The spin-1/2 square-lattice J1-J2 model: the spin-gap issue

Abstract

Using the coupled cluster method for high orders of approximation and Lanczos exact diagonal-ization we study the ground-state phase diagram of a quantum spin-1/2 J1-J2 model on the square lattice with plaquette structure. We consider antiferromagnetic (J1 > 0) as well as ferromagnetic (J1 < 0) nearest-neighbor interactions together with frustrating antiferromagnetic next-nearest-neighbor interaction J2 > 0. The strength of inter-plaquette interaction λ varies between λ = 1 (that corresponds to the uniform J1-J2 model) and λ = 0 (that corresponds to isolated frustrated 4-spin plaquettes). While on the classical level (s → ∞) both versions of models (i.e., with ferro-and antiferromagnetic J1) exhibit the same ground-state behavior, the ground-state phase diagram differs basically for the quantum case s = 1/2. For the antiferromagnetic case (J1 > 0) Néel antiferromagnetic long-range order at small J2/J1 and λ 0.47 as well as collinear striped an-tiferromagnetic long-range order at large J2/J1 and λ 0.30 appear which correspond to their classical counterparts. Both semi-classical magnetic phases are separated by a nonmagnetic quantum paramagnetic phase. The parameter region, where this nonmagnetic phase exists, increases with decreasing of λ. For the ferromagnetic case (J1 < 0) we have the trivial ferromagnetic ground state at small J2/|J1|. By increasing of J2 this classical phase gives way for a semi-classical pla-quette phase, where the plaquette block spins of length s = 2 are antiferromagnetically long-range ordered. Further increasing of J2 then yields collinear striped antiferromagnetic long-range order for λ 0.38, but a nonmagnetic quantum paramagnetic phase λ 0.38.

The spin-half XXZ antiferromagnet on the square lattice revisited: A high-order coupled cluster treatment

“…2, as a final step we need to extrapolate our LSUBm estimates for all physical quantities to the limit m → ∞ where the method becomes exact. Although exactly provable rules are not known for these extrapolations, robust empirical rules do exist, and these rules have successfully been tested for a wide range of quantum magnetic systems [33,35,38,39,43,51,53]. We use the "standard" rules in order to extrapolate all expectation values, namely: the ground-state energy per spin…”

Ground-state phases of the spin-1J1−J2Heisenberg antiferromagnet on the honeycomb lattice

“…CCM SUBn-n extrapolation schemes with a leading power 1/n have also been shown to fit the results very well for the corresponding approximants for each of the spin gap (n) (and see, e.g., Refs. [63,[75][76][77]): …”

Field-Induced Quantum Phase Transitions inS= 1/2J1–J2Heisenberg Model on Square Lattice

“…At J 2 /J 1 = 0.5, the classical ground state has macroscopic degeneracy and the thermodynamic properties are highly non-trivial. In the S = 1/2 quantum spin system, several novel ground states such as plaquette valence-bond crystal (PVBC), columnar valence-bond crystal (VBC), and spin liquids with or without a spin gap have been predicted by numerical studies such as density matrix renormalization group (DMRG) calculations [11,12], exact diagonalizations [13,14], and other numerical simulations [15][16][17][18][19][20][21], but the true nature of the ground state has not been determined, and no consensus exists yet.…”