Simultaneous charge ordering and spin dimerization in quasi-two-dimensional quarter-filled ladders

Abstract

We study the spin-pseudospin Hamiltonian of the Ising model in transverse field (IMTF) for pseudospins, coupled to the $\mathrm{XY}$ spins on a triangular lattice. This model appears from analyses of the quarter-filled ladder compound ${\mathrm{NaV}}_{2}{\mathrm{O}}_{5},$ and pseudospins represent its charge degrees of freedom. In the molecular-field approximation we find that the model possesses two phases: charge-disordered phase without spin gap and a low-temperature phase containing both the antiferroelectric (zigzag) charge order and spin dimerization (spin gap). The phase transition is of the second kind, and the calculated physical quantities are just as those one expects from the Landau theory. One of the particular features of the phase diagram is that the interladder spin-pseudospin coupling, responsible for the spin-gap generation, also destroys the IMTF quantum critical point, resulting in the exponential behavior of ${T}_{c}$ in the region of Ising's coupling where the IMTF is always disordered. We conclude that our mean-field results give a qualitatively correct description of the phase transition in ${\mathrm{NaV}}_{2}{\mathrm{O}}_{5},$ while a more sophisticated analysis is warranted to take into account the thermal fluctuations and, probably, the proximity of the IMTF quantum critical point.