Measurement-induced spatially nonuniform fluctuations of the local particle number and their crossover in a quasiperiodic free-fermion chain

Abstract:We study continuously monitored dynamics of a quasiperiodic free-fermion chain defined on a Fibonacci lattice. We focus on fluctuations of the local particle number, which do not exhibit quasiperiodic spatial modulation in the unitary limit. Remarkably, we demonstrate that they exhibit a nonuniform spatial pattern originating from the quasiperiodic long-range order under continuous measurement. Furthermore, employing both physicaland perpendicular-space analyses, we elucidate that a measurement-induced crossover emerges in fluctuations due to the interplay between the incommensurate modulation and the continuous measurement. While weak measurement yields a distribution reflecting the long-range spatial structure of the quasiperiodic system, an increase in measurement strength alters the distribution into one dominated by the local environment of each site. A structure-factor analysis further reveals that the weak-measurement regime is characterized by two dominant Bragg peaks corresponding to the golden-mean modulation, whereas the strong-measurement regime exhibits the characteristic Bragg-peak hierarchy of the Fibonacci pattern. We also elucidate that the measurement-induced crossover emerges in other physical quantities such as connected correlation functions. These findings offer insights into nonequilibrium quasiperiodic phenomena emerging in continuously monitored dynamics.

Statistical Mechanics (cond-mat.stat-mech); Disordered Systems and Neural Networks (cond-mat.dis-nn); Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)

arXiv:2607.03799 [cond-mat.stat-mech]

(or arXiv:2607.03799v2 [cond-mat.stat-mech] for this version)