Effect of anisotropy on the ground-state magnetic ordering of the spin-half quantumJ1XXZ–J2XXZmodel on the square lattice

Abstract

We study the zero-temperature phase diagram of the two-dimensional quantum J 1 XXZ-J 2 XXZ spin-1/2 anisotropic Heisenberg model on the square lattice. In particular, the effects of the anisotropy ⌬ on the z-aligned Néel and ͑collinear͒ stripe states, as well as on the xy-planar-aligned Néel and collinear stripe states, are examined. All four of these quasiclassical states are chosen in turn as model states, on top of which we systematically include the quantum correlations using a coupled cluster method analysis carried out to very high orders. We find strong evidence for two quantum triple points ͑QTPs͒ at ͑⌬ c = −0.10Ϯ 0.15, J 2 c / J 1 = 0.505Ϯ 0.015͒ and ͑⌬ c = 2.05Ϯ 0.15, J 2 c / J 1 = 0.530Ϯ 0.015͒, between which an intermediate magnetically disordered phase emerges to separate the quasiclassical Néel and stripe collinear phases. Above the upper QTP ͑⌬տ2.0͒ we find a direct first-order phase transition between the Néel and stripe phases, exactly as for the classical case. The z-aligned and xy-planar-aligned phases meet precisely at ⌬ = 1, also as for the classical case. For all values of the anisotropy parameter between those of the two QTPs there exists a narrow range of values of J 2 / J 1 , ␣ c 1 ͑⌬͒ Ͻ J 2 / J 1 Ͻ ␣ c 2 ͑⌬͒, centered near the point of maximum classical frustration, J 2 / J 1 = 1 2 , for which the intermediate phase exists. This range is widest precisely at the isotropic point, ⌬ = 1, where ␣ c 1 ͑1͒ = 0.44Ϯ 0.01 and ␣ c 2 ͑1͒ = 0.59Ϯ 0.01. The two QTPs are characterized by values ⌬ = ⌬ c at which ␣ c 1 ͑⌬ c ͒ = ␣ c 2 ͑⌬ c ͒.

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

“…[11][12][13]61,62 We have also performed extrapolations for the data set with m = {6, 8, 10}. Both sets of results agree well with one another, which gives added credence to our results.…”

“…It has been used to study various quantum magnets (see, e.g., Refs. [11][12][13][14][61][62][63][64][65][66][67][68][69][70][71] and references cited therein) very successfully. The method is particularly suitable for investigating frustrated systems, due to the fact that some of the main alternative methods are restricted by certain problems that arise in such cases.…”

“…[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-…”

Magnetic correlation in the square-lattice spin system (CuBr)Sr2Nb3O10: A neutron diffraction study

“…In the literature a large number of theoretical studies on systems with antiferromagnetic (AFM) J 1 and J 2 exist. [3][4][5][6][7][8][9][10][11][12][13][14] Here the J 1 -J 2 model 3-14 reveals several interesting magnetic ground states involving quantum phase transitions, such as (i) for α (=|J 2 / J 1 |) 0.4, a Néel AFM state [Q = (π π)], (ii) for α∼0. 4-0.6, a quantum spin-liquid state, and (iii) for α 0.6, an ordered collinear AFM state [Q = (π 0) or (0 π )], i.e., AFM coupling of ferromagnetic (FM) chains in a given plane (by disorder stabilization).…”

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] .…”