Field-driven quantum phase transitions in S=1/2 spin chains

Abstract

We study the magnetization process of a 1D extended Heisenberg model, the J-Q model, as a function of an external magnetic field. 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 twofold-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. We also investigate quantum-critical 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; 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, 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.