Magnetization plateaus in frustrated antiferromagnetic quantum spin models

Abstract

Plateaus can be observed in the zero-temperature magnetization curve of\nquantum spin systems at rational values of the magnetization. In one dimension,\nthe appearance of a plateau is controlled by a quantization condition for the\nmagnetization which involves the length of the local spin and the volume of a\ntranslational unit cell of the ground state. We discuss examples of\ngeometrically frustrated quantum spin systems with large (in general unbounded)\nperiodicities of spontaneous breaking of translational symmetry in the ground\nstate.\n In two dimensions, we discuss the square, triangular and Kagome lattices\nusing exact diagonalization (ED) for up to N=40 sites. For the spin-1/2 XXZ\nmodel on the triangular lattice we study the nature and stability region of a\nplateau at one third of the saturation magnetization. The Kagome lattice gives\nrise to particularly rich behaviour with several plateaus in the magnetization\ncurve and a jump due to local magnon excitations just below saturation.\n