Misc,
Principle of Maximum Entropy and Quantum Phase Transitions
(2014)cite arxiv:1406.5046Comment: 13 pages, 11 figures.
Abstract
We discuss quantum phase transitions from an information-theoretic point of
view, based on the information from local observable measurements. Two types of
transitions naturally arise from our approach, for smooth changes of local
Hamiltonians. One type can be detected by a non-smooth change of local
observable measurements while the other type cannot. The discontinuity of the
maximum entropy inference for local observable measurements signals the
non-local type of transitions, indicating the existence of long-range
irreducible many-body correlations. As commonly recognized, the topological
phase transitions are non-local where the maximum entropy inference are indeed
discontinuous at the transition points. We clarify that, however, the
`symmetry-breaking' phase transitions, for instance the one in the transverse
Ising model, are also non-local with discontinuity of the maximum entropy
inference. We propose to detect the non-local type of transitions by the
quantum conditional mutual information of two disconnect parts of the system.
The local/non-local types have intimate relationships with the
first-order/continuous types of quantum phase transitions.
