The problem of the logarithmic discretization of an arbitrary positive function (such as the density of states) is studied in general terms. Logarithmic discretization has arbitrary high resolution around some chosen point (such as Fermi level) and it finds application, for example, in the numerical renormalization group (NRG) approach to quantum impurity problems (Kondo model), where the continuum of the conduction band states needs to be reduced to a finite number of levels with good sampling near the Fermi level. The discretization schemes under discussion are required to reproduce the original function after averaging over different interleaved discretization meshes, thus systematic deviations which appear in the conventional logarithmic discretization are eliminated. An improved scheme is proposed in which the discretization-mesh points themselves are determined in an adaptive way; they are denser in the regions where the function has higher values. Such schemes help in reducing the residual numeric artefacts in NRG calculations in situations where the density of states approaches zero over extended intervals. A reference implementation of the solver for the differential equations which determine the full set of discretization coefficients is also described.
Anisotropic suppression of quasiparticle weight in two-dimensional electron system with partially flat Fermi surface: two-loop renormalization-group analysis
本文对具有部分平坦费米面的二维电子系统进行了双圈重整化群分析。我们发现，{ \it不考虑配对机制}，准粒子的重量是各向异性抑制由于在费米面的平坦区域的几何奇异过程。当能量标度减小时，准粒子重量在平坦区域的中心附近受到最强烈的抑制，这定性地同意通过角度分辨光电子能谱实验对欠掺杂Bi $_2$ Sr $_2$ CaCu $_2$ O $_8$提出的各向异性赝能隙行为。
Adaptive Density-Matrix Renormalization-Group study of the disordered antiferromagnetic spin-1/2 Heisenberg chain
利用最近提出的自适应密度矩阵重整化群方法，我们研究了具有随机耦合常数的自旋- $1/2$反铁磁海森堡链的多种自旋-自旋关联，即体关联和端-端关联的平均值、体关联的典型值以及体关联的分布.我们的结果与强无序重整化群方法的预言惊人地一致。我们在Shu等人最近报道的整体平均相关性[Phys. Rev. B 94，174442（2016）]和端到端平均相关性中均未发现对数校正的任何暗示。我们报告计算的对数校正的存在性的端到端的相关性的清洁链。最后，我们已经确定，当适当地重新调整相关的李雅普诺夫指数，是一个狭窄的和普遍的（无序无关）的概率函数的散装相关性的分布。
