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This short review aims to summarize on What the Charge Density Waves can tell to other inhomogeneous states in strongly correlated systems, particularly to spin-polarized superconductors. We shall update on expanding observations of solitons in quasi 1D CDW conductors and link them to the growing information and demands related to inhomogeneous spin-polarized states in superconductors. The related theory, existent or awaited for, stretches from solitons in 1D models to vortex-like elementary excitations in 2D,3D ordered incommensurate CDWs and superconductors.
Using a mix of numerical and analytic methods, we show that recent NMR $^{17}$O measurements provide detailed information about the structure of the charge-density wave (CDW) phase in underdoped YBa$_2$Cu$_3$O$_{6+x}$. We perform Bogoliubov-de Gennes
A number of spectacular experimental anomaliescite{li-2007,fujita-2005} have recently been discovered in certain cuprates, notably {LBCO} and {LNSCO}, which exhibit unidirectional spin and charge order (known as ``stripe order). We have recently prop
The electron-phonon (e-ph) interaction remains of great interest in condensed matter physics and plays a vital role in realizing superconductors, charge-density-waves (CDW), and polarons. We study the two-dimensional Holstein model for e-ph coupling
To understand the origin of unconventional charge-density-wave (CDW) states in cuprate superconductors, we establish the self-consistent CDW equation, and analyze the CDW instabilities based on the realistic Hubbard model, without assuming any $q$-de
By using variational wave functions and quantum Monte Carlo techniques, we investigate the interplay between electron-electron and electron-phonon interactions in the two-dimensional Hubbard-Holstein model. Here, the ground-state phase diagram is tri