The authors have numerically evaluated the energy of the staggered flux phase state (SFP), the d-wave resonating valence bond state, and the mixed SFP and d-wave state (SFP+d) of the extended t-J model at various hole densities ( delta ). The flux per plaquette and the size of the d-wave gap are taken as variational parameters. The calculation includes the kinetic energy, spin energy, the effective hole-hole interaction and the three-site pair-hopping term. They found that the SFP is stable against the projected Fermi liquid up to delta approximately=20%. For moderately large J, J/t>or=0.4, the SFP+d state may be favoured against the pure d-wave state but only at very low hole density ( delta approximately 20%). These calculations show that the pure SFP state is never the ground state at hole densities of experimental interest.
We study the stability of the Fermi-liquid and staggered flux phases in the t-J model for densities off half-filling using a large-N slave-boson approach. We examine the stability of the Fermi-liquid phase with respect to flux-density-wave (FDW) and bond-density-wave (BDW), or spin-Peierls, fluctuations at arbitrary wave vector as a function of doping \ensuremath{\delta} and the ratio \ensuremath{\delta}t/J. For densities near half-filling the Fermi liquid becomes unstable below a critical
tc towards an FDW state with an incommensurate wave vector k near (\ensuremath{\pi},\ensuremath{\pi}). The critical ratio \ensuremath{\delta}
tc/J for the Fermi-liquid--FDW transition diverges rapidly as \ensuremath{\delta}\ensuremath{\rightarrow}0. For \ensuremath{\delta}>18%, the FDW instability of the Fermi liquid is preempted by a BDW instability at incommensurate k. We examine the stability of the \ensuremath{\surd}2 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}2 staggered flux phase with respect to coupled FDW and BDW fluctuations and find that, upon lowering t/J at small \ensuremath{\delta}, the staggered flux phase remains stable for \ensuremath{\delta}t/J above a nonzero critical ratio and then develops an instability of primarily BDW character. At nonzero \ensuremath{\delta} and still lower \ensuremath{\delta}t/J, the staggered flux phase also develops an instability with respect to long-wavelength FDW fluctuations;
tc/J for this instability is approximately independent of \ensuremath{\delta}. We study the response function for such fluctuations analytically, showing the nontrivial k dependence induced by the presence of a small density of holes in the staggered phase. It is conjectured that this long-wavelength FDW instability is associated with the existence off half-filling of a commensurate flux phase with lower energy than the staggered flux phase.
Kinetic and magnetic energies of the staggered flux phase, with a fictitious flux of equal magnitude but opposite direction in adjacent square plaquettes, are calculated for the two-dimensional t-J model using the variational Monte Carlo method. They are compared to the energies of the resonating-valence-bond state, the flux phase with half a quantum per plaquette, and the projected Fermi-liquid state. For about 10% hole concentration the staggered flux phase has the lowest energy of the nonsuperconducting states, but its energy is still higher than that of the superconducting d-wave state.
Using a large-N slave-boson formulation of the t-J model on the square lattice that has explicit spinon-holon decoupling of the correlated electron, we study the stability and electromagnetic response of the commensurate flux phase in the limit near half filling. A region of stability for the flux phase is found located between a dimer phase region near half filling and a fluxless metallic phase region far from half filling. The commensurate flux phase itself is found to be a superconductor of the anyon type. Furthermore, it is shown that the parity--time-reversal--violating characteristic of this phase results in a frequency-dependent Faraday effect. This effect manifests itself as a zero-field Hall effect in the low-frequency limit, where the off-diagonal conductance scales with the hole concentration. Associated with this result, it is also found that the commensurate flux phase supports a series of optical absorption peaks at energies on the order of J. Lastly, inclusion of instanton tunneling events in the effective gauge-field action results in the confinement of the spinon and holon degrees of freedom. This confinement effect, however, weakens exponentially as one approaches the Mott transition. The present results are discussed in the context of the high-
Tc superconducting oxides.
We calculate the optical conductivity \ensuremath{\sigma}(\ensuremath{\omega}) of the Hubbard and t-J models on 10- and 16-site lattices, respectively, using a Lanczos method. Results are presented for various values of the couplings U/t, J/t, and band fillings, using free- and periodic-boundary conditions. We discuss the behavior of the kinetic energy in the ground state, the distribution of spectral weight of \ensuremath{\sigma}(\ensuremath{\omega}) between low and high energies and the sum rule. Indications of a Drude-like peak at low energy in the one-hole subspace are observed in both models. Assuming that holes behave like independent (mass-renormalized) particles in the normal state of the superconductors, our results also suggest that the optical midinfrared broadband observed experimentally can be explained by hole excitations of strongly correlated systems.
The optical conductivity of the 2D
t−J model and the origin of electron incoherence in the high-T
c cuprate superconductors: a variational study
Understanding the origin of electron incoherence is the first step toward a theoretical description of the non-Fermi liquid behavior of the high-T
c cuprate superconductors. Such electron incoherence manifests itself most evidently in the non-Drude behavior of the optical response of the system and the anomalous density fluctuation behavior in the long wave length limit. The spectral weight transfer related to such dissipative response, which is absent in conventional Fermi liquid metal, has direct consequence on the dc transport property of the system in the normal state and the superfluid stiffness in the superconducting state. It is found that such electron incoherence remains significant even in the clean limit and at low temperature and thus must be attributed to the strong electron correlation effect in the cuprate superconductors. Here we study such an intrinsic effect in the 2D
t−J model through the variational calculation of its optical conductivity
σ(ω). We assume a resonating valence bond ground state as our starting point and find that a significant portion of the total optical spectral weight remains incoherent throughout the phase diagram. The optical absorption is found to extend all the way to an energy of the order of the bare band width. We find that both the total optical weight
Kˉ and the integrated incoherent optical weight
I increase monotonically with doping, with their ratio
Rincoh=I/Kˉ decreasing monotonically with doping. Our results indicate that the majority part of electron incoherence in the 2D
t−J model can be attributed to the electron fractionalization mechanism assumed in such a treatment. We also find that the Drude weight deduced from
D=Kˉ−I scales linearly with hole doping, without any sign of a non-monotonic behavior in the overdoped regime.