Spin–Wave Description of Haldane-Gap Antiferromagnets

Abstract

Modifying the conventional antiferromagnetic spin-wave theory which is plagued by the difficulty of the zero-field sublattice magnetizations diverging in one dimension, we describe magnetic properties of Haldane-gap antiferromagnets. The modified spin waves, constituting a grand canonical bosonic ensemble so as to recover the sublattice symmetry, not only depict well the ground-state correlations but also give useful information on the finite-temperature properties.PACS numbers: 75.10. Jm, 05.30.Jp, 75.40.Mg Haldane's conjecture [1,2] that one-dimensional Heisenberg antiferromagnets should exhibit qualitatively different low-energy structures based on whether the constituent spins are integral or fractional sparked renewed interest in the field of quantum magnetism. An energy gap immediately above the ground state was indeed observed in a quasi-one-dimensional Heisenberg antiferromagnet Ni(C 2 H 8 N 2 ) 2 NO 2 (ClO 4 ) [3] and a rigorous example of such a massive phase was also found out [4,5]. The energy gaps in magnetic excitation spectra, that is, spin gaps, are now one of the most attractive and important topics. In the context of theoretical progress, we may be reminded of quantized plateaux in the groundstate magnetization curves [6], a dramatic crossover from one-to two-dimensional quantum antiferromagnets [7], and an antiferromagnetic excitation gap accompanied by ferromagnetic background [8][9][10][11]. From the experimental point of view, metal oxides such as spin-Peierls compounds Cu 1−x M x GeO 3 (M = Zn, Mg) [12,13], Haldanegap antiferromagnets R 2 BaNiO 5 (R = rare earth) [14] and ladder materials Sr n−1 Cu n+1 O 2n (n = 3, 5, 7, · · ·) [15] have significantly contributed to systematic investigations of the mechanism of gap formation.

Discrete antiferromagnetic spin-wave excitations in the giant ferric wheel Fe18

“…Here, we use full-diagonalization interacting modified SWT (IMSWT). 49 A conceptually different approach is to introduce Schwinger bosons and treat the resulting Hamiltonian at the mean-field level (Schwinger-boson mean field theory), 50,51 which, however, yields exactly the same excitation spectrum as LMSWT and is hence not further considered here. For the N = 8, s = 5/2 system it was found that a simple correction of the LSWT spectrum, called LSWT + c , gave the best agreement with the exact energies.…”

“…For these theories, the ground-state and one-magnon energies can be calculated analytically for AFM wheels. [44][45][46][47][48][49][50][51] The resulting ground-state energies, singlet-triplet gaps, and maximal energies (= heights of the dispersion curves) are listed in Table I, which also presents the corresponding values for the one-J model Hamiltonian obtained from (D)DMRG, see appendix B. Furthermore, the mean deviation of SWT and DDMRG excitation energies or χ 2 = k [ω(k) − ω DDMRG (k)] 2 /( 1 2 NJ s) is given.…”

Quantized antiferromagnetic spin waves in the molecular Heisenberg ringCsFe8

“…Fortunately, for all these theories, linear SWT (LSWT), interacting SWT (ISWT), linear modified SWT (LMSWT), interacting modified SWT (IMSWT), and SBMFT, analytical results are available for 1D, which can be directly applied to the AFM ring (various IMSWTs exist, we have used the full-diagonalization IMSWT of Ref. 78). Interestingly, the SBMFT yields exactly the same excitation energies as the LMSWT, and also the ground-state energy agree after introduction of a correction factor.…”

Spinless fermions versus spin waves in describing antiferromagnetic Heisenberg ladders

“…On the other hand, we may consider a bosonic description of ladder systems based on the spin-wave scheme [7]. Since the conventional spin-wave theory is plagued by the difficulty of the zerofield sublattice magnetizations diverging in one dimension, we construct a modified spin-wave theory [8,9] for spin-gapped antiferromagnets.It is along a snake-like path, ði; jÞ ¼ ð1; 1Þ-ð2; 1Þ-ð2; 2Þ-ð1; 2Þ-ð1; 3Þy; that we define spinless fermions. When we introduce renumbered spin operators * S i; j ¼ S i; j ðS % i; j Þ for an odd (even) j; where % i ¼ 3 À i; the spinless fermions are created as c w…”

“…On the other hand, we may consider a bosonic description of ladder systems based on the spin-wave scheme [7]. Since the conventional spin-wave theory is plagued by the difficulty of the zerofield sublattice magnetizations diverging in one dimension, we construct a modified spin-wave theory [8,9] for spin-gapped antiferromagnets.…”