Abstract
Field-induced quantum (zero temperature) criticality described using parameters that are not associated with a symmetry-breaking long-range order is found in the spin-$\frac{1}{2}$ antiferromagnetic three-leg Heisenberg ladder. These parameters represent the spin bond order, which is a consequence of the probability for spins on adjacent sites to be bound in a singletlike arrangement. They underwent two phase transitions, one at the lower critical field ${h}_{c1}$ and the other at the upper critical field ${h}_{c2}$. The field dependence of these bond parameters and of the magnetization is calculated for several values of the rung coupling in all regimes. This yields the coupling field phase diagram. It is found that the rung coupling must exceed a threshold value for the plateau, at one third of the saturation magnetization, to appear. The results obtained here within the bond mean-field theory compare well with existing numerical data.
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