Modified spin-wave theory with ordering vector optimization II: Spatially anisotropic triangular lattice and $J_1{J}_2{J}_3$ model with Heisenberg interactions

Abstract

We study the ground state phases of the $S=1/2$ Heisenberg quantum antiferromagnet on the spatially anisotropic triangular lattice and on the square lattice with up to next-next-nearest neighbor coupling (the $J_1{J}_2{J}_3$ model), making use of Takahashi's modified spin-wave (MSW) theory supplemented by ordering vector optimization. We compare the MSW results with exact diagonalization and projected-entangled-pair-states calculations, demonstrating their qualitative and quantitative reliability. We find that MSW theory correctly accounts for strong quantum effects on the ordering vector of the magnetic phases of the models under investigation: in particular collinear magnetic order is promoted at the expenses of non-collinear (spiral) order, and several spiral states which are stable at the classical level, disappear from the quantum phase diagram. Moreover, collinear states and non-collinear ones are never connected continuously, but they are separated by parameter regions in which MSW breaks down, signaling the possible appearance of a non-magnetic ground state. In the case of the spatially anisotropic triangular lattice, a large breakdown region appears also for weak couplings between the chains composing the lattice, suggesting the possible occurrence of a large non-magnetic region continuously connected with the spin-liquid state of the uncoupled chains.

References in corpus (13)

• Magnetic Order versus superconductivity in the Iron-based layered La(O1-xFx)FeAs systems
• Plaquette valence bond solid in the frustrated Heisenberg quantum antiferromagnet on the square lattice
• Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment
• Spinons and triplons in spatially anisotropic frustrated antiferromagnets
• Excitation spectra of the spin-1/2 triangular-lattice Heisenberg antiferromagnet
• Magnetic properties of BaCdVO(PO_4)_2: a strongly frustrated spin-1/2 square lattice close to the quantum critical regime
• The J1-J2 model: First order phase transition versus deconfinement of spinons
• Ordering in spatially anisotropic triangular antiferromagnets
• Spin Liquid Phase in Anisotropic Triangular Lattice Heisenberg Model: Exact diagonalization and density-matrix renormalization group calculations
• Quantum Phases of Trapped Ions in an Optical Lattice
• Magnetism and superconductivity of strongly correlated electrons on the triangular lattice
• Low temperature broken symmetry phases of spiral antiferromagnets
• Excitation spectra and ground state properties of the layered spin-1/2 frustrated antiferromagnets Cs_2CuCl_4 and Cs_2CuBr_4