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arXiv:cond-mat/9807249 · Physical review. B, Condensed matter

Metaplaquette expansion for the triplet excitation spectrum in CaV4O9

Zheng Weihong, J. Oitmaa, Chris J. Hamer

Published Dec 1, 1998• 10 citations
arXivHTMLPDF

Abstract

We study antiferromagnetic, $S=1/2$ Heisenberg models with nearest- and second-neighbor interactions on the one-fifth depleted square lattice which describes the spin degrees of freedom in the spin-gap system ${\mathrm{CaV}}_{4}{\mathrm{O}}_{9}.$ The metaplaquette expansion for the triplet excitation spectrum is extended to fifth order, and the results are compared with experimental data on ${\mathrm{CaV}}_{4}{\mathrm{O}}_{9}.$ We attempt to locate the phase boundary between magnetically ordered and gapped phases.

DOI
10.1103/physrevb.58.14147

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We study antiferromagnetic, S=1/2S=1/2S=1/2 Heisenberg models with nearest- and second-neighbor interactions on the one-fifth depleted square lattice which describes the spin degrees of freedom in the spin-gap system CaV4O9.{\mathrm{CaV}}_{4}{\mathrm{O}}_{9}.CaV4​O9​. The metaplaquette expansion for the triplet excitation spectrum is extended to fifth order, and the results are compared with experimental data on CaV4O9.{\mathrm{CaV}}_{4}{\mathrm{O}}_{9}.CaV4​O9​. We attempt to locate the phase boundary between magnetically ordered and gapped phases.
A theoretical model is presented to explain the spin gap observed for CaV4O9\mathrm{CaV}{}_{4}\mathrm{O}{}_{9}CaV4​O9​. The underlying lattice of the 1/5-depleted square lattice favors a formation of the plaquette resonating-valence-bond state. Inclusion of the frustrating second neighbor interaction enhances this tendency, leading to a quantum disordered state of a two-dimensional spin-1/2 Heisenberg model with a sufficiently big spin gap compatible with experiments.
We numerically study the Heisenberg models on triangular lattices by extending it from the simplest equilateral lattice with only the nearest-neighbor exchange interaction. We show that, by including an additional weak next-nearest-neighbor interaction, a quantum spin-liquid phase is stabilized against the antiferromagnetic order. The spin gap (triplet excitation gap) and spin correlation at long distances decay algebraically with increasing system size at the critical point between the antiferromagnetic phase and the spin-liquid phase. This algebraic behavior continues in the spin-liquid phase as well, indicating the presence of an unconventional critical (algebraic spin-liquid) phase characterized by the dynamical and anomalous critical exponents z+η∼1z+η\sim1z+η∼1. Unusually small triplet and singlet excitation energies found in extended points of the Brillouin zone impose constraints on this algebraic spin liquid.
We study the single-orbital Hubbard model on the 1/5-depleted square-lattice geometry, which arises in such diverse systems as the spin-gap magnetic insulator CaV4O9 and ordered-vacancy iron selenides, presenting new issues regarding the origin of both magnetic ordering and superconductivity in these materials. We find a rich phase diagram that includes a plaquette singlet phase, a dimer singlet phase, a Néel and a block-spin antiferromagnetic phase, and stripe phases. Quantum Monte Carlo simulations show that the dominant pairing correlations at half filling change character from d wave in the plaquette phase to extended s wave upon transition to the Néel phase. These findings have intriguing connections to iron-based superconductors, and suggest that some physics of multiorbital systems can be captured by a single-orbital model at different dopings.
We investigate the quantum dynamics of the spins on different Heisenberg antiferromagnetic spin lattice systems. Firstly, we applied the coupled-cluster method to the spin-1/2 antiferromagnetic \emph{XXZ} model on a square lattice by employing an approximation which contains two-body long-range correlations and high-order four-body local correlations. Improvement is found for the ground-state energy, sublattice magnetization, and the critical anisotropy when comparing with the approximation including the two-body correlations alone. We also obtain the full excitation spectrum which is in good agreement with the quantum Monte Carlo results and the high-order spin-wave theory.Secondly, we study the longitudinal excitations of quantum antiferromagnets on a triangular lattice by a recently proposed microscopic many-body approach based on magnon-density waves. We calculate the full longitudinal excitation spectra of the antiferromagnetic Heisenberg model for a general spin quantum number in the isotropic limit. Similar to the square lattice model, we find that, at the center of the first hexagonal Brillouin zone Γ(q=0)\Gamma(\mathbf q=0)Γ(q=0) and at the magnetic ordering wavevectors ±[Q=(4π/3,0)]\pm[\mathbf Q= (4\pi/3,0)]±[Q=(4π/3,0)], the excitation spectra become gapless in the thermodynamic limit, due to the slow, logarithmic divergence of the structure factor. However, these longitudinal modes on two-dimensional models may be considered as quasi-gapped, as any finite-size effect or small anisotropy will induce a large energy gap, when compared with the counterpart of the transverse spin-wave excitations. We have also investigated the excited states of the quasi-one-dimensional quantum antiferromagnets on hexagonal lattices, including the longitudinal modes based on the magnon-density waves. A model Hamiltonian with a uniaxial single-ion anisotropy is first studied by a spin-wave theory based on the one-boson method; the ground state thus obtained is employed for the study of the longitudinal modes. The full energy spectra of both the transverse modes (i.e., magnons) and the longitudinal modes are obtained as functions of the nearest-neighbor coupling and the anisotropy constants. We have found two longitudinal modes due to the non-collinear nature of the triangular antiferromagnetic order, similar to that of the phenomenological field theory approach by Affleck. The excitation energy gaps due to the anisotropy and the energy gaps of the longitudinal modes without anisotropy are then investigated. We then compares our results for the longitudinal energy gaps at the magnetic wavevectors with the experimental results for several antiferromagnetic compounds with both integer and non-integer spin quantum numbers, and we find good agreements after the higher-order contributions are included in our calculations.
We examine the ground state and the excitations of an one-dimensional Heisenberg spin 1/2 antiferromagnet with alternating dimers and four-spin plaquettes (dimer-plaquette chain). The properties of the system depend on the competing dimer and plaquette bonds. Several exact, exact-numerical and perturbational results are presented. We find that the system is gapped for all parameter values. For the latter one we find an effective S=1 Haldane like behaviour in the limit of dominating dimer bonds. The model considered is related to the recently found 1/5-depleted square-lattice Heisenberg system CaV4O9CaV_4O_9CaV4​O9​.
Based on a special variant of plaquette expansion, an operator is constructed whose eigenvalues give the low-energy singlet spectrum of spin-12\frac1221​ Heisenberg antiferromagnet on square lattice with nearest- and frustrating next-nearest-neighbor exchange couplings J1J_1J1​ and J2J_2J2​. It is well known that a non-magnetic phase arises in this model at 0.4≲J2/J1≲0.60.4\lesssim J_2/J_1\lesssim 0.60.4≲J2​/J1​≲0.6 sandwiched by two Neel ordered phases. In agreement with previous results, we observe a first-order quantum phase transition (QPT) at J2≈0.64J1J_2\approx 0.64J_1J2​≈0.64J1​ from the non-magnetic phase to the Neel one. Large gap (≳0.4J1\gtrsim0.4J_1≳0.4J1​) is found in the singlet spectrum at J2<0.64J1J_2<0.64J_1J2​<0.64J1​ that excludes a gapless spin-liquid state at 0.4≲J2/J1≲0.60.4\lesssim J_2/J_1\lesssim 0.60.4≲J2​/J1​≲0.6 and the deconfined quantum criticality scenario for the QPT to another Neel phase. We observe a first-order QPT at J2≈0.55J1J_2\approx 0.55J_1J2​≈0.55J1​ presumably between two non-magnetic phases.