Singularities of one-particle Green's function in doped antiferromagnet

Abstract

We analyze the continued fraction expansion of a fermion Green's function G( k,ω) in a quantum antiferromagnet. In the frameworks of mode coupling approximation we calculate recursively the coefficients a n , b n of the expansion. The result has always the correct analytic properties: (i) G( k,ω) is an analytic function of ω everywhere but not on the real axis; (ii) on the real axis G may have isolated (quasiparticle) poles and branch cuts; (iii) the spectral density is positive. When G has no poles on the real axis, a low-energy sharp peak in the spectral density may be interpreted as a quasiparticle with finite lifetime. We observe all kinds of singularities depending on k .