Square Lattice Quantum Antiferromagnet Research Articles

Mutually attracting spin waves in the square-lattice quantum antiferromagnet

Spin waves (magnons) in two dimensions are the potential glue in high-temperature superconductors so that their quantitative understanding is mandatory. Yet even for the fundamental case of the undoped Heisenberg model on the square lattice a consistent picture is still lacking. Significant spectral continua are taken as evidence of the existence of fractional excitations (spinons), but descriptions in terms of spinons fail to show the established absence of an energy gap. Here a fully consistent picture of the dynamics in the square-lattice quantum antiferromagnet is provided which agrees with the experimental findings. The key step is to capture (i) the strong attractive interaction between the spin waves and (ii) the vertex corrections of the observables.

Real-space renormalization-group studies of low-dimensional quantum antiferromagnets.

We study the ground state of one- and two-dimensional (square-lattice) spin-1/2 quantum antiferromagnets using a numerical real-space renormalization-group (RG) approach. In our RG approach we consider blocks of various sizes but with an odd number of sites; we retain only the doublet ground state and we integrate out the higher-energy states by means of second-order quasidegenerate perturbation theory. That is, we assume that the role of the excited states of a block, in the RG iteration process, is to renormalize the effective coupling parameters between blocks. We compute the ground-state energy of a spin-1/2 linear chain for various block sizes and find close agreement with the Bethe-ansatz exact solution. In the case of the spin-1/2 square-lattice quantum antiferromagnet, the obtained ground-state energy is in reasonable agreement with the available numerical estimates.

Dimer stability region in a frustrated quantum Heisenberg antiferromagnet.

We study the stability region for the columnar dimer state proposed as a candidate ground state for the square-lattice quantum antiferromagnet with first- and second-neighbor antiferromagnetic couplings (${\mathit{J}}_{1}$-${\mathit{J}}_{2}$ model). We use a boson representation of the spin operators suited to the perturbative expansion around a dimer ground state. At lowest order, the columnar dimer is found to be stable only at the classical critical value ${\mathit{J}}_{2}$/${\mathit{J}}_{2}$=1/2. However, we show that the leading anharmonic corrections stabilize the dimerized phase in a region of a finite width around ${\mathit{J}}_{2}$/${\mathit{J}}_{1}$=1/2. A comparison of the ground-state energies shows that among the possible dimerized states the columnar dimer is the most favorable candidate to separate the two ordered states in the S=1/2 antiferromagnetic with first- and second-neighbor exchange.

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.