Spin-half Heisenberg antiferromagnet on two archimedian lattices: From the bounce lattice to the maple-leaf lattice and beyond

Abstract

We investigate the ground state of the two-dimensional Heisenberg antiferromagnet on two Archimedean lattices, namely, the maple-leaf and bounce lattices as well as a generalized J-J ′ model interpolating between both systems by varying J ′ /J from J ′ /J = 0 (bounce limit) to J ′ /J = 1 (maple-leaf limit) and beyond. We use the coupled cluster method to high orders of approximation and also exact diagonalization of finite-sized lattices to discuss the ground-state magnetic long-range order based on data for the ground-state energy, the magnetic order parameter, the spin-spin correlation functions as well as the pitch angle between neighboring spins. Our results indicate that the "pure" bounce (J ′ /J = 0) and maple-leaf (J ′ /J = 1) Heisenberg antiferromagnets are magnetically ordered, however, with a sublattice magnetization drastically reduced by frustration and quantum fluctuations. We found that magnetic long-range order is present in a wide parameter range 0 ≤ J ′ /J J ′ c /J and that the magnetic order parameter varies only weakly with J ′ /J. At J ′ c ≈ 1.45J a direct first-order transition to a quantum orthogonal-dimer singlet ground state without magnetic long-range order takes place. The orthogonal-dimer state is the exact ground state in this large-J ′ regime, and so our model has similarities to the Shastry-Sutherland model. Finally, we use the exact diagonalization to investigate the magnetization curve. We a find a 1/3 magnetization plateau for J ′ /J 1.07 and another one at 2/3 of saturation emerging only at large J ′ /J 3.

Heisenberg antiferromagnet on the kagome lattice with arbitrary spin: A higher-order coupled cluster treatment

“…14, 26, and [35][36][37][38][39][40][41][42]. In the present paper we apply the CCM in high orders of approximation to the kagome HAFM.…”

Quantums=12antiferromagnets on Archimedean lattices: The route from semiclassical magnetic order to nonmagnetic quantum states

“…CCM has recently been applied computationally at high orders of approximation to quantum magnetic systems with much success, see, e.g., Refs. [14,[32][33][34][35][36][37]. In the field of quantum magnetism, advantages of this approach are that it can be applied to strongly frustrated quantum spin systems in any dimension and with arbitrary spin quantum numbers.…”

“…For the maple-leaf and bounce lattices the classical GS used as model state has six sublattices with a characteristic pitch angle [4,37]. The classical GS of the trellis lattice is an incommensurate spiral one along a chain [4,40].…”

“…For the GS energy the extrapolation scheme [14,[32][33][34][35][36][37]. For the magnetic order parameter M the choice of an appropriate extrapolation scheme is more subtle.…”

Analytical and numerical studies of the one-dimensional sawtooth chain

“…Since the classical Néel order is absent in the quantum sawtooth chain at 0 α = , one can judge reasonably that the sawtooth chain is in the quasi-Néel state in the small α parameter region. To investigate whether the sawtooth chain possesses the above two non-linear states, we resort to CCM which is a powerful tool to obtain valid and reliable results of the ground state for frustrated quantum spin systems with the non-linear quantum corrections [7,[15][16][17][18][19][20][21][22][23]. In Refs.…”