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Area of Science:

  • Quantum Physics
  • Condensed Matter Physics
  • Many-Body Systems

Background:

  • Continuous local measurements in quantum systems can induce phase transitions.
  • Free fermions with long-range hopping exhibit complex dynamics under such measurements.
  • Understanding these measurement-induced phase transitions is crucial for quantum information science.

Purpose of the Study:

  • To identify and characterize novel quantum phases in monitored long-range interacting fermionic systems.
  • To investigate the nature of entanglement and correlation functions within these phases.
  • To explore the theoretical framework governing these measurement-induced transitions.

Main Methods:

  • Analysis of quantum dynamics of free fermions with long-range hopping under continuous local measurements.
  • Perturbative renormalization group analysis to predict phase transitions.
  • Exact numerical simulations of monitored wave functions.
  • Analytical replica field theory approach.

Main Results:

  • Identification of an unconventional algebraic scaling phase for hopping decay exponents 1
  • Observation of algebraic entanglement entropy growth and slow algebraic decay of density-density correlations with fractional exponents.
  • Characterization of transitions to critical (logarithmic entanglement growth) and area law (constant entanglement entropy) phases.
  • Prediction of unconventional, modified sine-Gordon theory for phase transitions.

Conclusions:

  • The study reveals a distinct algebraic scaling phase in monitored quantum systems.
  • Measurement-induced phase transitions can be viewed as quantum phase transitions in effective non-Hermitian Hamiltonians.
  • The findings provide new insights into the interplay of interactions, measurements, and quantum phases.