The question of the breakdown of Fermi liquid theory in two dimensions is examined in the context of perturbation theory for a dilute interacting Fermi gas. The quasiparticle interaction function, fic;u;, is calculated for such a system. The interaction function, calculated to second order in terms of the dimensionless coupling constant, shows various singularities. The most divergent terms appear in the cross channel, but cancel out leaving a much weaker singularity in the limit of two moment a approaching each other (0 —f 0 ). As in the case of the three dimensional Fermi gas, the Cooper channel contains a logarithmic singularity in the limit 0 —f 7r. This singularity can be summed and is known to be harmless to the structure of Fermi liquid theory. A different feature in two dimensions is the existence of such a singularity for 0 —p 0. This feature needs further investigation. Calculations have also been extended to a polarized Fermi gas and the result is equivalent to the unpolarized case and does not show any additional features. In conclusion, the results do not indicate the presence of strong divergences which could cause the breakdown of Fermi liquid theory in two dimensions for a dilute interacting Fermi gas.The question of the breakdown of Fermi liquid theory in two dimensions is examined in the context of perturbation theory for a dilute interacting Fermi gas. The quasiparticle interaction function, fic;u;, is calculated for such a system. The interaction function, calculated to second order in terms of the dimensionless coupling constant, shows various singularities. The most divergent terms appear in the cross channel, but cancel out leaving a much weaker singularity in the limit of two moment a approaching each other (0 —f 0 ). As in the case of the three dimensional Fermi gas, the Cooper channel contains a logarithmic singularity in the limit 0 —f 7r. This singularity can be summed and is known to be harmless to the structure of Fermi liquid theory. A different feature in two dimensions is the existence of such a singularity for 0 —p 0. This feature needs further investigation. Calculations have also been extended to a polarized Fermi gas and the result is equivalent to the unpolarized case and does not show any additional features. In conclusion, the results do not indicate the presence of strong divergences which could cause the breakdown of Fermi liquid theory in two dimensions for a dilute interacting Fermi gas.

Jan 1, 20080 citations

Perturbative non-Fermi liquids from dimensional regularization

Denis Dalidovich, Sung-Sik Lee

We devise a dimensional regularization scheme for quantum field theories with a Fermi surface to study scaling behavior of non-Fermi liquid states in a controlled approximation. Starting from two space dimensions, the co-dimension of the Fermi surface is extended to a general value while its dimension is fixed. When the Fermi surface is coupled with a critical boson centered at zero momentum, the interaction becomes marginal at a critical space dimension ${d}_{c}=5/2$ . A deviation from the critical dimension is used as a small parameter for a systematic expansion. We apply this method to the theory where two patches of the Fermi surface are coupled with a critical boson, and show that the Ising-nematic critical point is described by a stable non-Fermi liquid state slightly below the critical dimension. Critical exponents are computed up to the two-loop order.We devise a dimensional regularization scheme for quantum field theories with a Fermi surface to study scaling behavior of non-Fermi liquid states in a controlled approximation. Starting from two space dimensions, the co-dimension of the Fermi surface is extended to a general value while its dimension is fixed. When the Fermi surface is coupled with a critical boson centered at zero momentum, the interaction becomes marginal at a critical space dimension ${d}_{c}=5/2$. A deviation from the critical dimension is used as a small parameter for a systematic expansion. We apply this method to the theory where two patches of the Fermi surface are coupled with a critical boson, and show that the Ising-nematic critical point is described by a stable non-Fermi liquid state slightly below the critical dimension. Critical exponents are computed up to the two-loop order.

arXiv:1307.3170Physical Review BDec 4, 2013149 citations

Fermi liquids in two-space dimensions

Joel Feldman, Detlef Lehmann, Horst Knörrer +1 more

Springer eBooksApr 6, 200815 citations

Non-Fermi-liquid behavior in two dimensions due to long-ranged current-current interactions

Dmitri V. Khveshchenko, R. Hlubina, Thomas Maurice Rice

We examine the low-energy behavior of two-dimensional electrons with current-current interactions. The interactions are long range, cannot be screened, and result in anomalies in perturbation theory. In the Hartree-Fock theory, we find an instability of the Landau Fermi-liquid state resulting in ``fermion-condensate'' states with a high degeneracy of levels at the Fermi energy. This degeneracy may be removed to give a Fermi-liquid state with vanishing Fermi velocity. As an example, we investigate further the Fermi-liquid state with the quasiparticle spectrum \ensuremath{\epsilon}(p)\ensuremath{\propto}(p- ${\mathit{p}}_{\mathit{F}}$ ${)}^{3/2}$ proposed by Halperin et al. Application of the recent Haldane scheme of bosonization in higher dimensions to this state leads to coupling between bosons, which has the form required for a breakdown of the Landau Fermi-liquid behavior. A generalized form of the Luttinger liquid is obtained.We examine the low-energy behavior of two-dimensional electrons with current-current interactions. The interactions are long range, cannot be screened, and result in anomalies in perturbation theory. In the Hartree-Fock theory, we find an instability of the Landau Fermi-liquid state resulting in ``fermion-condensate'' states with a high degeneracy of levels at the Fermi energy. This degeneracy may be removed to give a Fermi-liquid state with vanishing Fermi velocity. As an example, we investigate further the Fermi-liquid state with the quasiparticle spectrum \ensuremath{\epsilon}(p)\ensuremath{\propto}(p-${\mathit{p}}_{\mathit{F}}$${)}^{3/2}$ proposed by Halperin et al. Application of the recent Haldane scheme of bosonization in higher dimensions to this state leads to coupling between bosons, which has the form required for a breakdown of the Landau Fermi-liquid behavior. A generalized form of the Luttinger liquid is obtained.

Physical review. B, Condensed matterOct 15, 199344 citations

{d}_{c}=5/2

. A deviation from the critical dimension is used as a small parameter for a systematic expansion. We apply this method to the theory where two patches of the Fermi surface are coupled with a critical boson, and show that the Ising-nematic critical point is described by a stable non-Fermi liquid state slightly below the critical dimension. Critical exponents are computed up to the two-loop order.

{\mathit{p}}_{\mathit{F}}

{)}^{3/2}

proposed by Halperin et al. Application of the recent Haldane scheme of bosonization in higher dimensions to this state leads to coupling between bosons, which has the form required for a breakdown of the Landau Fermi-liquid behavior. A generalized form of the Luttinger liquid is obtained.