Quantum breakdown model: From many-body localization to chaos with scars
Quantum breakdown model: From many-body localization to chaos with scars
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DOI：
10.1103/physrevb.107.115171
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发表时间：
2022-08
影响因子：
3.7
通讯作者：
Biao Lian
中科院分区：
文献类型：
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作者：
Biao Lian
我们提出了一个费米子的量子模型来模拟电介质的电击穿过程。该模型包括 $M$ 有 $N$ 每个点的费米子模式，并且有一个守恒电荷 $Q$． 它有一个原位化学势 $\mu$ 有障碍 $W$，以及力量的相互作用 $J$ 当每个费米子向前移动一个位置时，限制每个费米子激发两个以上的费米子。我们展示 $N=3$ 紊乱模型 $W=0$ 显示了一个希尔伯特空间碎片化，并且除了极少数的Krylov子空间外是完全可解的。解析解表明 $N=3$ 模型表现出多体局部化（MBL） $M\rightarrow\infty$，它是稳定的 $W>0$ 正如我们的精确对角化（ED）所示。在 $N>3$，我们的ED提出了MBL到量子混沌的小交叉 $W$ as $M/N$ 横向减少 $1$，以及持久的MBL $W$． 在 $W=0$，在多电荷处存在着精确可解的多体疤痕平带 $Q$ 扇区，它在热力学极限中具有非零度量。我们进一步计算了加入粒子真空中的费米子的时间演化，当 $\mu/J1/2$)如果 $W\ll J$，没有故障 $W\gg J$。
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 $\mu$ 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 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 $\mu/J1/2$) if $W\ll J$, and no breakdown if $W\gg J$.