An analysis of the t2- V (or extreme anisotropic next-nearest-neighbor Heisen-berg) model

The t2 - V model (involving next-nearest-neighbor hopping and nearest-neighbor repulsion) has been shown to be the strong electron-phonon limiting case of a molecular chain with cooperative breathing mode [Phys. Rev. B 86, 035453 (2012)]. We derive microscopically, using Green�s functions, the exact instability conditions in the two limiting cases of the t2 - V model for hard-core-bosons: the two-particle system and the half-filled system. We show explicitly that the critical repulsion Vc for the two-particle case is Vc /t2 = 4 for a ring of any size while for the half-filled case the Vc /t2 = 2 2 in the thermodynamic limit. Our t2 - V model can be mapped onto an extreme anisotropic Heisenberg model (with nearest-neighbor XY interaction and next-nearest-neighbor ising interaction) and is of the form J? i (Si+ Si+2 + H.c.) + J i Siz Si+1; our spin model correspondingly lends itself to exact instability solutions (by the Green�s function method) in the two limiting cases of two-magnons (the non-trivial highest excited state) and N � eel antiferromagnet ground state. Using finite size scaling, at other fillings of the t2 - V model (or other magnetizations of the spin model), we also obtain the critical repulsion numerically by using modified Lanczos. During the phase transition, away from half-filling (zero magnetization), the system undergoes a striking discontinuous transition from a superfluid to a supersolid [i.e., a superfluid homogeneously coexisting with a period-doubling charge-density-wave (antiferromagnetic) state]. At half-filling, the CDW (N eel) state and the superfluid state are mutually exclusive.