We study a two-dimensional Fermi gas with an arbitrary short-range repulsive interaction. We show that the vertex part has an unusual singularity in the particle-particle channel for all momenta q2 ${\mathit{k}}_{\mathit{F}}$ , which is not found in higher dimensions. We interpret this as a collective mode representing a bound excitation of two holes. This mode, however, does not lead to an instability, or to a breakdown of Fermi-liquid theory in the low-density limit. The resulting Fermi-surface phase shift vanishes, and a \ensuremath{\Vert}\ensuremath{\omega}${\mathrm{\ensuremath{\Vert}}}^{5/2}$ correction to \ensuremath{\Sigma}''( ${\mathit{k}}_{\mathit{F}}$ ,\ensuremath{\omega}) is obtained. The 2D case is also contrasted with a similar calculation in 1D.We study a two-dimensional Fermi gas with an arbitrary short-range repulsive interaction. We show that the vertex part has an unusual singularity in the particle-particle channel for all momenta q2${\mathit{k}}_{\mathit{F}}$, which is not found in higher dimensions. We interpret this as a collective mode representing a bound excitation of two holes. This mode, however, does not lead to an instability, or to a breakdown of Fermi-liquid theory in the low-density limit. The resulting Fermi-surface phase shift vanishes, and a \ensuremath{\Vert}\ensuremath{\omega}${\mathrm{\ensuremath{\Vert}}}^{5/2}$ correction to \ensuremath{\Sigma}''(${\mathit{k}}_{\mathit{F}}$,\ensuremath{\omega}) is obtained. The 2D case is also contrasted with a similar calculation in 1D.

Physical Review LettersAug 20, 1990121 citations

Pair Excitations and Vertex Corrections in Fermi Fluids

Helga M. Böhm, E. Krotscheck, Martin Panholzer

arXiv:cond-mat/0609373Journal of Low Temperature PhysicsJun 11, 20071 citation

Anisotropic non-Fermi liquids

Shouvik Sur, Sung-Sik Lee

We study non-Fermi-liquid states that arise at the quantum critical points associated with the spin density wave (SDW) and charge density wave (CDW) transitions in metals with twofold rotational symmetry. We use the dimensional regularization scheme, where a one-dimensional Fermi surface is embedded in $(3\ensuremath{-}\ensuremath{\epsilon})$-dimensional momentum space. In three dimensions, quasilocal marginal Fermi liquids arise both at the SDW and CDW critical points: the speed of the collective mode along the ordering wave vector is logarithmically renormalized to zero compared to that of Fermi velocity. Below three dimensions, however, the SDW and CDW critical points exhibit drastically different behaviors. At the SDW critical point, a stable anisotropic non-Fermi-liquid state is realized for small $\ensuremath{\epsilon}$, where not only time but also different spatial coordinates develop distinct anomalous dimensions. The non-Fermi liquid exhibits an emergent algebraic nesting as the patches of Fermi surface are deformed into a universal power-law shape near the hot spots. Due to the anisotropic scaling, the energy of incoherent spin fluctuations disperse with different power laws in different momentum directions. At the CDW critical point, on the other hand, the perturbative expansion breaks down immediately below three dimensions as the interaction renormalizes the speed of charge fluctuations to zero within a finite renormalization group scale through a two-loop effect. The difference originates from the fact that the vertex correction antiscreens the coupling at the SDW critical point whereas it screens at the CDW critical point.We study non-Fermi-liquid states that arise at the quantum critical points associated with the spin density wave (SDW) and charge density wave (CDW) transitions in metals with twofold rotational symmetry. We use the dimensional regularization scheme, where a one-dimensional Fermi surface is embedded in $(3\ensuremath{-}\ensuremath{\epsilon})$-dimensional momentum space. In three dimensions, quasilocal marginal Fermi liquids arise both at the SDW and CDW critical points: the speed of the collective mode along the ordering wave vector is logarithmically renormalized to zero compared to that of Fermi velocity. Below three dimensions, however, the SDW and CDW critical points exhibit drastically different behaviors. At the SDW critical point, a stable anisotropic non-Fermi-liquid state is realized for small $\ensuremath{\epsilon}$, where not only time but also different spatial coordinates develop distinct anomalous dimensions. The non-Fermi liquid exhibits an emergent algebraic nesting as the patches of Fermi surface are deformed into a universal power-law shape near the hot spots. Due to the anisotropic scaling, the energy of incoherent spin fluctuations disperse with different power laws in different momentum directions. At the CDW critical point, on the other hand, the perturbative expansion breaks down immediately below three dimensions as the interaction renormalizes the speed of charge fluctuations to zero within a finite renormalization group scale through a two-loop effect. The difference originates from the fact that the vertex correction antiscreens the coupling at the SDW critical point whereas it screens at the CDW critical point.

arXiv:1606.06694Physical review. B./Physical review. BNov 18, 201632 citations

Leading Corrections to Fermi Liquid Behavior at Low Density in Two Dimensions

Jungsoo Kim, Dermot Coffey

APSMar 1, 19960 citations

Vertex effects in many-fermion systems

Arthur J. Layzer

Physics LettersNov 1, 19646 citations

First temperature corrections to the Fermi-liquid fixed point in two dimensions

Gennady Y. Chitov, Andrew J. Millis

We calculate, using perturbative calculations and Ward identities, the basic parameters of the Fermi liquid: the scattering vertex, the Landau interaction function, the effective mass, specific heat, and physical susceptibilities for a model of two-dimensional (2D) fermions with a short-ranged interaction at nonzero temperature. The leading temperature dependence of the spin components of the scattering vertex, the Landau function, and the spin susceptibility is found to be linear. We find that the standard $T=0$ relationships for a Galilean-invariant Fermi liquid are violated by finite-temperature terms. The coefficients in the temperature corrections to these relationships involve a subtle interplay between contributions from small and large $(\ensuremath{\sim}{2k}_{F})$ momentum processes. A connection with previous studies of the 2D Fermi-liquid parameters is discussed. We conclude that the linear leading temperature dependence of the parameters is a generic feature of the 2D Fermi liquid.We calculate, using perturbative calculations and Ward identities, the basic parameters of the Fermi liquid: the scattering vertex, the Landau interaction function, the effective mass, specific heat, and physical susceptibilities for a model of two-dimensional (2D) fermions with a short-ranged interaction at nonzero temperature. The leading temperature dependence of the spin components of the scattering vertex, the Landau function, and the spin susceptibility is found to be linear. We find that the standard $T=0$ relationships for a Galilean-invariant Fermi liquid are violated by finite-temperature terms. The coefficients in the temperature corrections to these relationships involve a subtle interplay between contributions from small and large $(\ensuremath{\sim}{2k}_{F})$ momentum processes. A connection with previous studies of the 2D Fermi-liquid parameters is discussed. We conclude that the linear leading temperature dependence of the parameters is a generic feature of the 2D Fermi liquid.

arXiv:cond-mat/0103155Physical review. B, Condensed matterJul 11, 200144 citations

We study a two-dimensional Fermi gas with an arbitrary short-range repulsive interaction. We show that the vertex part has an unusual singularity in the particle-particle channel for all momenta q2

{\mathit{k}}_{\mathit{F}}

, which is not found in higher dimensions. We interpret this as a collective mode representing a bound excitation of two holes. This mode, however, does not lead to an instability, or to a breakdown of Fermi-liquid theory in the low-density limit. The resulting Fermi-surface phase shift vanishes, and a \ensuremath{\Vert}\ensuremath{\omega}${\mathrm{\ensuremath{\Vert}}}^{5/2}$ correction to \ensuremath{\Sigma}''(

{\mathit{k}}_{\mathit{F}}

,\ensuremath{\omega}) is obtained. The 2D case is also contrasted with a similar calculation in 1D.

T=0

relationships for a Galilean-invariant Fermi liquid are violated by finite-temperature terms. The coefficients in the temperature corrections to these relationships involve a subtle interplay between contributions from small and large $(\ensuremath{\sim}{2k}_{F})$ momentum processes. A connection with previous studies of the 2D Fermi-liquid parameters is discussed. We conclude that the linear leading temperature dependence of the parameters is a generic feature of the 2D Fermi liquid.