  We study the information quantities, including the holographic entanglement
entropy (HEE), mutual information (MI) and entanglement of purification (EoP),
over Gubser-Rocha model. The remarkable property of this model is the zero
entropy density at ground state, in term of which we expect to extract novel,
even singular informational properties in zero temperature limit. Surprisedly,
we do not observe any singular behavior of entanglement-related physical
quantities under the zero temperature limit. Nevertheless, we find a peculiar
property from Gubser-Rocha model that in low temperature region, the HEE
decreases with the increase of temperature, which is contrary to that in most
holographic models. We argue that this novel phenomenon is brought by the
singular property of the zero temperature limit, of which the analytical
verification is present. In addition, we also compare the features of the
information quantities in Gubser-Rocha model with those in Reissner-Nordstrom
Anti-de Sitter (RN-AdS) black hole model. It is shown that the HEE and MI of
Gubser-Rocha model are always larger than those of RN-AdS model, while the EoP
behaves in an opposite way. Our results indicate that MI and EoP could have
different abilities in describing mixed state entanglement.
