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Approaching many-body localization from disordered Luttinger liquids via the functional renormalization group

机译:通过功能重整化组从乱序的Luttinger液体中进行多体定位

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We study the interplay of interactions and disorder in a one-dimensional fermion lattice coupled adiabatically to infinite reservoirs. We employ both the functional renormalization group (FRG) as well as matrix product state techniques, which serve as an accurate benchmark for small systems. Using the FRG, we compute the length-and temperature-dependence of the conductance averaged over 10~4 samples for lattices as large as 10~5 sites. We identify regimes in which non-Ohmic power law behavior can be observed and demonstrate that the corresponding exponents can be understood by adapting earlier predictions obtained perturbatively for disordered Luttinger liquids. In the presence of both disorder and isolated impurities, the conductance has a universal single-parameter scaling form. This lays the groundwork for an application of the functional renormalization group to the realm of many-body localization.
机译:我们研究了与绝热耦合的一维费米子晶格中相互作用和无序的相互作用。我们同时使用功能重整化组(FRG)和矩阵乘积状态技术,它们可作为小型系统的准确基准。使用FRG,我们可以计算10〜5个点的晶格在10〜4个样本中平均的电导的长度和温度依赖性。我们确定了可以观察到非欧姆幂律行为的制度,并证明可以通过适应对无序Luttinger液体扰动而获得的早期预测来理解相应的指数。在存在无序和孤立的杂质的情况下,电导具有通用的单参数缩放形式。这为功能重整化组应用于多体定位领域奠定了基础。

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