Date of Original Version
The impact of the spin-flip terms on the (static and dynamic) charge and spin correlations in the Luttingerliquid ground state of the one-dimensional (1D) t-J model is assessed by comparison with the same quantities in the 1D t-Jz model, where spin-flip terms are absent. We employ the recursion method combined with a weak-coupling or a strong-coupling continued-fraction analysis. At Jz /t=0+ we use the Pfaffian representation of dynamic spin correlations. The changing nature of the dynamically relevant charge and spin excitations on approach of the transition to phase separation is investigated in detail. At the transition point, the t-Jz ground state has zero (static) charge correlations and very short-ranged (static) spin correlations, whereas the t-J ground state is critical. The t-Jz charge excitations (but not the spin excitations) at the transition have a single-mode nature, whereas charge and spin excitations have a complicated structure in the t-J model. A major transformation of the t-J spin excitations takes place between two distinct regimes within the Luttingerliquid phase, while the t-Jz spin excitations are found to change much more gradually. In the t-Jz model, phase separation is accompanied by Néel long-range order, caused by the condensation of electron clusters with an already existing alternating up-down spin configuration (topological long-range order). In the t-J model, by contrast, the spin-flip processes in the exchange coupling are responsible for continued strong spin fluctuations (dominated by two-spinon excitations) in the phase-separated state.
Shu Zhang, Michael Karbach, Gerhard Müller, and Joachim Stolze. Charge and spin dynamics in the one-dimensional t-Jz and t-J models. Phys. Rev. B 55 (1997), 6491-6503.
Available at: http://dx.doi.org/10.1103/PhysRevB.55.6491