Abstract
We show that a new glassy phase can emerge in the presence of strong magnetic frustration and quantum fluctuations. It is a valence bond glass (VBG). We study its properties solving the Hubbard-Heisenberg model on a Bethe lattice within the large-N limit introduced by Affleck and Marston. We work out the phase diagram that contains Fermi liquid, dimer and valence bond glass phases. This new glassy phase has no electronic or spin gap (although a pseudo-gap is observed), it is characterized by long-range critical valence bond correlations and is not related to any magnetic ordering. As a consequence, it is quite different from both valence bond crystals and spin glasses.