Exact effective action for the O(N) vector model in the large N limit

We present the solution of the exact RG equation at the critical fixed point of the interacting O(N) vector model in the large $N$ limit. Below four dimensions, the exact effective action at the fixed point is a transcendental function of two leading scaling operators with infinitely many derivatives.Comment: 6+12 pages, 1 figur

Fermi liquids beyond the forward scattering limit: the role of non-forward scatterings for scale invariance and instabilities

Landau Fermi liquid theory is a fixed point theory of metals that includes the forward scattering amplitudes as exact marginal couplings. However, the fixed point theory that only includes the strict forward scatterings is non-local in real space. In this paper, we revisit the Fermi liquid theory using the field-theoretic functional renormalization group formalism and show how the scale invariant fixed point emerges as a local theory. The local low-energy effective field theory for Fermi liquids includes not only the forward scatterings but also non-forward scatterings with small but non-zero momentum transfers. In the low-energy limit, the non-forward scattering amplitude takes a scale invariant form if the momentum transfer is scaled along with the energy. If the bare coupling is attractive beyond a critical strength, the coupling function exhibits a run-away flow, signifying potential instabilities in particle-hole channels. What drives those instabilities is the non-trivial renormalization group flow of the non-forward scattering amplitudes. The pairing interaction also obeys a scaling relation if the center of mass momentum of Cooper pairs is comparable with energy

Generalized Numerical Index and Denseness of Numerical Peak Holomorphic Functions on a Banach Space

The generalized numerical index of a Banach space is introduced, and its properties on certain Banach spaces are studied. Ed-dari's theorem on the numerical index is extended to the generalized index and polynomial numerical index of a Banach space. The denseness of numerical strong peak holomorphic functions is also studied

Correlated electronic states at domain walls of a Mott-charge-density-wave insulator 1T-TaS2

Domain walls in interacting electronic systems can have distinct localized states, which often govern physical properties and may lead to unprecedented functionalities and novel devices. However, electronic states within domain walls themselves have not been clearly identified and understood for strongly correlated electron systems. Here, we resolve the electronic states localized on domain walls in a Mott-charge-density-wave(CDW) insulator 1T-TaS2 using scanning tunneling spectroscopy. We establish that the domain wall state decomposes into two nonconducting states located at the center of domain walls and edges of domains. Theoretical calculations reveal their atomistic origin as the local reconstruction of domain walls under the strong influence of electron correlation. Our results introduce a concept for the domain wall electronic property, the wall's own internal degrees of freedom, which is potentially related to the controllability of domain wall electronic properties