In this paper, by using two dimensional (2D) Hubbard models with-flux phase and that on a hexagonal lattice as examples, we explore spin-charge-separated solitons in nodal antiferromagnetic (AF) insulator-an AF order with massive Dirac fermionic excitations (see detail in the paper). We calculate fermion zero modes and induced quantum numbers on solitons (half skyrmions) in the continuum limit, which are similar to that in the quasi one-dimensional conductor polyacetylene (CH)x and that in topological band insulator. In particular, we find some novel phenomena: thanks to an induced staggered spin moment, a mobile half skyrmion becomes a fermionic particle; when a hole or an electron is added, the half skyrmion turns into a bosonic particle with charge degree of freedom only. Our results imply that nontrivial induced quantum number on solitons may be a universal feature of spin-charge separation in di erent systems.

A mutual-Chern-Simons Lagrangian is derived as a minimal field theory description of the phasestring model for doped antiferromagnets. Such an e ective Lagrangian is shown to retain the full symmetries of parity, time-reversal, and global SU (2) spin rotation, in contrast to conventional Chern-Simons theories where first two symmetries are usually broken. Two ordered phases, i.e., antiferromagnetic and superconducting states, are found at low temperatures as characterized by "dual" Meissner e ects and dual flux quantization conditions due to the mutual-Chern-Simons gauge structure. A "dual" confinement in charge/spin degrees of freedom occurs such that no true spincharge separation is present in these ordered phases, but the spin-charge separation/deconfinement serves as a driving force in the unconventional phase transitions of these ordered states to disordered states.

In this paper a duality between the d=2 Wen-plaquette model in a transverse field and the d=1 Ising model in a transverse field is used to learn the nature of the quantum phase transition (QPT) between a spin-polarized phase and a topological ordered state with the string-net condensation. The QPT is not induced by spontaneous symmetry breaking and there are no conventional Landautype local order parameters. Instead the string-like non-local order parameters are introduced to describe the QPT. In particular, the duality character between the open-string and closed string for the QPT are explored.

The properties of a class of topological quantum phase transition (TQPT) are analyzed based on a model proposed by Haldane. We study the effect of finite temperature on this phase transition. We have found that finite temperature would drive this TQPT to be a crossover, while it is stable against the weak short range interaction. When the interaction is strong enough, however, this TQPT is unstable and other states would emerge. Then we investigate the effect of the on-site energy in the original haldane model. The critical di erence between our TQPT and the topological phase transition in conventional quantum Hall system is discussed. Finally, we discuss the potential application of our analysis to a topological phase transition proposed in a realistic system.

Based on an e ective model of a doped antiferromagnetic Mott insulator, we show that a doped hole will induce a dipole-like spin configuration in a spin ordered phase at low doping. The kinetic energy of doped holes is severely frustrated and a hole-dipole object is actually localized or selftrapped in space. Without a balance from the kinetic energy, the long-range dipole-dipole interaction between doped holes will dominate the low-energy physics, leading to an inhomogeneity instability as hole-dipoles collapse into stripes. Both antiphase metallic stripes of quarter-filling and antiphase insulating stripes along a diagonal direction are discussed as composed of hole-dipoles as elementary building blocks. Stripe melting and competing phases are also discussed.