***New paper in PRX***: Order parameters from entanglement


In their new paper "Entanglement order parameters and critical behavior for topological phase transitions and beyond", published in Physical Review X, authors Mohsin Iqbal and Norbert Schuch show how to construct entanglement-based order parameters which provide novel ways to probe topological and conventional phase transitions alike.

Different phases of matter are characterized by the symmetries they break. This is detected by local order parameters, which also provide universal fingerprints ­­(called "critical exponents") revealing structures common to seemingly different phase transitions. Exotic quantum phases, whose order manifests in global quantum entanglement rather than local properties, defy this picture. But how can we extract universal fingerprints for such phases? Will suitable entanglement-based order parameters match the behavior of known ones, or can novel universal fingerprints appear? And if the latter, might this yield novel probes even for conventional phases?

In their recent work, which has just been published in Physical Review X, Mohsin Iqbal and our group leader Norbert Schuch successfully address these questions: They devise a way to construct and measure entanglement-based order parameters in computer simulations, and apply them to exotic as well as conventional phase transitions. They find that on the one hand, these order parameters reproduce well-known universal fingerprints associated to those transitions, but on the other hand, they also yield hitherto unknown critical exponents and thus give access to additional information.

They achieve this by using tensor network wavefunctions, which describe the system through local tensors carrying physical and entanglement degrees of freedom. Physical symmetries and topological order can be equally encoded through symmetries on those degrees of freedom. By constructing order and disorder parameters from all symmetries of the tensor, probes can be obtained which are sensitive to conventional symmetry breaking and topological order alike. On the one hand, this allows them to define order parameters and to measure critical exponents for topological transitions. On the other hand, however, they show that this also provides a way for constructing an entirely novel disorder operator for the 2D quantum Ising model (and other symmetry breaking transitions) which they find to exhibit a hitherto unknown critical exponent. This shows that order parameters directly probing the entanglement provide a way to access new information about critical behavior for both topological and conventional phase transitions.

More information, including a popular summary and the full manuscript (open access), can be found on the Physical Review X website.

This work has received support through the ERC grant SEQUAM.

figure from Entanglement order parameters and critical behavior for topological phase transitions and beyond” by Mohsin Iqbal and Norbert Schuch