Critical Properties of Condensation of Field‐Induced Triplet Quasiparticles

Abstract

A review on the field-induced magnetic ordering is given, together with some results of a quantum Monte Carlo simulation focused on the critical behevior near the quantum critical point.KEYWORDS: quantum spin system, Heisenberg model, quantum Monte Carlo, XY model, XXZ model, cluster algorithm, loop algorithm, worm algorithm, directed-loop algorithm IntroductionIn this article we discuss phenomena observed in systems with a singlet ground state with triplet excitations separated by a finite spin gap. The focus of researchers' attention has been on the magnetic phase transition induced by a magnetic field and/or a pressure. While the field-(or pressure-) induced magnetic ordering were observed in various materials, the character of the phase transition, in particular the one at the quantum critical point (QCP) seems to be insensitive to the the nature of the ground state and to the origin of the gap. In one class of materials, localized magnetic spins are bound strongly in pairs to form singlet dimers, and the inter-dimer interaction is not strong enough to induce any long-range magnetic ordering. In these materials, the excited states consist of excitations of quasiparticles, recently often referred to as tripletons or triplons. They originate from the triplet states at each site. The magnetic ordering in the dimer systems with a sufficiently strong magnetic field was suggested based on a mean-field theory. 1, 2 Later, two possibilities were suggested 3 depending on the relative strength of the repulsive interaction among the quasiparticles and their kinetic energy. If the kinetic term dominates, the system may undergo a condensation transition as suggested by the mean-field theory 1, 2 and later also by the Hartree-Fock (HF) theory with the bosonic representation. 4 On the other hand, when the repulsive force dominates, the ordered state is the super lattice where the quasiparticles are located periodically to form a lattice with a larger unit cell than that of the original lattice, which gives rise to magnetization plateaus in the magnetization-field curve. This scenario is realized in materials for which the effective dimer-dimer couplings vanish due to the cancellation among the exchange couplings and higher order interactions play essential roles. 5 A well-known example is SrCu 2 (BO 3 ) 2 . 6-8 In the rest of the present article, however, we only discuss the first case, i.e., the case where the kinetic-term is dominant.