Citation: Chen, Jianxin, et al. "Discontinuity of maximum entropy inference and quantum phase transitions." New Journal of Physics 17.8 (2015): 083019.
Web: https://arxiv.org/abs/1406.5046
Tags: Phase-transition, Information-theory
This paper gives a lovely perspective on zero-temperature quantum phase transitions. The idea is as follows. A general principle in TQO is that in every phase there is a representative Hamiltonian such that its ground states are local terms which project into the +1 eigenspace if the reduced density matrix of a state has a desired form and goes into the 0 eigenspace otherwise. In this way, perturbing quantum phases can be imagined be like changing what the local reduced density matrices should be like.
Now, given a set of reduced density matrices, the principle of maximum entropy states that the best inference of the global state should be the maximum entropy state compatible with all of the restrictions. In the classical case, continuously changing the local reduction of a state continuously changes its maximum entropy inference. However, in the quantum case, this is not true! A continuous deformation can lead to a discontinuous jump in the maximum entropy inference! This phenominon is exactly what a zero-temperature phase transition is.
This paper is filled with examples. They give toy examples designed to show universal features, and then they apply their principles to the analysis of the Ising model. They also go deeper into their results by getting more detail about the phase transition from examining conditional mutual entropy in the ground states.