一种数值可达的多体热渡越定域的构造性理论
A constructive theory of the numerically accessible many-body localized to thermal crossover
摘要：
在精确对角化研究中观察到的多体局部化（MBL）到热交叉仍然知之甚少，因为可访问的系统尺寸太小，无法在渐近缩放制度。我们开发了一个模型的交叉短一维链中的MBL阶段是不稳定的多体共振的形成。该模型再现了几个属性的数值观察到的交叉，包括一个明显的相关长度指数$ν=1$，指数增长的无序强度，线性漂移的临界无序强度与系统大小，无标度共振，明显的$1/ω$依赖于无序平均光谱函数，和亚热纠缠熵的小的子系统。在交叉中，由局部扰动引起的共振在小于\emph{resonance length} $λ$的数值可达系统尺寸$L$处是罕见的。对于$L \gg \sqrtλ$，共振通常重叠，并且该模型不描述渐近转变。该模型进一步再现了有争议的数值观测，参考文献。[Šuntajs et al，2019]和[Sels & Polkovnikov，2020]声称与MBL不一致。因此，我们认为，迄今为止的数值是一致的MBL阶段的热力学极限。
英文摘要：
The many-body localised (MBL) to thermal crossover observed in exact diagonalisation studies remains poorly understood as the accessible system sizes are too small to be in an asymptotic scaling regime. We develop a model of the crossover in short 1D chains in which the MBL phase is destabilised by the formation of many-body resonances. The model reproduces several properties of the numerically observed crossover, including an apparent correlation length exponent $ν=1$, exponential growth of the Thouless time with disorder strength, linear drift of the critical disorder strength with system size, scale-free resonances, apparent $1/ω$ dependence of disorder-averaged spectral functions, and sub-thermal entanglement entropy of small subsystems. In the crossover, resonances induced by a local perturbation are rare at numerically accessible system sizes $L$ which are smaller than a \emph{resonance length} $λ$. For $L \gg \sqrtλ$, resonances typically overlap, and this model does not describe the asymptotic transition. The model further reproduces controversial numerical observations which Refs. [Šuntajs et al, 2019] and [Sels & Polkovnikov, 2020] claimed to be inconsistent with MBL. We thus argue that the numerics to date is consistent with a MBL phase in the thermodynamic limit.
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