Magnetic Field Effects in Low-Dimensional Quantum Magnets
This event is part of the PhD Final Oral Exams.
Examining Committee: Anders Sandvik, David Campbell, Robert Carey, Shyam Erramilli, Claudio Chamon
We present a comprehensive study of a low-dimensional spin-half quantum antiferromagnet, the J-Q model, in the presence of an external (Zeeman) magnetic field using numerical methods, chiefly stochastic series expansion quantum Monte Carlo with directed loop updates and quantum replica exchange. The J-Q model is a many-body Hamiltonian acting on a lattice of localized spin-half degrees of freedom; it augments the Heisenberg exchange with a four-spin interaction of strength Q. This model has been extensively studied at zero field, where the Q term drives a quantum phase transition from a Neel-like state to a valence-bond solid (a nonmagnetic state consisting of a long-range-ordered arrangement of local singlet bonds between sites). This transition is believed to be an example of deconfined quantum criticality, where the excitations are spinons—exotic spin-half bosons. We study the J-Q model in the presence of a magnetic field in both one and two dimensions. In one dimension, there is metamagnetism above a critical coupling ratio (Q/J )min. Metamagnetism is a first-order quantum phase transition characterized by discontinuities in the magnetization as a function of field (magnetization jumps). We derive an exact expression for (Q/J)min = 2/9, and show that the metamagnetism is caused by the onset of attractive interactions between magnons (flipped spins on a polarized background). We predict that the same mechanisms will produce metamagnetism in the unfrustrated antiferromagnetic J1-J2 model with anisotropy. Below (Q/J)min, the saturation transition is continuous and we show that it is governed by the expected zero-scale-factor universality. In two dimensions, we also find metamagnetism above a critical coupling ratio (Q/J)min=0.417, caused by the same mechanism as in the one-dimensional case. In two dimensions we also show evidence of an anomalous temperature dependence of specific heat arising from field-induced Bose-Einstein condensation of spinons at the deconfined quantum critical point.