Question

what physical meaning of spin gap, why we can relate spin gap with spin correlation function by fitting $G_{sp}(\tau, 0)$?

Answer 1

In non-interacting limit, single particle gap is the energy between fermi-level and occupied/unoccupied energy band. And we can get this gap by the formulation: Gk(τ,0)=<c+k(τ)ck(0)>∼exp(−∑unocck(Ek−Ef)τ)Gk(τ,0)=<ck+(τ)ck(0)>∼exp(−∑kunocc(Ek−Ef)τ) . So, we can get lowest value of Ek−EfEk−Ef which is smallest excited energy of adding one electron with wavevector kk into the system. My question is:

While, in the interacting system, c+kck+ is not a well defined quasi-particle, and the DOS of electron with wavevector kk is no longer δδ function and we can't read (Ek−Ef)(Ek−Ef)from energy band at kk point more. So, is there exist any relation between single particle gap with correlated electron energy band with ρk(ω)=1πIm(Grk(ω))ρk(ω)=1πIm(Gkr(ω))?

Does spin gap can obtained by fitting Gsp(τ,0)=<szk(τ)sz−k(0)>∼exp(−∑k(Ek(spin)−Ef(spin))τ)Gsp(τ,0)=<skz(τ)s−kz(0)>∼exp(−∑k(Ek(spin)−Ef(spin))τ)? And what the physical meaning of E_k(spin)-E_f(spin)?

Answer 2

hope it's help you friend ☺ ☺