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We have developed the mean-field theory of coexisting charge-density waves (CDW) and unconventional charge-density waves (UCDW). The double phase transition manifests itself in the thermodynamic quantities and in the magnetic response, such as spin susceptibility and spin-lattice relaxation rate. Our theory applies to quasi-one dimensional (TaSe_4)_2I, where above the CDW transition, thermal fluctuations die out rapidly, but robust pseudogap behaviour is still detected. We argue, that the fluctuations are suppressed due to UCDW, which partially gaps the Fermi surface, and causes non-Fermi-liquid (pseudogap) behaviour.

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