Entanglement transitions and multifractality in monitored free-fermions with random long-range hopping

This paper investigates how random long-range power-law hopping affects the entanglement dynamics of monitored one-dimensional non-interacting complex fermions. While previous research established that standard 1D non-interacting fermions (with nearest-neighbor hopping) remain in an area-law phase under any finite monitoring, this study explores whether long-range hopping—which suppresses Anderson localization—can drive the system into different entanglement phases.

The authors model a 1D chain of spinless complex fermions with random power-law hopping, where the hopping strength decays as a function of distance with an exponent alpha. They apply a continuous monitoring protocol (Quantum State Diffusion) on the local occupation numbers. Because the Hamiltonian is quadratic, the Gaussian nature of the fermionic states is preserved, allowing for efficient numerical simulation. The researchers analyze the steady-state entanglement entropy (EE), mutual information (MI), and density-density correlation functions to map the phase diagram across varying monitoring strengths and hopping exponents.

The study reveals a rich phase diagram governed by the exponent alpha. For alpha <= 1, the entanglement entropy scales faster than logarithmically, approaching a volume-law scaling for alpha <= 1/2. For alpha > 3/2, the system is always in an area-law phase. In the intermediate regime (1 < alpha <= 3/2), the system undergoes a measurement-induced phase transition (MIPT) at a critical monitoring strength. At this critical point, the entanglement entropy scales logarithmically with system size, and the density-density correlation function exhibits multifractal features. These results demonstrate that superdiffusive classical hopping is a powerful mechanism for generating entanglement in monitored quantum systems.