We study $2+1$ dimensional massless Dirac fermions and bosons coupled to a U(1) gauge field as a model for underdoped cuprates. We find that the uniform susceptibility and the specific heat coefficient are logarithmically enhanced (compared to linear-in- $T$ behavior) due to the fluctuation of a transverse gauge field which is the only massless mode at finite boson density. We analyze existing data, and find good agreement in the spin gap phase. Within our picture, the drop of the susceptibility below the superconducting $T_c$ arises from the suppression of gauge fluctuations.

• Received 26 February 1997

DOI:https://doi.org/10.1103/PhysRevLett.79.2109