论文标题
量子分解模型：从多体定位到疤痕的混乱
A Quantum Breakdown Model: from Many-body Localization to Chaos with Scars
论文作者
论文摘要
我们提出了一个模拟电介质电解过程的费米斯的量子模型。该型号由每个站点的$ n $ fermion模式组成，并具有保守的费用$ q $。它具有带有混乱$ W $的现场化学势$μ$，以及强度的相互作用$ j $限制了每个费米昂在一个站点前进时会更加激发两个费米子。我们显示了$ n = 3 $模型，$ w = 0 $显示了希尔伯特太空碎片化，除了很少的Krylov子空间外，完全可以解决。分析解决方案表明，$ n = 3 $模型以$ m \ rightarrow \ infty $的形式显示多体定位（MBL），这是稳定的，因为$ w> 0 $，正如我们的确切对角线化（ED）所示。在$ n> 3 $时，我们的ED建议以$ W $ $ w $的量子混乱为$ m/n $减少$ 1 $的量子混乱，并在$ w $ $ w $上持续下降。在$ w = 0 $时，有许多充电$ q $扇区中存在一个完全可解决的多体疤痕扁平带，在热力学限制中具有非零度量。我们进一步计算添加到粒子真空中的费米的时间演变，如果$ w \ ll j $，当$μ/j <1/2 $（$μ/j> 1/2 $）时显示出崩溃（介电）阶段，如果$ w \ w \ gg j $，则没有崩溃。
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 the $N=3$ model with disorder $W=0$ show 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 $M\rightarrow\infty$, which is stable against $W>0$ as our exact diagonalization (ED) shows. At $N>3$, our ED suggests a 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 $W\ll J$, and no breakdown if $W\gg J$.
