The ground state phase diagram of the quantumJ₁–J₂spin-1/2 Heisenberg antiferromagnet on an anisotropic square lattice

Abstract

We have studied the ground state phase diagram of the quantum spin-1/2 frustrated Heisenberg antiferromagnet on a square lattice by using the framework of the differential operator technique. The Hamiltonian is solved by using an effective-field theory for a cluster with two spins (EFT-2). The model is described using the Heisenberg Hamiltonian with two competing antiferromagnetic interactions: nearest neighbor (NN) with different coupling strengths J 1 and J 1 along the x and y directions and next nearest neighbor (NNN) with coupling J 2 . We propose a functional for the free energy (similar to the Landau expansion) and using Maxwell construction we obtain the phase diagram in the (λ, α) space, where λ = J 1 /J 1 and α = J 2 /J 1 . We obtain three different states depending on the values of λ and α: antiferromagnetic (AF), collinear antiferromagnetic (CAF) and quantum paramagnetic (QP). For an intermediate

Second-order quantum corrections for the frustrated spatially anisotropic spin-12Heisenberg antiferromagnet on a square lattice

“…This is in contrary to the findings in Refs. [43][44][45]. Instead from our calculations we find that there are two ordered phases separated by the magnetically disordered phase.…”

“…Below this point they predicted a second-order phase transition between the quantum Neél and stripe phases, whereas above it these two phases are separated by an intermediate phase. Existence of a QTP has also been reported by other authors 42,43 where they used effective field theory and effective renormalization group approach to obtain a QTP at ζ = 0.51, η ≈ 0.28. In a DMRG study it was predicted that there is no intermediate phase (no spin gap) for η lower than 0.287 when ζ = 1 (isotropic case).…”

“…[4][5][6] In addition these experiments on Li 2 VOSiO 4 have shown that it undergoes a phase transition at a low temperature ͑2.8 K͒ to collinear antiferromagnetic order with magnetic moments lying in the a-b plane with J 2 + J 1 ϳ 8.2͑1͒ K and J 2 / J 1 ϳ 1.1͑1͒. 6,7 Quantum spin-1 2 antiferromagnetic J 1 -J 2 model on a square lattice has been studied extensively by various analytical and numerical techniques such as the diagrammatic perturbation theory based on spin-wave expansion, [13][14][15][16][17][18][19][20][21][22][23][24] modified spin-wave theory, 25 field theory, [26][27][28][29][30][31][32] series expansion, [33][34][35][36][37][38] exact diagonalization, 39 density matrix renormalization group ͑DMRG͒, [40][41][42] effective field theory, 43,44 coupled cluster method, 45 band-structure calculations, 46 and Quantum Monte Carlo. [47][48][49] It is now well known that at low temperatures these systems exhibit new types of magnetic order and novel quantum phases.…”

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

“…A generalization of the J 1 − J 2 Heisenberg antiferromagnetic model on a square lattice was introduced by Nersesyan and Tsvelik 26 and studied by other groups [27][28][29][30][31][32][33][34] , the so-called destroys it completely at a certain value of the interchain parameter λ.…”

Two-Dimensional Spin-1/2 J1 – J'1 – J2 Heisenberg Model within Jordan–Wigner Transformation

“…Like its spatially isotropic 1 − 2 counterpart, the spin-1/2 1 − ′ 1 − 2 Heisenberg model on a square lattice has already been studied, by using several methods; in particular, the spin-wave expansion method [49,50], the density-matrix renormalization group method [51], the effective-field method [52], in the variational approach [53], the method of coupled clusters [54], and the exact diagonalization method [55]. Some results obtained in the cited works will be mentioned below, while discussing our numerical results.…”