Studies on the interplay between the charge order and the d-wave superconductivity in the copper-oxide high T_c superconductors are reviewed with a special emphasis on the exploration based on the unconventional concept of the electron fractionalization and its consequences supported by solutions of high-accuracy quantum many-body solvers. Severe competitions between the superconducting states and the charge inhomogeneity including the charge/spin striped states revealed by the quantum many-body solvers are first addressed for the Hubbard models and then for the ab initio Hamiltonians of the cuprates derived without adjustable parameters to represent the low-energy physics of the cuprates. The charge inhomogeneity and superconductivity are born out of the same mother, namely, the carrier attraction arising from the strong Coulomb repulsion near the Mott insulator (Mottness) and accompanied electron fractionalization. The same mother makes the severe competition of the two brothers inevitable. The electron fractionalization has remarkable consequences on the mechanism of the superconductivity. Recent explorations motivated by the concept of the fractionalization and their consequences on experimental observations in energy-momentum resolved spectroscopic measurements including the angle resolved photoemission spectroscopy (ARPES) and the resonant inelastic X-ray spectroscopy (RIXS) are overviewed, with future vision for the integrated spectroscopy to challenge the long-standing difficulties in the cuprates as well as in other strongly correlated matter in general.

中文翻译：

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电荷序和超导性作为铜酸盐高温超导体中的竞争兄弟

氧化铜高T _{c 中}电荷顺序与d波超导相互作用的研究回顾了超导体，特别强调了基于电子分馏的非常规概念及其由高精度量子多体求解器的解决方案支持的后果的探索。超导态和电荷不均匀性（包括由量子多体求解器揭示的电荷/自旋条纹态）之间的严重竞争首先针对哈伯德模型进行解决，然后针对没有可调参数导出的铜酸盐的从头算哈密顿量来表示低-铜酸盐的能量物理学。电荷不均匀性和超导性源于同一个母体，即由莫特绝缘体（Mottness）附近的强库仑斥力引起的载流子吸引力并伴随电子分馏。同一个母亲，让两兄弟的激烈竞争在所难免。电子分馏对超导机理具有显着影响。概述了由分馏概念及其对能量动量分辨光谱测量中实验观察结果的影响，包括角分辨光电子能谱 (ARPES) 和共振非弹性 X 射线光谱 (RIXS) 的最新探索，以及对集成光谱来挑战铜酸盐以及其他强相关物质中长期存在的困难。