论文标题
一种固定在热跨界的数值可访问多体的建设性理论
A constructive theory of the numerically accessible many-body localized to thermal crossover
论文作者
论文摘要
在精确的对角线化研究中观察到的多体局部（MBL）到热跨界，因为可访问的系统尺寸太小，无法处于渐近缩放状态，因此仍然对其进行了众多理解。我们开发了一个在短的1D链中的交叉模型，其中MBL相通过多体共振的形成破坏了稳定。该模型重现了数值观察到的交叉的多种特性，包括明显的相关长度指数$ν= 1 $，无序强度的无效时间的指数增长，临界无序强度的线性漂移，无限制的谐振，无尺度的无限量，明显的$ 1/ω$依赖于无序的光谱功能和子细分的依赖性分子和分子的依赖性，并依赖于子细分的杂物。在交叉中，局部扰动引起的共振在数值可访问的系统尺寸$ l $上很少，该系统尺寸$ l $小于\ emph {resonance Length} $λ$。对于$ l \ gg \sqrtλ$，共振通常重叠，并且该模型不会描述渐近转变。该模型进一步再现了有争议的数值观察结果。 [šuntajs等人，2019年]和[Sels＆Polkovnikov，2020年]声称与MBL不一致。因此，我们认为迄今为止的数字与热力学极限中的MBL相一致。
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.
