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

• URL: http://arxiv.org/abs/2109.06882v3
• Date: Fri, 28 Jan 2022 11:39:59 GMT
• Title: Universal behavior beyond multifractality of wave-functions at measurement--induced phase transitions
• Authors: Piotr Sierant, Xhek Turkeshi
• Abstract summary: 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 non-zero measurement rate.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 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 constant non-zero 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.

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