Fock空间传播子的标度性与多体局域化跃迁的多重分形
Scaling of Fock-space propagator and multifractality across the many-body localization transition
摘要：
我们实现了一个递归的格林函数方法来提取的Fock空间（FS）传播子和相关的自能跨越多体局域化（MBL）的过渡，在一个随机现场势的一维相互作用费米子。结果表明，局域FS自能虚部的典型值Δ t与初始局域态的衰变率有关，它是热态到MBL相变的概率序参量，可以用来表征相变的临界性质以及MBL态作为无序强度W的函数的多重分形性质.特别地，我们证明了从Δ t中提取的分形维数D_s从MBL相的D_s<1到热相的D_s= 1的不连续跳跃。此外，Δ t在热-MBL相变过程中遵循非对称的有限尺寸标度形式，在临界点W_c处，热相的非遍历体积发散为Kosterlitz-less-like本质奇点，并控制着Δ t在接近W_c时的连续消失.而从Δ t提取的相关长度（λ）在从MBL相位向W c方向逼近时呈现幂律发散。
英文摘要：
We implement a recursive Green function method to extract the Fock space (FS) propagator and associated self-energy across the many-body localization (MBL) transition, for one-dimensional interacting fermions in a random onsite potential. We show that the typical value of the imaginary part of the local FS self-energy, Δ_t, related to the decay rate of an initially localized state, acts as a probabilistic order parameter for the thermal to MBL phase transition; and can be used to characterize critical properties of the transition as well as the multifractal nature of MBL states as a function of disorder strength W. In particular, we show that a fractal dimension D_s extracted from Δ_t jumps discontinuously across the transition, from D_s<1 in the MBL phase to D_s= 1 in the thermal phase. Moreover, Δ_t follows an asymmetrical finite-size scaling form across the thermal-MBL transition, where a non-ergodic volume in the thermal phase diverges with a Kosterlitz-Thouless like essential singularity at the critical point W_c, and controls the continuous vanishing of Δ_t as W_c is approached. In contrast, a correlation length (ξ) extracted from Δ_t exhibits a power-law divergence on approaching W_c from the MBL phase.
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