Role of symmetry and dimension on pseudogap phenomena

The attractive Hubbard model in d=2 is studied through Monte Carlo simulations at intermediate coupling. There is a crossover temperature $T_X$ where a pseudogap appears with concomitant precursors of Bogoliubov quasiparticles that are not local pairs. The pseudogap in $A(k,\omega)$ occurs in the renormalized classical regime when the correlation length is larger than the direction-dependent thermal de Broglie wave length, $\xi_{th}=\hbar v_{F}(k)/k_{B}T.$ The ratio $T_{X}/T_{c}$ for the pseudogap may be made arbitrarily large when the system is close to a point where the order parameter has SO(n) symmetry with n>2. This is relevant in the context of SO(5) theories of high $T_c$ but has more general applicability.