Phase diagram study of a dimerized spin-S zig–zag ladder

Abstract

The phase diagram of a frustrated spin-S zig-zag ladder is studied through different numerical and analytical methods. We show that for arbitrary S, there is a family of Hamiltonians for which a fully-dimerized state is an exact ground state, being the Majumdar-Ghosh point for a particular member of the family. We show that the system presents a transition between a dimerized phase to a Néel-like phase for S = 1/2, and spiral phases can appear for large S. The phase diagram is characterized by means of a generalization of the usual mean field approximation. The novelty in the present implementation is to consider the strongest coupled sites as the unit cell. The gap and the excitation spectrum is analyzed through the random phase approximation. Also, a perturbative treatment to obtain the critical points is discussed. Comparisons of the results with numerical methods like the Density Matrix Renormalization Group are also presented.

Dimerized ground states inspin−Sfrustrated systems

“…A similar result can be obtained by the method of variational cluster mean field + RPA discussed in 34 . This treatment predicts that the GS is well approximate by |ψ plus small Gaussian correlations for |γ| < 1.…”

“…Further improvements can be obtained by mean of a cluster mean field + RPA expansion as we have shown in a previous work 34 . This opens a way to solve some effective models associated to certain quasi-one dimensional materials like KCuCl 3 .…”

“…Due to the SU (2) symmetry, for local states of a single rung the entanglement entropy is a function of the fidelity to the singlet state. As we could expect from a composite mean field treatment 34,39 , the local state of a single rung can be accurately approximated by a pure singlet state in a relatively wide region around the condition J ′ = 2J 2 , even if J 2 is moderately large.…”

Magnetization process in a frustrated plaquette dimerized ladder

“…Following the lines scketched in Ref. 23 we can show that, provided the conditions J d = 2J and K d = 2K, the ground state of the system corresponds to the fully dimerized state |ψ = Nr i=1 |s i , with…”

Nematic quantum phases in the bilayer honeycomb antiferromagnet

“…First indications of quantum disordered phases, genuinely related to the bilayer geometry and not present in the single layer case have been provided in a small parameter window in [46], following ideas of [49,50] and similar works [51][52][53][54][55]. However a complete understanding of the quantum phase diagram of the bilayer is missing.…”