Frustrated Quantum Antiferromagnets Research Articles

Self-consistent interaction of magnons in a frustrated quantum antiferromagnet

Self-consistent interaction of magnons in a frustrated quantum antiferromagnet

J1-J2model: Energy, correlations, and order-parameter fluctuations on finite lattices

A modified spin-wave theory is applied to frustrated quantum antiferromagnets on finite square lattices. The results for the energy and for the correlation functions are found to agree very well with exact values obtained by numerical methods. The fluctuations of different order parameters, previously proposed to characterize possible different phases of purely quantum origin, are investigated. Our results suggest that the enhancement of long-range dimer and twist order seen numerically is not significant, and is due to the finite size of the lattices considered.

Low-temperature properties of two-dimensional frustrated quantum antiferromagnets.

Though much of the recent work on 2D quantum canted antiferromagnets has been devoted to the study of disordered states, there is evidence that some of these systems have N\'eel ground states, even for spin 1/2. Following Chakravarty, Halperin, and Nelson, we study the quantum nonlinear sigma model suited to these systems and obtain, for the correlation length, \ensuremath{\xi}=${\mathit{C}}_{\ensuremath{\xi}}$[A/(${\mathit{k}}_{\mathit{B}}$T${)}^{1/2}$]${\mathit{e}}_{\mathit{B}}^{2\mathrm{\ensuremath{\pi}}\mathit{B}/\mathit{k}}$T, where A and B depend on the spin stiffness and spin-wave velocities renormalized by quantum fluctuations. We discuss experiments on $^{3}\mathrm{He}$ adsorbed on Grafoil.

Incommensurate correlations in quantum spin models.

Frustrated quantum antiferromagnets in two dimensions are studied by analyzing, using a 1/N expansion, the phase properties of associated (2+1)-dimensional nonlinear continuum models. The spin system on square lattice with isotropic couplings that include up to the third-nearest neighbors is considered. Periodic, commensurate, or incommensurate correlations are found to be stable. The relevance in some phase regions of effective (1+1)-dimensional nonlinear models is discussed.

First-order transition in frustrated quantum antiferromagnets.

A two-dimensional frustrated quantum Heisenberg model with first-, second- (diagonal), and third-neighbor couplings (${\mathit{J}}_{1}$-${\mathit{J}}_{2}$-${\mathit{J}}_{3}$ model) is studied near the phase boundary of the antiferromagnetic (\ensuremath{\pi},\ensuremath{\pi}) phase. It is shown that quantum corrections remove accidental classical degeneracy and ensure a nonzero hysteresis width for the ${\mathit{J}}_{3}$=0 transition between commensurate (\ensuremath{\pi},\ensuremath{\pi}) and (\ensuremath{\pi},0) phases, so that finite ${\mathit{J}}_{3}$ is necessary to produce a continuous transition through the intermediate disordered phase.

Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model.

The Ising model on a three-dimensional cubic lattice with all plaquettes in the x-y frustrated plane is studied by use of a Monte Carlo technique; the exchange constants are of equal magnitude, but have varying signs. At zero temperature, the model has a finite entropy and no long-range order. The low-temperature phase is characterized by an order parameter measuring the ${\mathit{openZ}}_{4}$ symmetry of lattice rotations which is invariant under Mattis gauge transformation; fluctuations lead to the alignment of frustrated bonds into columns and a fourfold degeneracy. An additional factor-of-2 degeneracy is obtained from a global spin flip. The order vanishes at a critical temperature by a transition that appears to be in the universality class of the D=3, XY model. These results are consistent with the theoretical predictions of Blankschtein et al. This Ising model is related by duality to phenomenological models of two-dimensional frustrated quantum antiferromagnets.

Large-N expansion for frustrated quantum antiferromagnets.

A large-N expansion technique based on symplectic [Sp(N)] symmetry for frustrated magnetic systems is proposed and applied to the square-lattice quantum antiferromagnet with first-, second-, and third-neighbor antiferromangetic coupling. In addition to disordered states similar to those in unfrustrated systems, phases with incommensurate coplanar spin correlations and unconfined bosonic spinons are found. The occurrence of ``order from disorder'' is discussed. Neither chirally ordered nor spin-nematic states are found.

Series investigations of magnetically disordered ground states in two-dimensional frustrated quantum antiferromagnets.

An extensive series-expansion study of the square-lattice, spin-1/2 Heisenberg antiferromagnet with nearest- and second-neighbor couplings has been carried out to investigate the nature of the ground state for ${\mathit{J}}_{2}$/${\mathit{J}}_{1}$\ensuremath{\approxeq}1/2. In agreement with an earlier numerical study along similar lines, we find that the magnetically disordered phase exhibits columnar spontaneous dimerization, but the magnitude of such order may not be as large as had been suggested previously. Although the magnetically disordered phase is not critical, it appears to have both spin-spin and energy-energy correlations of range greater than a few lattice spacings. The possibility of ``spin-nematic'' order, as proposed by Chandra, Coleman, and Larkin, has not been directly ruled out, but the balance of circumstantial evidence weighs against it in this system.