R\'enyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions
Abstract
Discovering and classifying non-trivial mixed states and mixed state phase transitions are some of the most important current issues in condensed matter and quantum information. In this study, we investigate some non-trivial mixed states and phase transitions between them by using the second R\'enyi conditional mutual information (CMI). The CMI can measure mixed state ``gap'', estimated by the exponential decay rate of the second R\'enyi CMI under a tripartition of system, which provides the second R\'enyi version of the Markov length. We introduce an efficient numerical scheme for the calculation of the second R\'enyi CMI based on the doubled Hilbert space formalism, and study the classification of non-trivial mixed states and the emergence of mixed state phase transitions for (i) the cluster model under odd-site local Z decoherence and (ii) transverse field Ising model under both ZZ and X decoherence. The second R\'enyi CMI is a powerful measure to study non-trivial mixed ``gapped" quantum matters and mixed phase transitions. In addition to this, the present study shows that the second R\'enyi CMI exhibits specific behavior for the transition to strong-to-weak spontaneous symmetry breaking mixed phase.
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