摘要：

  Recently many experiments reported various charge density waves (CDW) in different cuprate families. Some of these have been carefully measured in great detail  by scanning tunneling microscopy (STM) in the low temperature superconducting states. Based on the well-known strongly correlated t-J model and by using  a renormalized mean field theory[1], we obtain self-consistent solutions of a number of nearly degenerate states with intertwined orders. Besides CDW order, these states also include pair density wave (PDW) order and/or possibly spin density wave (SDW).  PDW with finite momentum for the pairing order may or may not have superconducting long range order.    Spectra of one of these states without SDW will be discussed in detail  and shown excellent agreement  with spectra of  STM even for the Oxygen sites not included in the t-J model [2].  The calculated quasi-particle spectra are compared with  the angle-resolved photoemission spectra(ARPES) for cuprates in the normal and superconducting states. These results show many exotic properties of cuprates, such as Fermi arc at normal state, two gaps and particle-hole asymmetry at the antinodal direction at superconducting state, etc.. The effect of strong correlation will be discussed.