| Spin and charge are two fundamental degrees of freedom in strongly correlated electron systems. In this thesis we study low-energy effective theory and phase transitions of spin and charge in a variety of strongly correlated systems.;First, we study effective theory of magnetic phase transition in Sp(4) spin system and iron-based superconductors. Quantum phase transitions beyond Landau paradigm has been proposed in SU(2) spill model. We generalize this paradigm to Sp(4) model, which can be realized using spin- 32 cold atoms on optical lattice. In iron-based superconductors, we study low-energy effective theory for magnetic and structural phase transitions, and present a global phase diagram of the two phase transitions.;Second, we study spin and charge fluctuations on triangular lattice, and compare our results with experiments on organic Mott insulator kappa-(ET) 2(CN)2. We show that the spin liquid state observed in experiments can be explained by Z2 spin liquid theory which contains spin-½ spinon and Z2 vison excitations. We also argue that near the Mott-insulator-to-metal transition there are fractionalized spinless charge excitations, which form exciton bound states near the transition.;At last, we study spin and charge excitations in high-T c cuprates. We describe fluctuating two-dimensional metallic antiferromagnets by a gauge-theoretic description of an 'algebraic charge liquid' involving spinless fermions and a spin S = 1/2 complex scalar. We propose a phenomenological effective lattice Hamiltonian which describes the binding of these particles into gauge-neutral, electron-like excitations, and describe its implications for the electron spectral function across the entire Brillouin zone. We discuss connections of our results to photoemission experiments in the pseudogap regime of the cuprate superconductors. |
