  The pseudogap phase is considered as a new state of matter in the phase
string model of the doped Mott insulator, which is composed of two distinct
regimes known as upper and lower pseudogap phases, respectively. The former
corresponds to the formation of spin singlet pairing and the latter is
characterized by the formation of the Cooper pair amplitude and described by a
generalized Gingzburg-Landau theory. Elementary excitation in this phase is a
charge-neutral object carrying spin-1/2 and locking with a supercurrent vortex,
known as spinon-vortex composite. Here thermally excited spinon-vortices
destroy the phase coherence and are responsible for nontrivial Nernst effect
and diamagnetism. The transport entropy and core energy associated with a
spinon-vortex are determined by the spin degrees of freedom. Such a spontaneous
vortex liquid phase can be also considered as a spin liquid with a finite
correlation length and gapped S=1/2 excitations, where a resonancelike
non-propagating spin mode emerges at the antiferromagnetic wavevector with a
doping-dependent characteristic energy. A quantitative phase diagram in the
parameter space of doping, temperature, and magnetic field is determined.
Comparisons with experiments are also made.
