Universal Behavior beyond Multifractality of Wave Functions at Measurement-Induced Phase Transitions

• Main Authors: Sierant, P. (Author), Turkeshi, X. (Author)
• Format: Article
• Language: English
• Published: American Physical Society 2022
• Subjects: article; entropy; Entropy; Induced phase transition; Leading terms; Local measurement; Many body wave functions; Multifractal scaling; Multifractality; Order parameter; partition coefficient; phase transition; Quantum circuit; System size dependence; Universal behaviors; Wave functions
• Online Access: View Fulltext in Publisher
• ISBN: 00319007 (ISSN)
• DOI: 10.1103/PhysRevLett.128.130605

We investigate the structure of many-body wave functions of 1D quantum circuits with local measurements employing the participation entropies. The leading term in system size dependence of participation entropy indicates a model-dependent multifractal scaling of the wave functions at any nonzero measurement rate. The subleading term contains universal information about measurement-induced phase transitions and plays the role of an order parameter, being constant nonzero in the error-correcting phase and vanishing in the quantum Zeno phase. We provide robust numerical evidence investigating a variety of quantum many-body systems and provide an analytical interpretation of this behavior expressing the participation entropy in terms of partition functions of classical statistical models in 2D. © 2022 American Physical Society.