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The pseudogap phase is considered as a new state of matter in the phasestring model of the doped Mott insulator, which is composed of two distinctregimes known as upper and lower pseudogap phases, respectively. The formercorresponds to the formation of spin singlet pairing and the latter ischaracterized by the formation of the Cooper pair amplitude and described by ageneralized Gingzburg-Landau theory. Elementary excitation in this phase is acharge-neutral object carrying spin-1/2 and locking with a supercurrent vortex,known as spinon-vortex composite. Here thermally excited spinon-vorticesdestroy the phase coherence and are responsible for nontrivial Nernst effectand diamagnetism. The transport entropy and core energy associated with aspinon-vortex are determined by the spin degrees of freedom. Such a spontaneousvortex liquid phase can be also considered as a spin liquid with a finitecorrelation length and gapped S=1/2 excitations, where a resonancelikenon-propagating spin mode emerges at the antiferromagnetic wavevector with adoping-dependent characteristic energy. A quantitative phase diagram in theparameter space of doping, temperature, and magnetic field is determined.Comparisons with experiments are also made.Comment: 22 pages, 12 figure

Lower pseudogap phase of Mott insulators: A spin/vortex liquid state