In this study, the problem of strong Coulomb interactions in topological superconducting wire is analyzed by means of the density-matrix-renormalization-group (DMRG) approach. To analyze properties of edge states in the BDI-class structure, a quantity called Majorana polarization is used. From its dependence on wire length and an entanglement-spectrum degeneracy, topological phase diagrams are obtained. The DMRG calculations for the Shubin-Vonsovsky–type model of the wire show the transformation of phases with Majorana single and double modes (MSMs and MDMs, respectively) under the increase of onsite and intersite correlations. In particular, we demonstrate different scenarios including the possibilities of both induction and suppression of the MSMs and MDMs. It is shown that in the strongly correlated regime, the contributions of single-particle excitations to the Majorana-type states significantly decrease at low magnetic fxields. Moreover, the $t-J^{*}-V$ model is derived allowing to study the effective interactions and improve the DMRG numerics. It is found out that in the limiting case of the effective Hamiltonian with infinitely strong onsite repulsion, $t$ model, the topological phases are destroyed. Finally, the ways to probe the MSMs and MDMs via the features of caloric functions are discussed.

中文翻译：

---

非平凡拓扑类BDI中的Majorana模问题中的强库仑相互作用

在这项研究中，通过密度矩阵重整化组（DMRG）方法分析了拓扑超导线中的强库仑相互作用问题。为了分析BDI类结构中边缘状态的属性，使用了称为Majorana极化的量。从其对导线长度的依赖性和纠缠光谱的简并性，获得拓扑相图。导线的Shubin-Vonsovsky型模型的DMRG计算表明，在现场和现场间相关性增加的情况下，具有Majorana单模和双模（分别为MSM和MDM）的相变。特别是，我们展示了不同的方案，包括感应和抑制MSM和MDM的可能性。结果表明，在高度相关的制度下，在低磁场下，单粒子激发对马约拉那型态的贡献显着降低。而且，$Ť-{Ĵ}^{*}-V$推导出模型，以研究有效的相互作用并改善DMRG数值。发现在无限强现场排斥的有效哈密顿量的极限情况下，$Ť$模型，拓扑阶段被破坏。最后，讨论了通过热量函数的特征探测MSM和MDM的方法。