Universal behavior beyond multifractality of wave-functions at measurement–induced and localization phase transitions

Piotr Sierant,1, 2 Xhek Turkeshi3

1ICFO – Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain

2The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151, Trieste, Italy

3JEIP, USR 3573 CNRS, Collège de France, PSL Research University, 11 Place Marcelin Berthelot, 75321 Paris Cedex 05, France

The competition between unitary evolution that spreads information throughout the manybody system, and the monitoring action of an environment gives rise to dynamical phases separated by measurement-induced phase transitions. The first part of the talk will be devoted to numerical investigations of the structure of many-body wave functions of 1D random quantum circuits with local measurements across a measurement-induced transition between phases with volume-law and area-law scaling of entanglement entropy. The many-body wave functions are investigated by means of the participation entropies. The leading term in system size dependence of participation entropies indicates a multifractal scaling of the wavefunctions at any non-zero measurement rate. The sub-leading term contains universal information about measurement-induced phase transitions and plays the role of an order parameter, being non-zero in the volume-law phase and vanishing in the area-law phase. We provide an analytical interpretation of this behavior expressing the participation entropy in terms of partition functions of classical statistical models in 2D. The second part of the talk will concern the structure of many-body wave functions in systems that undergo localization transitions – both in presence and in absence of interactions. The ensuing measures of localization in the system alongside with the more conventional quantities will be used to discuss the stability of many-body localization in the Kicked Ising model.

1. P. Sierant, X. Turkeshi, arXiv:2109.06882

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