We study the magnetization process of a one-dimensional extended Heisenberg model-the J-Q model-as a function of an external magnetic field, h. In this model, J represents the traditional antiferromagnetic Heisenberg exchange and Q is the strength of a competing four-spin interaction. Without external field, this system hosts a two-fold degenerate dimerized (valence-bond solid) state above a critical value qc ≈ 0.85 where q ≡ Q/J. The dimer order is destroyed and replaced by a partially polarized translationally invariant state at a critical field value. We find magnetization jumps (metamagnetism) between the partially polarized and fully polarized state for q > qmin, where we have calculated qmin = 2/9 exactly. For q > qmin two magnons (flipped spins on a fully polarized background) attract and form a bound state. Quantum Monte Carlo studies confirm that the bound state corresponds to the first step of an instability leading to a finite magnetization jump for q > qmin. Our results show that neither geometric frustration nor spin-anisotropy are necessary conditions for metamagnetism. Working in the two-magnon subspace, we also find evidence pointing to the existence of metamagnetism in the unfrustrated J1-J2 chain (J1 > 0, J2 < 0), but only if J2 is spin-anisotropic. In addition to the studies at zero temperature, we also investigate quantumcritical scaling near the transition into the fully polarized state for q ≤ qmin at T > 0. While the expected "zero-scale-factor" universality is clearly seen for q = 0 and q qmin, for q closer to qmin we find that extremely low temperatures are required to observe the asymptotic behavior, due to the influence of the tricritical point at qmin. In the low-energy theory, one can expect the quartic nonlinearity to vanish at qmin and a marginal sixth-order term should govern the scaling, which leads to a cross-over at a temperature T * (q) between logarithmic tricritical scaling and zero-scale-factor universality, with T * (q) → 0 when q → qmin.
A Valence bond solid (VBS) is a nonmagnetic, long-range ordered state of a quantum spin system where local spin singlets are formed in some regular pattern. We here study the competition between VBS order and a fully polarized ferromagnetic state as function of an external magnetic field in a one-dimensional extended Heisenberg model-the J-Q2 modelusing stochastic series expansion (SSE) quantum Monte Carlo simulations with directed loop updates. We discuss the ground state phase diagram.
Using a combination of quantum Monte Carlo and exact methods, we study the field-driven saturation transition of the two-dimensional J-Q model, in which the antiferromagnetic Heisenberg exchange (J) coupling competes with an additional four-spin interaction (Q) that favors valencebond solid order. For small values of Q, the saturation transition is continuous, and is expected to be governed by zero-scale-factor universality at its upper critical dimension, with a specific form of logarithmic corrections to scaling (first proposed by Sachdev et al. [Phys. Rev. B 50, 258 (1994)]). Our results conform to this expectation, but the logarithmic corrections to scaling do not match the form predicted by Sachdev et al. We also show that the saturation transition becomes first order above a critical coupling ratio (Q/J)min and is accompanied by magnetization jumpsmetamagnetism. We obtain an exact solution for (Q/J)min using a high magnetization expansion, and confirm the existence of the magnetization jumps beyond this value of coupling using quantum Monte Carlo simulations. arXiv:1804.06045v2 [cond-mat.str-el]
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