Holographic informational properties for a specific Einstein-Maxwell-dilaton gravity theory

We study the holographic information quantities, including the holographic entanglement entropy (HEE), the holographic mutual information (HMI) and the minimum cross section of the entanglement wedge (EWCS), over a special black brane geometry, which has a vanishing ground-state entropy. Thanks to the zero entropy density at the ground state, we expect to extract novel, even singular informational properties in the zero-temperature limit. Surprisingly, we do not observe any singular behavior of entanglement-related physical quantities in the zero-temperature limit. Nevertheless, we find a peculiar property from this model that in the low-temperature region, the HEE decreases with the 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. In addition, we also compare the features of the information quantities in this special black brane geometry with those in Reissner-Nordstrom anti–de Sitter (RN-AdS) black brane geometry. It is shown that the HEE and HMI of this vanishing ground-state entropy model are always larger than those of RN-AdS geometry, while the EWCS behaves oppositely. Our results indicate that the HMI and EWCS could have different abilities in describing mixed state entanglement.