S. Zhang et al., CHARGE AND SPIN DYNAMICS IN THE ONE-DIMENSIONAL T-J(Z) AND T-J MODELS, Physical review. B, Condensed matter, 55(10), 1997, pp. 6491-6503
The impact of the spin-flip terms on the (static and dynamic) charge a
nd spin-correlations in the Luttinger-liquid ground state of the one-d
imensional (ID) t-J model is assessed by comparison with the same quan
tities in the 1D t-J(z) model, where spin-flip terms are absent. We em
ploy the recursion method combined with a weak-coupling or a strong-co
upling continued-fraction analysis. At J(z)/t=0(+) we use the Pfaffian
representation of dynamic spin correlation's. The changing nature of
the dynamically relevant charge and spin excitations on approach of th
e transition to phase separation is investigated in detail. At the tra
nsition point, the t-J(z) ground state has zero (static) charge correl
ations and very short-ranged (static) spin correlations, whereas the t
-J ground state is critical. The t-J(z) charge excitations (but not th
e spin excitations) at the transition have a single-mode nature, where
as 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 Luttinger-liquid phase, while
the t-J(z) spin excitations are found to change much more gradually.
In the t-J(z) model, phase separation is accompanied by Neel long-rang
e order, caused by the condensation of electron clusters with an alrea
dy existing alternating up-down spin configuration (topological long-r
ange order). In the t-J model, by contrast, the spin-flip processes in
the exchange coupling are responsible for continued strong spin fluct
uations(dominated by two-spinon excitations) in the phase-separated st
ate.