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GLAM Special Seminar: A Quantum Breakdown Model: from Many-body Localization to Chaos with Scars

Biao Lian (Princeton University)
McCullough, room #335

Abstract: 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 u 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 the N=3 model with zero disorder shows a Hilbert space fragmentation in all charge Q sectors and is exactly solvable except for very few Krylov subspaces. It exhibits many-body localization (MBL) as M tends to infinity, which is stable against disorders as exact diagonalization (ED) shows. At N>3, ED suggests a MBL to quantum chaos crossover as M/N decreases across 1. The zero disorder model also shows an exactly solvable many-body scar flat band exists in many charge Q sectors. The time evolution of the model with a fermion added to the particle vacuum shows the model is in a breakdown (dielectric) phase when u/J<1/2 (u/J>1/2). The breakdown is local when M/N>>1, and is global when M/N<<1.