Measurement-induced dark state phase transitions in long-ranged fermion systems

Understand

We identify an unconventional algebraic scaling phase in the quantum dynamics of free fermions with long range hopping, which are exposed to continuous local density measurements.

• The unconventional phase is characterized by an algebraic entanglement entropy growth, and by a slow algebraic decay of the density-density correlation function, both with a fractional exponent.
• It occurs for hopping decay exponents $1< p \lesssim 3/2$ independently of the measurement rate.
• The algebraic phase gives rise to two critical lines, separating it from a critical phase with logarithmic entanglement growth at small, and an area law phase with constant entanglement entropy at large monitoring rates.