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We argue that our analysis of the J-Q model, presented in Phys. Rev. B 80, 174403 (2009), and based on a field-theory description of coupled dimers, captures properly the strong quantum fluctuations tendencies, and the objections outlined by L. Isaev, G. Ortiz, and J. Dukelsky, arXiv:1003.5205, are misplaced.
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We study the S=1/2 Heisenberg antiferromagnet on a square lattice with nearest-neighbor and plaquette four-spin exchanges (introduced by A.W. Sandvik, Phys. Rev. Lett. {bf 98}, 227202 (2007).) This model undergoes a quantum phase transition from a spontaneously dimerized phase to Neel order at a critical coupling. We show that as the critical point is approached from the dimerized side, the system exhibits strong fluctuations in the dimer background, reflected in the presence of a low-energy singlet mode, with a simultaneous rise in the triplet quasiparticle density. We find that both singlet and triplet modes of high density condense at the transition, signaling restoration of lattice symmetry. In our approach, which goes beyond mean-field theory in terms of the triplet excitations, the transition appears sharp; however since our method breaks down near the critical point, we argue that we cannot make a definite conclusion regarding the order of the transition.
In a recent comment to the paper Chaotic Integrable transition in the SYK model, it was claimed that, in a certain region of parameters, the Lyapunov exponent of the N Majoranas Sachdev-Ye-Kitaev model with a quadratic perturbation, is always positive. This implies that the model is quantum chaotic. In this reply, we show that the employed perturbative formalism breaks down precisely in the range of parameters investigated in the comment due to a lack of separation of time scales. Moreover, based on recent analytical results, we show that for any large and fixed N, the model has indeed a chaotic-integrable transition that invalidate the results of the comment.
It is shown that the experiments of A.M. Toader, J. P. Goff, M. Roger, N. Shannon, J. R. Stewart, and M. Enderle, Phys. Rev. Lett. 94, 197202 (2005) do not provide definitive experimental evidence for ring exchange terms in the Hamiltonian of La2CuO4, even though such terms may be present.
First version: del Barco et al. submitted recently a comment [arXiv:0812.4070] on our latest Phys. Rev. Lett. [Phys. Rev. Lett. 101, 237204 (2008)], claiming three basic mistakes. We show here that their claims are unjustified and based on erroneous calculations and hasty conclusions. Second version: reply to the modified version of del Barco et al. submitted to Phys. Rev. Lett.
In a recent publication [M. B. Stone et al., New Journal of Physics 9, 31 (2007)] a Renormalized Classical 2D (RC) phase has been reported in a quasi-two-dimensional quantum antiferromagnet PHCC. Its key signature is a sharp cusp-like feature in the magnetic susceptibility which appears below the critical field of magnetic ordering indicated by specific heat anomaly and emergence of a Bragg peak. Here we present experimental data which shows that regardless of experimental geometry, the specific heat and susceptibility anomalies in PHCC both coincide with the onset of true long range order. This leaves no room for any additional intermediate RC phase.
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