Ground state phases of the spin-1/2J1–J2Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment

Abstract

Using the coupled cluster method for high orders of approximation and complementary exact diagonalization studies we investigate the ground state properties of the spin-1/2 J 1 -J 2 frustrated Heisenberg antiferromagnet on the square lattice. We have calculated the ground state energy, the magnetic order parameter, the spin stiffness, and several generalized susceptibilities to probe magnetically disordered quantum valence-bond phases. We have found that the quantum critical points for both the Néel and collinear orders are J 2 c1 Ϸ͑0.44Ϯ 0.01͒J 1 and J 2 c2 Ϸ͑0.59Ϯ 0.01͒J 1 , respectively, which are in good agreement with the results obtained by other approximations. In contrast to the recent study by ͓Sirker et al. Phys. Rev. B 73, 184420 ͑2006͔͒, our data do not provide evidence for the transition from the Néel to the valence-bond solid state to be first order. Moreover, our results are in favor of the deconfinement scenario for that phase transition. We also discuss the nature of the magnetically disordered quantum phase.

Hierarchical mean-field approach to theJ1−J2Heisenberg model on a square lattice

“…Indeed, the results of spinwave calculations, 12 large-N expansions, 14 and calculations using the density-matrix renormalization group combined with Monte Carlo simulations 8 are believed to indicate the emergence of a dimer order. On the other hand, Monte Carlo 6 and coupled cluster calculations, 9 and analytical results 11 seem to support the presence of C 4 symmetry ͑plaquette-type ordering͒ in the paramagnetic phase. In the absence of a reliable numerical or analytical proof of existence of any particular order in the nonmagnetic region, there is no apparent reason to believe in the exotic deconfined quantum criticality scenario.…”

“…12,14 It follows then that these two phases cannot be joined by the usual Landau second-order critical point. This phase transition can either be of the first order 19 ͑the latest coupled cluster calculations, 9 however, seem to rule out this possibility͒, or represent an example of a second-order critical point, which cannot be described in terms of a bulk order parameter, but rather in terms of emergent fractional excitations ͑spinons͒, which become deconfined right at the critical point. 15 However, evidence regarding the structure of the nonmagnetic phase is quite controversial.…”

“…Particularly, the correlated nature of the intermediate state and the kind of quantum phase transition separating it from the Néel state, attract most attention. Various methods have been recently applied to characterize the quantum paramagnetic phase, such as Green's-function Monte Carlo, [6][7][8] coupled cluster methods, 9 series expansions, 10 and field-theoretical methods. [11][12][13] As a result, several possible candidate ground states were proposed, namely, spin liquid, 7 preserving translational, and rotational symmetries of the lattice, as well as various lattice symmetry breaking phases, out of which the dimer 12,14 and the plaquette resonating valence bond phases 6 are worth mentioning.…”

The quantum J1−J′1−J2 spin-1/2 Heisenberg antiferromagnet: A variational method study

“…Heisenberg antiferromagnet on a square lattice with competing nearest-neighbor (NN) and next-nearest-neighbor (NNN) antiferromagnetic exchange interactions (known as J 1 − J 2 model) [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] .…”

Ground-state phases of the frustrated spin-12J1–J2–Li1, Bishop2, Farnell3 et al. 2012Phys. Rev. BSelf Cite

“…[7][8][9][10]). Amongst several methods that have been very successfully applied to the J 1 -J 2 model has been the coupled cluster method (CCM), [11][12][13][14] which has also been applied to many similar strongly-interacting and highly frustrated spin-lattice models with comparable success. Other frustrated 2D models that have similarly engendered great recent interest include the spin-…”