{\eta}}$ with $\ensuremath{\eta}=2(d\ensuremath{-}1).$ In this case the single-particle Green's function shows Luttinger-liquid behavior. However, in contrast to $d=1,$ in higher dimensions the singularity of the momentum distribution ${n}_{\mathbf{k}}$ for wave vectors k close to the Fermi wave vector ${k}_{F}$ is characterized by a different exponent than the singularity of the density of states \ensuremath{\rho}(\ensuremath{\omega}) for frequencies \ensuremath{\omega} close to zero. We also calculate the irreducible polarization ${\ensuremath{\Pi}}_{\ensuremath{\star}}(\mathbf{q},\ensuremath{\omega})$ for $|\mathbf{q}|\ensuremath{\approx}{2k}_{F}.$ Whereas in the one-dimensional Tomonaga-Luttinger model ${\ensuremath{\Pi}}_{\ensuremath{\star}}(\ifmmode\pm\else\textpm\fi{}{2k}_{F}+q,\ensuremath{\omega})$ exhibits anomalous scaling, we show that in $d>1$ the leading singular corrections cancel. Thus, even though singular density-density interactions in $d>1$ lead to Luttinger liquid behavior of the single-particle Green's function, gauge invariant correlation functions such as the polarization or the conductivity show conventional Fermi-liquid behavior. We discuss consequences for the effect of disorder on higher-dimensional Luttinger liquids.

arXiv:cond-mat/9805005Physical review. B, Condensed matterFeb 15, 199912 citations

Symmetry obstruction to Fermi liquid behavior in the unitary limit

Ira Z. Rothstein, Prashant Shrivastava

We show that a Fermi gas, in three dimensions, at temperatures above the superconducting phase transition $({T}_{c})$ but below the Fermi temperature $({T}_{F})$ , cannot be described by Fermi liquid theory (FLT) in the unitary limit where the scattering length diverges. The result follows by showing that there are no effective field theory descriptions that both behave like a Fermi liquid and properly nonlinearly realize the spontaneously broken boost and conformal invariance of the system. We have also derived an exact result for the beta function for the coupling function in the unitary limit.We show that a Fermi gas, in three dimensions, at temperatures above the superconducting phase transition $({T}_{c})$ but below the Fermi temperature $({T}_{F})$, cannot be described by Fermi liquid theory (FLT) in the unitary limit where the scattering length diverges. The result follows by showing that there are no effective field theory descriptions that both behave like a Fermi liquid and properly nonlinearly realize the spontaneously broken boost and conformal invariance of the system. We have also derived an exact result for the beta function for the coupling function in the unitary limit.

arXiv:1712.07797Physical review. B./Physical review. BJan 2, 201920 citations

The Theory of a Fermi Liquid

D. ter Haar

Elsevier eBooksJan 1, 19650 citations

d

dimensions that diverge in Fourier space for small momentum transfers |q| as $|\mathbf{q}{|}^{\ensuremath{-}\ensuremath{\eta}}$ with $\ensuremath{\eta}=2(d\ensuremath{-}1).$ In this case the single-particle Green's function shows Luttinger-liquid behavior. However, in contrast to

d=1,

in higher dimensions the singularity of the momentum distribution

{n}_{\mathbf{k}}

for wave vectors k close to the Fermi wave vector

{k}_{F}

is characterized by a different exponent than the singularity of the density of states \ensuremath{\rho}(\ensuremath{\omega}) for frequencies \ensuremath{\omega} close to zero. We also calculate the irreducible polarization ${\ensuremath{\Pi}}_{\ensuremath{\star}}(\mathbf{q},\ensuremath{\omega})$ for $|\mathbf{q}|\ensuremath{\approx}{2k}_{F}.$ Whereas in the one-dimensional Tomonaga-Luttinger model ${\ensuremath{\Pi}}_{\ensuremath{\star}}(\ifmmode\pm\else\textpm\fi{}{2k}_{F}+q,\ensuremath{\omega})$ exhibits anomalous scaling, we show that in

d>1

the leading singular corrections cancel. Thus, even though singular density-density interactions in

d>1

lead to Luttinger liquid behavior of the single-particle Green's function, gauge invariant correlation functions such as the polarization or the conductivity show conventional Fermi-liquid behavior. We discuss consequences for the effect of disorder on higher-dimensional Luttinger liquids.

We show that a Fermi gas, in three dimensions, at temperatures above the superconducting phase transition

({T}_{c})

but below the Fermi temperature

({T}_{F})

, cannot be described by Fermi liquid theory (FLT) in the unitary limit where the scattering length diverges. The result follows by showing that there are no effective field theory descriptions that both behave like a Fermi liquid and properly nonlinearly realize the spontaneously broken boost and conformal invariance of the system. We have also derived an exact result for the beta function for the coupling function in the unitary limit.