论文标题
在随机场海森贝格链中多体定位的嵌套迭代转移对角线化
Nested Iterative Shift-invert Diagonalization for Many-body Localization in the Random-field Heisenberg Chain
论文作者
论文摘要
我们使用带有迭代线性求解器的嵌套移动兰开斯方法研究了随机场海森堡链的多体定位。我们在每个兰开斯迭代中使用最小剩余方法（minres）。所提出方法的记忆消耗仅与希尔伯特空间的维度成正比。我们还引入了一个预处理，该预处理考虑了随机场海森堡链中疾病和相互作用的影响。作为多体定位过渡的探测，我们提出了一个名为Twist Operator的统一操作员，该操作员在真实空间中具有明确的解释。我们讨论了其热和局部本征态的行为。我们证明了嵌套迭代转换对角线化方法的效率，该方法具有多体定位问题的拟议预调节器，并更精确地基于对扭曲操作员的期望值的有限尺寸分析，以更精确地估算随机场海森贝格链的过渡点。
We study the many-body localization of the random-field Heisenberg chain using the nested shift-invert Lanczos method with an iterative linear solver. We use the minimum residual method (MINRES) inside each Lanczos iteration. The memory consumption of the proposed method is only proportional to the dimension of the Hilbert space. We also introduce a preconditioner that takes into account the effects of disorder and interaction in the random-field Heisenberg chain. As a probe of many-body localization transition, we propose a unitary operator called the twist operator, which has a clear interpretation in the real space. We discuss its behavior for thermal and localized eigenstates. We demonstrate the efficiency of the nested iterative shift-invert diagonalization method with the proposed preconditioner for the many-body localization problem and estimate the transition point of the random-field Heisenberg chain more precisely based on the finite-size analysis of the expectation value of the twist operator.
