R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions

TL;DR

This paper introduces a second Rényi conditional mutual information measure to classify non-trivial mixed states and phase transitions in quantum systems, providing a new tool for understanding complex quantum phases.

Contribution

It develops an efficient numerical scheme for calculating the second Rényi CMI and applies it to classify mixed states and phase transitions in specific quantum models.

Findings

Second Rényi CMI effectively characterizes mixed state gaps.

It reveals behavior of phase transitions under decoherence.

The measure detects symmetry-breaking 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\'{e}nyi conditional mutual information (CMI). The CMI can measure mixed state ``gap'', estimated by the exponential decay rate of the second R\'{e}nyi CMI under a tripartition of system, which provides the second R\'{e}nyi version of the Markov length. We introduce an efficient numerical scheme for the calculation of the second R\'{e}nyi 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\'{e}nyi 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\'{e}nyi CMI exhibits specific behavior for the transition to strong-to-weak spontaneous symmetry breaking mixed phase.