We diagnose the stability of the Migdal-Eliashberg theory for a Fermi surface coupled to a gapless boson in 2+1 dimensions. We provide a scheme for diagonalizing the Bethe-Salpeter ladder when small-angle scattering mediated by the boson plays a dominant role. We found a large number of soft modes which correspond to shape fluctuations of the Fermi surface, and these shape deformations follow a diffusion-like dynamics on the Fermi surface. Surprisingly, the odd-parity deformations of a convex Fermi surface becomes unstable near the non-Fermi liquid regime of the Ising-Nematic quantum critical point and our finding calls for revisit of the Migdal-Eliashberg framework. The implication of the Bethe-Salpeter eigenvalues in transport will be discussed in the companion paper [H.Guo,arXiv:2311.03458].We diagnose the stability of the Migdal-Eliashberg theory for a Fermi surface coupled to a gapless boson in 2+1 dimensions. We provide a scheme for diagonalizing the Bethe-Salpeter ladder when small-angle scattering mediated by the boson plays a dominant role. We found a large number of soft modes which correspond to shape fluctuations of the Fermi surface, and these shape deformations follow a diffusion-like dynamics on the Fermi surface. Surprisingly, the odd-parity deformations of a convex Fermi surface becomes unstable near the non-Fermi liquid regime of the Ising-Nematic quantum critical point and our finding calls for revisit of the Migdal-Eliashberg framework. The implication of the Bethe-Salpeter eigenvalues in transport will be discussed in the companion paper [H.Guo,arXiv:2311.03458].

arXiv:2311.03455Nov 6, 20230 citations

Fermions and the Fermi surface

Lecture notes in physics. M, MonographsJan 1, 19970 citations

Probing critical surfaces in momentum space using real-space entanglement entropy: Bose versus Fermi

Hsin-Hua Lai, Kun Yang

A codimension-one critical surface in momentum space can be either a familiar Fermi surface, which separates occupied states from empty ones in the noninteracting fermion case, or a novel Bose surface, where gapless bosonic excitations are anchored. The presence of such surfaces gives rise to logarithmic violation of entanglement entropy area law. When they are convex, we show that the shape of these critical surfaces can be determined by inspecting the leading logarithmic term of real-space entanglement entropy. The fundamental difference between a Fermi surface and a Bose surface is revealed by the fact that the logarithmic terms in entanglement entropies differ by a factor of 2: ${S}_{\mathrm{log}}^{\mathrm{Bose}}=2{S}_{\mathrm{log}}^{\mathrm{Fermi}}$ , even when they have identical geometry. Our method has remarkable similarity with determining Fermi surface shape using quantum oscillation. We also discuss possible probes of concave critical surfaces in momentum space.A codimension-one critical surface in momentum space can be either a familiar Fermi surface, which separates occupied states from empty ones in the noninteracting fermion case, or a novel Bose surface, where gapless bosonic excitations are anchored. The presence of such surfaces gives rise to logarithmic violation of entanglement entropy area law. When they are convex, we show that the shape of these critical surfaces can be determined by inspecting the leading logarithmic term of real-space entanglement entropy. The fundamental difference between a Fermi surface and a Bose surface is revealed by the fact that the logarithmic terms in entanglement entropies differ by a factor of 2: ${S}_{\mathrm{log}}^{\mathrm{Bose}}=2{S}_{\mathrm{log}}^{\mathrm{Fermi}}$, even when they have identical geometry. Our method has remarkable similarity with determining Fermi surface shape using quantum oscillation. We also discuss possible probes of concave critical surfaces in momentum space.

arXiv:1510.03428Physical review. B./Physical review. BMar 23, 201610 citations

One Dimensional Anomaly of the Fermi Surface

Giovanni Gallavotti

NATO ASI series. Series B : PhysicsJan 1, 19940 citations

A Two Dimensional Fermi Liquid. Part 3: The Fermi Surface

Joel Feldman, Horst Kn�rrer, Eugene Trubowitz B

arXiv:math-ph/0209049Communications in Mathematical PhysicsApr 7, 200419 citations

Deformation of anisotropic Fermi surfaces due to electron-electron interactions

Rafael Roldán, María P. López-Sancho, F. Guinea +1 more

We analyze the deformations of the Fermi surface induced by electron-electron interactions in anisotropic two-dimensional systems. We use perturbation theory to treat, on the same footing, the regular and singular regions of the Fermi surface. It is shown that, even for weak local coupling, the self-energy presents a nontrivial behavior showing momentum dependence and interplay with the Fermi surface shape. Our scheme gives simple analytical expressions based on local features of the Fermi surface.We analyze the deformations of the Fermi surface induced by electron-electron interactions in anisotropic two-dimensional systems. We use perturbation theory to treat, on the same footing, the regular and singular regions of the Fermi surface. It is shown that, even for weak local coupling, the self-energy presents a nontrivial behavior showing momentum dependence and interplay with the Fermi surface shape. Our scheme gives simple analytical expressions based on local features of the Fermi surface.

arXiv:cond-mat/0603673Europhysics Letters (EPL)Dec 1, 20062 citations

{S}_{\mathrm{log}}^{\mathrm{Bose}}=2{S}_{\mathrm{log}}^{\mathrm{Fermi}}

, even when they have identical geometry. Our method has remarkable similarity with determining Fermi surface shape using quantum oscillation. We also discuss possible probes of concave critical surfaces in momentum space.