On the Density-Density Critical Indices�in Interacting Fermi Systems

Abstract

The behaviour of correlation functions of d = 1 interacting fermionic systems is determined by a small number of critical indices. We prove that one of them is exactly zero. As a consequence, the behavior of the Fourier transform of the density-density correlation at zero momentum is qualitatively unaffected by the interaction, contrary to what happens at ±2p F , if pF is the Fermi momentum. The result is obtained by implementing Ward identities in a Renormalization Group approach.

Universality Relations in Non-solvable Quantum Spin Chains

“…It is also easy to see that (see [13], §3.4), since the propagator (77) satisfies the symmetry property…”

“…The proof of the lemma is based on the RG analysis of the Grassmann integrals (24) and (29), described in [12,13] and [17,19], respectively.…”

“…By proceeding as in §2.2 of [13], we can show that, by performing in (37) the change of the variables ψ ± x,ω → e ±iαx,ω ψ ± x,ω , the following identity is obtained:…”

Functional Integral Construction of the Massive Thirring model: Verification of Axioms and Massless Limit

“…In particular, -T j 0 ,n,2m ϕ ,n J is a family of trees (identical to the those defined in §3.2 of [BM2], up to the (trivial) difference that the maximum scale of the vertices is N + 1 instead of +1), with root at scale j 0 , n normal endpoints (i.e. endpoints not associated to ϕ or J fields), n ϕ = 2m ϕ endpoints of type ϕ and n J endpoints of type J.…”

“…; we refer to [BM2] §2.2 for its exact definition. We then substitute [C h,N (k)] −1 with [C ε h,N (k)] −1 in the r.h.s.…”