We calculate the entropy of a two-dimensional Fermi liquid using a model with a contact interaction between fermions. We find that there are ${\mathit{T}}^{2}$ contributions to the entropy from interactions separate from those due to the collective modes. These ${\mathit{T}}^{2}$ contributions arise fron nonanalytic corrections to the real part of the self-energy which may be calculated from the leading-log dependence of the imaginary part of the self-energy through the Kramers-Kronig relation. We find no evidence of a breakdown in Fermi liquid theory in 2D and conclude that Fermi liquids in 2D are similar to 3D Fermi liquids.We calculate the entropy of a two-dimensional Fermi liquid using a model with a contact interaction between fermions. We find that there are ${\mathit{T}}^{2}$ contributions to the entropy from interactions separate from those due to the collective modes. These ${\mathit{T}}^{2}$ contributions arise fron nonanalytic corrections to the real part of the self-energy which may be calculated from the leading-log dependence of the imaginary part of the self-energy through the Kramers-Kronig relation. We find no evidence of a breakdown in Fermi liquid theory in 2D and conclude that Fermi liquids in 2D are similar to 3D Fermi liquids.

arXiv:cond-mat/9302036Physical Review LettersAug 16, 199350 citations

Fermi liquid theory in two dimensions

Sudhakar Yarlagadda, Susumu Kurihara

Physica B Condensed MatterMay 1, 19930 citations

Fluctuation diagnostics of the finite-temperature quasi-antiferromagnetic regime of the two-dimensional Hubbard model

Behnam Arzhang, Andrey E. Antipov, J. P. F. LeBlanc

We study the finite-temperature Fermi-liquid to non-Fermi-liquid crossover in the two-dimensional Hubbard model for a range of dopings using the self-consistent ladder dual fermion method. We consider relatively high temperatures where by comparing the single-particle self-energy and the two-particle spin susceptibility we identify a suppression of the density of states near the Fermi level caused by a quasi-antiferromagnetic behavior that is itself characterized by a long, but finite, correlation length scale which we extract. We compute the single-particle self-energy, and the charge/spin susceptibilities for the entire doping range at relatively high temperature, and also for the half-filled weak-coupling case at relatively low temperatures. We perform fluctuation diagnostics to decompose the single-particle self-energy into scattering $q$ -vector and bosonic frequency contributions in the spin channel. Within this framework we find that the key contributions to the single-particle self-energy that give non-Fermi-liquid character show complicated dependence on zero, positive, and negative frequency bosonic modes. We find that for a nominal choice of ${t}^{\ensuremath{'}}$ that electron- and hole-doped systems with similar Fermi-liquid character have distinct spin and charge susceptibility and distinct spin-fluctuation diagnostics spectra.We study the finite-temperature Fermi-liquid to non-Fermi-liquid crossover in the two-dimensional Hubbard model for a range of dopings using the self-consistent ladder dual fermion method. We consider relatively high temperatures where by comparing the single-particle self-energy and the two-particle spin susceptibility we identify a suppression of the density of states near the Fermi level caused by a quasi-antiferromagnetic behavior that is itself characterized by a long, but finite, correlation length scale which we extract. We compute the single-particle self-energy, and the charge/spin susceptibilities for the entire doping range at relatively high temperature, and also for the half-filled weak-coupling case at relatively low temperatures. We perform fluctuation diagnostics to decompose the single-particle self-energy into scattering $q$-vector and bosonic frequency contributions in the spin channel. Within this framework we find that the key contributions to the single-particle self-energy that give non-Fermi-liquid character show complicated dependence on zero, positive, and negative frequency bosonic modes. We find that for a nominal choice of ${t}^{\ensuremath{'}}$ that electron- and hole-doped systems with similar Fermi-liquid character have distinct spin and charge susceptibility and distinct spin-fluctuation diagnostics spectra.

arXiv:1905.07462Physical review. B./Physical review. BJan 21, 202010 citations

Universal and nonuniversal renormalizations in Fermi liquids

Andrey V. Chubukov, Dmitrii L. Maslov

We discuss an interplay between the Fermi-liquid (FL) theory and diagrammatic perturbative approach to interacting Fermi systems. In the FL theory for Galilean-invariant systems, mass renormalization ${m}^{\ensuremath{\ast}}/m$ comes exclusively from fermions at the Fermi surface. We show that in a diagrammatic perturbation theory the same result for ${m}^{\ensuremath{\ast}}/m$ comes from fermions both at and away from the Fermi surface. The equivalence of the FL and perturbative approaches is based on a particular relation between self-energy contributions from high- and low-energy fermions. We argue that care has to be exercised in the renormalization-group approach to a FL in order not to miss the high-energy contribution to ${m}^{\ensuremath{\ast}}/m$. As particular examples, we discuss ${m}^{\ensuremath{\ast}}/m$ and the quasiparticle residue $Z$ for two-dimensional and three-dimensional systems with both SU(2) and $\text{SU}(N)$ symmetries, and with a short-range interaction. We derive an expression for the anisotropic part of the Fermi-liquid vertex in the large- $N$ limit of the $\text{SU}(N)$ case.We discuss an interplay between the Fermi-liquid (FL) theory and diagrammatic perturbative approach to interacting Fermi systems. In the FL theory for Galilean-invariant systems, mass renormalization ${m}^{\ensuremath{\ast}}/m$ comes exclusively from fermions at the Fermi surface. We show that in a diagrammatic perturbation theory the same result for ${m}^{\ensuremath{\ast}}/m$ comes from fermions both at and away from the Fermi surface. The equivalence of the FL and perturbative approaches is based on a particular relation between self-energy contributions from high- and low-energy fermions. We argue that care has to be exercised in the renormalization-group approach to a FL in order not to miss the high-energy contribution to ${m}^{\ensuremath{\ast}}/m$. As particular examples, we discuss ${m}^{\ensuremath{\ast}}/m$ and the quasiparticle residue $Z$ for two-dimensional and three-dimensional systems with both SU(2) and $\text{SU}(N)$ symmetries, and with a short-range interaction. We derive an expression for the anisotropic part of the Fermi-liquid vertex in the large-$N$ limit of the $\text{SU}(N)$ case.

arXiv:1003.4032Physical Review BJun 3, 201013 citations

Fermi Liquids in Two Dimensions

WORLD SCIENTIFIC eBooksMar 1, 20080 citations

We calculate the entropy of a two-dimensional Fermi liquid using a model with a contact interaction between fermions. We find that there are

{\mathit{T}}^{2}

contributions to the entropy from interactions separate from those due to the collective modes. These

{\mathit{T}}^{2}

contributions arise fron nonanalytic corrections to the real part of the self-energy which may be calculated from the leading-log dependence of the imaginary part of the self-energy through the Kramers-Kronig relation. We find no evidence of a breakdown in Fermi liquid theory in 2D and conclude that Fermi liquids in 2D are similar to 3D Fermi liquids.

q

-vector and bosonic frequency contributions in the spin channel. Within this framework we find that the key contributions to the single-particle self-energy that give non-Fermi-liquid character show complicated dependence on zero, positive, and negative frequency bosonic modes. We find that for a nominal choice of ${t}^{\ensuremath{'}}$ that electron- and hole-doped systems with similar Fermi-liquid character have distinct spin and charge susceptibility and distinct spin-fluctuation diagnostics spectra.

Z

for two-dimensional and three-dimensional systems with both SU(2) and

\text{SU}(N)

symmetries, and with a short-range interaction. We derive an expression for the anisotropic part of the Fermi-liquid vertex in the large-

N

limit of the

\text{SU}(N)

case.