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Abstract
In this paper, we discuss the connection between two genuinely quantum phenomena—the discontinuity of quantum maximum entropy inference and quantum phase transitions at zero temperature. It is shown that the discontinuity of the maximum entropy inference of local observable measurements signals the non-local type of transitions, where local density matrices of the ground state change smoothly at the transition point. We then propose to use the quantum conditional mutual information of the ground state as an indicator to detect the discontinuity and the non-local type of quantum phase transitions in the thermodynamic limit.
Highlights
Quantum phase transitions happen at zero temperature with no classical counterparts and are believed to be driven by quantum fluctuations [22]
We propose to solve the problem by using the quantum conditional mutual information of two disconnected parts of the system for the ground states
We start from introducing two natural types of quantum phase transitions: a local type that can be detected by a non-smooth change of local observable measurements, and a non-local type which can not
Summary
Quantum phase transitions happen at zero temperature with no classical counterparts and are believed to be driven by quantum fluctuations [22]. Given the observation on the relation between discontinuity of ρ* and the non-local level-crossings, it is natural to consider signaling quantum phase transitions by directly computing where the discontinuity happens. This approach works well in finite systems, but may fail in the thermodynamic limit of infinite size systems as the places of discontinuity (i.e. where the system ‘closes gap’) may change when the system size goes to infinity.
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