Exact magnetization plateaus and phase transitions in spin-SHeisenberg antiferromagnets in arbitrary dimensions

Abstract

We generalize a class of Heisenberg antiferromagnets in one, two and three dimensions, which have been shown to exhibit magnetization plateaus for spin-1 2. In a certain parameter range of the general model, which is formally defined in D dimensions, we obtain the exact ground state(s) in the presence of an external magnetic field for arbitrary values of spin. In this range, the magnetization remains a constant as a function of the external field, except at some special values of the field where there is a jump from one plateau to the next. The plateaus are formed at certain specific fractions of the full magnetization which are determined by the spin and the lattice. Our general spin-S result reproduces the known cases for spin-1 2 in various lattices. Furthermore, we argue that outside the exact regime, the mechanism for the plateau formation is different. This results in first order phase transitions along some of the plateaus as the coupling constant is varied. We rigorously show the existence of such transitions for some particular cases. Finally, we numerically analyze a spin-1 model in one dimension using exact diagonalization to obtain its complete phase diagram. It agrees with our analytic results.

Multiple magnetization plateaus induced by farther neighbor interactions in an S=1 two-leg Heisenberg spin ladder

“…. , 4) plateaus was also found by Chandra and Surendran [4]. The values of plateaus are not limited to the multiples of 1/4; Heidrich-Meisner et al found a 1/3 plateau in a frustrated spin-S chain with particular next-nearest exchange interaction [5].…”

“…If the J 2 term is absent, this model is called the S = 1 Gelfand ladder [4,18,19]. The S = 1/2 Gelfand ladder has been studied by Honecker,Mila,and Troyer [19] and later, the general spin cases are studied by Chandra and Surendran [4]. They analytically revealed that the S = 1 Gelfand ladder holds the 1/4-plateau state depicted in Fig.…”

“…We can exactly discuss the ground state including the 1/3 plateau in the same way as in the Gelfand ladder [4,18]. Let us consider a decomposition of the Hamiltonian into a sum of the local Hamiltonian H = L i=1 H i .…”

“…( 7) and (8). On the other hand, the Gelfand ladder (J 2 = 0, 0 < J 1 ≤ J 0 /2) has the 1/4 series of plateaus [4]. The 1/4-and 3/4plateau states are also direct-product states with the twosite unit-cell structure as…”

“…In previous theoretical studies [3][4][5][6][7][8][9][10][11][12], plateaus always appear only at multiples of 1/4 or only at multiples of 1/3, whereas 1/2, 1/3, and 1/4 plateaus have been observed in the recent experiment of BIP-TENO [16]. Such many series of plateaus appearing simultaneously are rare in (quasi-)one-dimensional systems.…”