论文标题
在多体定位过渡中的Fock空间传播器的缩放和多重纹理的缩放
Scaling of Fock-space propagator and multifractality across the many-body localization transition
论文作者
论文摘要
我们实施了一种递归绿色功能方法，以在多体定位（MBL）过渡中提取Fock空间（FS）传播器和相关的自能量，以在现场潜力中以一维相互作用的费用进行一维相互作用。我们表明，与最初局部状态的衰减速率有关的局部FS自能的虚拟部分的典型值是热热到MBL相变的概率阶参数；并且可以用来表征过渡的临界特性以及MBL状态的多型性质作为无序强度W的函数。特别是，我们表明，从Δ_T中提取的分形维度D_S不连续地跳过整个过渡，从MBL相位的D_S <1到MBL相位的D_S = 1在热相位的D_S = 1。此外，Δ_T遵循整个热MBL过渡的不对称有限尺寸缩放形式，在热相中，热相中的非刚性体积与kosterlitz-y-thouse the-thoune the the the the the Priendital sigental in the Criendent w_c处的奇异性，并控制Δ_T的连续消失Δ_T与w_c接近。相反，从Δ_T提取的相关长度（ξ）在接近MBL相的W_C时表现出幂律分歧。
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.
