Covariant gaussian approximation in Ginzburg–Landau model

Abstract

h i g h l i g h t s• A symmetry conserving approximation based on Dyson-Schwinger equations is proposed.• The approximation keeps all the Ward Identities in a theory with continuous symmetry. • The approximation is more accurate than other mean-field type approximations.• The penetration depth of Ginzburg-Landau model shows a downward cusp near T c . a b s t r a c tCondensed matter systems undergoing second order transition away from the critical fluctuation region are usually described sufficiently well by the mean field approximation. The critical fluctuation region, determined by the Ginzburg criterion, |T /T c − 1| ≪ Gi, is narrow even in high T c superconductors and has universal features well captured by the renormalization group method. However recent experiments on magnetization, conductivity and Nernst effect suggest that fluctuations effects are large in a wider region both above and below T c . In particular some ''pseudogap'' phenomena and strong renormalization of the mean field critical temperature T mf can be interpreted as strong fluctuations effects that are nonperturbative (cannot be accounted for by ''gaussian fluctuations''). The physics in a broader region therefore requires more accurate approach. Self consistent methods are generally ''non-conserving'' in the sense that the Ward identities are not obeyed. This is especially detrimental in the symmetry * 229 broken phase where, for example, Goldstone bosons become massive. Covariant gaussian approximation remedies these problems. The Green's functions obey all the Ward identities and describe the fluctuations much better. The results for the order parameter correlator and magnetic penetration depth of the Ginzburg-Landau model of superconductivity are compared with both Monte Carlo simulations and experiments in high T c cuprates.

Covariant Bethe-Salpeter approximation in models of strongly correlated electron systems

“…The exact result can be obtained by analogue with the quantum anharmonic oscillator [18,24]. We calculate g k for a = −1, 0.5, 0, 1 in Fig.…”

“…The covariant correlators G x1...xn could be different from G tr x1...xn , and the covariant correlators satisfy the Ward identities [18,24]. In our case, differentiating Eq.…”

“…will be called the "minimization equations". They will determine the "truncated" correlators that should be distinguished [13,24] from an approximant to the "physical" correlators defined in Eq. (2).…”

“…The method was compared with available exact results for the S-matrix in the Gross -Neveu model [25] (a local four Fermion interactions in 1D Dirac excitations recently considered in condensed matter physics) and with MC simulations in various scalar models, see Ref. 24 . Applied to the electronic field correlator in electronic systems, CGA becomes roughly equivalent to Hartree -Fock (HF) approximation that is generally not precise enough.…”

Dynamical instability of the electric transport in superconductors

“…The nonlinear | ψ | 2 ψ term in the TDGL Eq. (7) is approximated by a linear one 2〈| ψ | 2 〉 ψ (there are two possible contractions between ψ * , ψ in | ψ | 2 ψ , see discussion of this point in 19–21 ):…”