Mesoscopic Fluctuations and Multifractality at and across Measurement-Induced Phase Transition
by
WBBC/111
We study a problem of many-body fermionic system in d dimensions subjected to random measurements of local particle numbers. For free fermions, we have developed an analytical approach based on the Keldysh path-integral formalism and replica trick, and derived a non-linear sigma model in d+1 dimensions as an effective field theory of the problem [1]. This theory predicts, in d>1 dimensions, a measurement-induced phase transition, which has a meaning of localization transition for entanglement and quantum charge correlations [2], as supported by also supported by numerical simulations for d=2.
The talk will focus on statistical fluctuations of observables characterizing measurement-induced many-body quantum states over the ensemble of quantum trajectories [3]. The key observables are the two-point density correlation function C(r) and the particle-number covariance between spatially separated regions, G_{AB}. We explore their fluctuations in the delocalized and localized phases, as well as at the transition point. Our results exhibit a remarkable analogy to Anderson localization and mesoscopic physics of disordered systems, with C(r) and G_{AB} corresponding to two-point and two-terminal conductances, respectively. Our numerical and analytical findings lay the groundwork for mesoscopic theory of monitored systems, paving the way for various extensions.
If the time permits, I will also briefly discuss the emergence of Levy flights of quantum information in monitored systems [4] as well as the effect of interaction between fermions [5].
[1] I. Poboiko, P. Pöpperl, I.V. Gornyi, A.D. Mirlin, Phys. Rev. X 13, 041046 (2023)
[2] I. Poboiko, I.V. Gornyi, A.D. Mirlin, Phys. Rev. Lett. 132, 110403 (2024)
[3] I. Poboiko, I.V. Gornyi, A.D. Mirlin, arXiv: 2507.11312
[4] I. Poboiko, M. Szyniszewski, C.J. Turner, I.V. Gornyi, A.D. Mirlin, A. Pal, arXiv: 2501.12903
[5] I. Poboiko, P. Pöpperl, I.V. Gornyi, A.D. Mirlin, Phys. Rev. B 111, 024204 (2025)
Laboratory for Theoretical and Computational Physics