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 $\ensuremath{\mu}$ 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 $M\ensuremath{\rightarrow}\ensuremath{\infty}$, 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 $\ensuremath{\mu}/J<1/2$ ($\ensuremath{\mu}/J>1/2$) if $W\ensuremath{\ll}J$, and no breakdown if $W\ensuremath{\gg}J$.