Quantum breakdown model: From many-body localization to chaos with scars

We propose a quantum model of fermions simulating the electrical breakdown process of dielectrics. The model consists of M sites with N fermion modes per site and has a conserved charge Q. It has an on-site chemical potential μ with disorder W and an interaction of strength J restricting each fermion to excite two more fermions when moving forward by one site. We show that the N=3 model with disorder W=0 shows a Hilbert space fragmentation and is exactly solvable except for very few Krylov subspaces. The analytical solution shows that the N=3 model exhibits many-body localization (MBL) as M→∞, which is stable against W>0 as our exact diagonalization (ED) shows. At N>3, our ED suggests an MBL to quantum chaos crossover at small W as M/N decreases across 1, and persistent MBL at large W. At W=0, an exactly solvable many-body scar flat band exists in many charge Q sectors, which has a nonzero measure in the thermodynamic limit. We further calculate the time evolution of a fermion added to the particle vacuum, which shows a breakdown (dielectric) phase when μ/J<1/2 (μ/J>1/2) if W≪J, and no breakdown if W≫J.