Excitation spectrum of Heisenberg spin ladders

• Published in: Physical review. B, Condensed matter Condensed matter, 1993-02, Vol.47 (6), p.3196-3203
• Main Authors: BARNES, T, DAGOTTO, E, RIERA, J, SWANSON, E. S
• Format: Article
• Language: English
• Subjects: 665000 - Physics of Condensed Matter- (1992-); ANTIFERROMAGNETISM; CALCULATION METHODS; CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Condensed matter: electronic structure, electrical, magnetic, and optical properties; COUPLING; CRYSTAL MODELS; ENERGY GAP; ENERGY LEVELS; Exact sciences and technology; EXCITED STATES; General theory and models of magnetic ordering; HEISENBERG MODEL; Magnetic properties and materials; MAGNETISM; MATHEMATICAL MODELS; MONTE CARLO METHOD; OXYGEN COMPOUNDS; PARTICLE MODELS; PERTURBATION THEORY; PHOSPHATES; PHOSPHORUS COMPOUNDS; Physics; Quantized spin models; SPIN WAVES; STRONG-COUPLING MODEL; TRANSITION ELEMENT COMPOUNDS; VANADIUM COMPOUNDS; VANADIUM PHOSPHATES
• ISSN: 0163-1829; 1095-3795
• DOI: 10.1103/physrevb.47.3196

Heisenberg antiferromagnetic spin ladders'' (two coupled spin chains) are low-dimensional magnetic systems which for [ital S]=1/2 interpolate between half-integer-spin chains, when the chains are decoupled, and effective integer-spin one-dimensional chains in the strong-coupling limit. The spin-1/2 ladder may be realized in nature by vanadyl pyrophosphate, (VO)[sub 2]P[sub 2]O[sub 7]. In this paper we apply strong-coupling perturbation theory, spin-wave theory, Lanczos techniques, and a Monte Carlo method to determine the ground-state energy and the low-lying excitation spectrum of the ladder. We find evidence of a nonzero spin gap for [ital all] interchain couplings [ital J][sub [perpendicular]][gt]0. A band of spin-triplet excitations above the gap is also analyzed. These excitations are unusual for an antiferromagnet, since their long-wavelength dispersion relation behaves as ([ital k][minus][ital k][sub 0])[sup 2] (in the strong-coupling limit [ital J][sub [perpendicular]][much gt][ital J], where [ital J] is the in-chain antiferromagnetic coupling). Their band is folded, with a minimum energy at [ital k][sub 0]=[pi], and a maximum between [ital k][sub 1]=[pi]/2 (for [ital J][sub [perpendicular]]=0) and 0 (for [ital J][sub [perpendicular]]=[infinity]). We also give numerical results for the dynamical structure factor [ital S]([ital q],[omega]), which can be determined in neutron scattering experiments. Finally, possible experimental techniques for studying the excitation spectrum are discussed.