1304.3007 (A. Ghosh et al.)

An analysis of the $t_2-V$ (or extremely anisotropic
next-nearest-neighbor Heisenberg) model    [PDF]

A. Ghosh, S. Yarlagadda

The $t_2-V$ model (involving next-nearest-neighbor hopping and nearest-neighbor repulsion) has been shown to depict the limiting case of strong electron-phonon coupling in a molecular chain with cooperative breathing mode [R. Pankaj and S. Yarlagadda, Phys. Rev. B {\bf 86}, 035453 (2012)]. Our $t_2-V$ model can be mapped onto an extremely anisotropic Heisenberg model (with next-nearest-neighbor XY interaction and nearest-neighbor ising interaction) and is of the form $J_{\perp}\sum_i (S^+_{i-1} S^-_{i+1} + {\rm H.c.}) + J_{\parallel} \sum_i S^z_i S^z_{i+1}$. Using finite size scaling, at non-half-fillings of the $t_2-V$ model (or non-zero magnetizations of the spin model), we numerically obtain the critical repulsion for a quantum phase transition by using modified Lanczos method. During the 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 charge-density-wave (N\'eel) state and the superfluid state are mutually exclusive. We also derive microscopically, using Green's functions, the exact instability conditions in the two limiting cases of the $t_2-V$ model for hard-core-bosons: the two-particle system and the half-filled system. We show explicitly that the critical repulsion $V_c$ for the two-particle case is $V_c/t_2 = 4$ for a ring of any size while for the half-filled case the $V_c/t_2 = 2 \sqrt{2}$ in the thermodynamic limit. 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.

View original: http://arxiv.org/abs/1304.3007