Mutual information of spin systems from autoregressive neural networks

The discovery of topological order in quantum many-body systems [1] initiated a very fruitful exchange of ideas between solid-state physics and information theory. Many new theoretical tools developed to quantitatively describe the flow of information or the amount of information shared by different parts of the total system have been employed in the studies of physical systems [2]. Among these tools, quantum entanglement entropy or mutual information and their various alternatives were found to be particularly useful [3-10]. With their help, it was understood that some new phases of matter respect the same set of symmetries but differ in long-range correlations quantified by bipartite, tripartite, or higher information-theoretic measures such as mutual information [11, 12]. Turning this fact around, it is expected that calculating mutual information can provide hints about the topological phase of the system, playing a role similar to order parameters in the usual Landau picture of phase transitions (see for example [13, 14]). Indeed, such quantities are not only useful for theoretical understanding but are also measurable observables in experiments. For example, in Ref. [15] the mutual information in a quantum spin chain was measured demonstrating the area law [16] governing the scaling of mutual information with the volume of the bipartite partition.