2016/03/31 by Adam Iaizzi, Kedar Damle, Anders W. Sandvik
Physics and Astronomy · #Antiferromagnetism #Condensed matter physics #Frustration #Heisenberg model #Ising model #Magnetic field #Magnetization #Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #Quantum mechanics #Theoretical and Computational Physics #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.95.174436
published as Phys. Rev. B 95, 174436 (2017)
openalex created_date 2016/06/24 · openalex publication_date 2017/05/25 · arxiv created 2017/05/26 · arxiv updated 2017/05/30 · openalex updated_date 2026/08/06
We study the magnetization process of a one-dimensional extended Heisenberg model, the J\text\ensuremath-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 twofold-degenerate dimerized (valence-bond solid) state above a critical value qc\ensuremath≈0.85 where q\ensuremath≡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\text\ensuremath-J2 chain (J1>0,J2<0), but only if J2 is spin anisotropic. In addition to the studies at zero temperature, we also investigate quantum-critical scaling near the transition into the fully polarized state for q\ensuremath≤qmin at T>0. While the expected ``zero-scale-factor'' universality is clearly seen for q=0 and q\ensuremath≪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 crossover at a temperature T*(q) between logarithmic tricritical scaling and zero-scale-factor universality, with T*(q)\ensuremath→0 when q\ensuremath→qmin.