Spectrum of short-wavelength magnons in a two-dimensional quantum Heisenberg antiferromagnet on a square lattice: third-order expansion in 1/S

Abstract

The spectrum of short-wavelength magnons in a two-dimensional quantum Heisenberg antiferromagnet on a square lattice is calculated to the third order in a 1/S expansion. It is shown that a 1/S series for S = 1/2 converges quickly in the whole Brillouin zone except in the neighborhood of the point k = (π, 0), at which absolute values of the third-and the second-order 1/S-corrections are approximately equal to each other. It is shown that the third-order corrections make deeper the roton-like local minimum at k = (π, 0), improving the agreement with recent experiments and numerical results in the neighborhood of this point. It is suggested that the 1/S series converges slowly near k = (π, 0) also for S = 1 although the spectrum renormalization would be small in this case due to the very small values of high-order 1/S corrections.

Spin excitation spectra of the two-dimensional S=12 Heisenberg model with a checkerboard structure

“…However, LSWT can be improved by considering 1/S expansion and performing highorder perturbation to obtain a multi-particle continuum [57,61,62], such as a 3-magnon continuum in transverse DSF and a 2-magnon continuum in longitudinal DSF, but the results are not satisfactory even in the bipartite case. This standard perturbation method converges slowly [63], and cannot give a reasonable prediction for the energy difference between (π, 0) and (π/2, π/2) and spectral weight at these momenta in the bipartite case. Many theories have been proposed to account for these anomalies, for example nearly deconfined spinons [19,64], non-perturbative renormalization of magnons [65], singlons [66].…”

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

“…We extrapolate these results using the fitting function A + B / N L + C / N L 2 + D / N L 3 to obtain A for N L → ϱ and reproduce the numerical results E ͑,0͒ AF / J 1 Ϸ 2.3585, E ͑/2,/2͒ AF / J 1 Ϸ 2.3908 reported earlier 15 with a 1.4% decrease between these two energy values. Recently a third order in 1 / S expansion has been done to obtain the spectrum of short-wavelength magnons 23,63 where it was shown that the 1 / S series converges slowly near the wave vector ͑ ,0͒. With the third order correction the excitation energy at ͑ ,0͒ was found to be 3.2% smaller than at ͑ / 2, / 2͒.…”

“…[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.…”

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“…Physically, it represents the repeated interaction processes between an α-magnon and a β-magnon. Our results, in combination with the slow convergence found in the direct perturbative approach [31], indicate that the O4 and higher terms are quantitatively significant. In our non-perturbative renormalizing approach the flow of all coefficients up to scaling dimension d = 2 is evaluated including all mutual dependencies.…”