Role of Symmetry and Dimension in Pseudogap Phenomena

The attractive Hubbard model in $d=2\mathrm{}$ 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 $A({\mathbf{k}}_F,\omega )$ occurs in the renormalized classical regime when the correlation length is larger than the direction-dependent thermal de Broglie wavelength, ${\xi }_{\mathrm{th}}=ħv_F\left(\mathbf{k}\right)/k_{B}T$. 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 $\mathrm{SO}\left(n\right)$ symmetry with $n>\mathrm{}2\mathrm{}$. This is relevant in the context of $\mathrm{SO}\left(5\right)$ theories of high $T_c$ but has more general applicability.