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Physica A Statistical Mechanics and its Applications

The magnetic properties of spin-1/2 two-leg ladders with dimerized legs and trimerized modulation of rung exchange

M. Shahri Naseri, S. Mahdavifar

Published Jan 18, 2017• 9 citations
Publisher
DOI
10.1016/j.physa.2017.01.070

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The ground-state magnetic phase diagram of a two-leg spin ladder with trimerized modulated rung exchange is studied using the continuum-limit bosonization approach. In the limit where the rung exchange is dominant, the model is mapped onto the effective quantum sine-Gordon model with topological term. Six quantum phase transitions at different critical magnetic fields are identified. We have shown that the magnetization curve of the system exhibits two plateaus at magnetization equal to the 1/3 and 2/3 of the saturation value. The width of the plateaus is proportional to the excitation gap at given magnetization and scales as   , where  is the amplitude of rung exchange modulation and the critical
The physical properties of the edge states of the cut two-leg spin ladder are investigated by means of the bosonization approach. By carefully treating boundary conditions, we derive the existence of spin-1/2 edge states in the spin ladder with a ferromagnetic rung exchange and for the open spin-1 Heisenberg chain. In contrast, such states are absent in the antiferromagnetic rung coupling case. The approach, based on a mapping onto decoupled semi-infinite off-critical Ising models, allows us to compute several physical quantities of interest. In particular, we determine the magnetization and dimerization profiles of the cut two-leg spin ladder and of the open biquadratic spin-1 chain in the vicinity of the SU(2)2\mathrm{SU}{(2)}_{2}SU(2)2​ Wess-Zumino-Novikov-Witten critical point.
We study the antiferromagnetic spin-half Heisenberg ladder in the presence of an additional frustrating rung spin that is motivated and relevant also for the description of real two-dimensional materials such as the two-dimensional trimer magnet Ba4Ir3O10{\mathrm{Ba}}_{4}{\mathrm{Ir}}_{3}{\mathrm{O}}_{10}Ba4​Ir3​O10​. We study the zero-temperature phase diagram, where we combine numerical and analytical methods into an overall consistent description. All numerical simulations are also accompanied by studies of the dynamical spin structure factor obtained via the density matrix renormalization group. Overall, we find in the regime of strong rung coupling a gapped dimerized phase related to competing symmetry sectors in Hilbert space that ultimately results in frustration-driven spin-Peierls transition. In the weak rung-coupling regime, the system is uniform yet shows a gapped spinon continuum together with a sharp coherent low-energy branch that renders the system critical overall. In either case, the additional rung spin quickly gets sidelined and nearly decouples once its bare coupling to the ladder drops somewhat below the direct Heisenberg coupling of the legs.