Scaling of Critical Temperature and Ground State Magnetization near a Quantum Phase Transition

Abstract

We investigate a simple model antiferromagnet which shows a Quantum Phase Transition between a conventional Neel antiferromagnetic phase and a dimerized ‘Valence Bond Solid’ phase. Both the critical temperature and the ground state magnetization in the Neel phase approach zero at the critical point, and are found to scale according to power laws, with exponents 0.5, as expected from general considerations. 1. Introduction The subject of Quantum Phase Transitions (QPT’s) in condensed matter systems remains a frontier area of research [1]. These are transitions, at temperature T = 0, in the nature of the ground state of a strongly correlated quantum system. At QPT’s large quantum fluctuations play the same role as do large thermal fluctuations at normal phase transitions, and analogous universal scaling laws are to be expected. In real materials QPT’s can be induced by pressure, by applied magnetic fields, or by disorder. Theoretical studies of QPT’s are largely based on various simplified models, particularly low dimensional antiferromagnets, where the system can be tuned through a QPT by varying a particular parameter g in the Hamiltonian. Most of the models hereto studied have been two-dimensional. Examples include antiferromagnets with strong and weak bonds, with or without frustration, and bilayer systems, where the QPT separates a conventional Neel antiferromagnetic phase from a dimerized phase with only short-range correlations and no magnetic order. In such systems the magnetic order present in the ground state does not extend to finite temperatures. In the present work we study a three-dimensional model where magnetic order persists to some critical temperature Tc(g). We expect Tc(g) to vanish as g → gc, and we are interested in comparing the vanishing of Tc with the vanishing of the ground state magnetization M0. The magnetization is expected to vanish as (gc – g) β , where the critical exponent β is expected to have the value 0.5, corresponding to a classical thermally driven transition in four spatial dimensions, which is mean-field like (with possible logarithmic corrections). Does Tc(g) scale with (gc – g) in the same way? 2. The model and results