Mechanism of CDW-SDW Transition in One Dimension

The phase transition between charge- and spin-density-wave (CDW, SDW)phases is studied in the one-dimensional extended Hubbard model athalf-filling. We discuss whether the transition can be described by Gaussian and spin-gap transitions under charge-spin separation, orby the direct CDW-SDW transition. These phase boundaries are determinedby level crossings of excitation spectra which are identified accordingto discrete symmetries of wave functions. We conclude that the Gaussianand spin-gap transitions take place separately from the weak- tointermediate-coupling region, and a bond-order-wave phase existsbetween the CDW and the SDW states. Our results are also consistentwith those of the strong-coupling theory and of the direct evaluationof the CDW order parameters.