Quantum criticality in Heisenberg chains and ladders with long range antiferromagnetic interactions

In order to circumvent the Mermin-Wagner theorem and realize true spontaneous symmetry breaking in 1D and quasi-1D spin systems, we include RKKY-like long-range antiferromagnetic (AFM) interactions to effectively increase their dimensionality. For a critical value of the exponent in the long-range term, both Heisenberg chains and ladders exhibit a second order phase transition from a disordered to a spontaneously symmetry broken Néel phase. We study the spectral function of both models across the transition with the time-dependent DMRG method. In chains, deconfined spinons form gapless coherent bound states (magnons) and push the two spinon continuum to higher energies, while in ladders we observe a transition from well-defined gapless magnons to gapped triplons accompanied by a coherent amplitude mode. The dynamic critical exponent for the transition on ladders is found to be z=1, raising the possibility of deconfined criticality in this model. We complement our results with linear spin-wave and bond-operator calculations.