Spin wave analysis of square lattice anisotropic frustrated Heisenberg quantum antiferromagnet (original) (raw)
Related papers
Spin-wave analysis to the spatially anisotropic Heisenberg antiferromagnet on a triangular lattice
Physical Review B
We study the phase diagram at T = 0 of the antiferromagnetic Heisenberg model on the triangular lattice with spatially-anisotropic interactions. For values of the anisotropy very close to Jα/J β = 0.5, conventional spin wave theory predicts that quantum fluctuations melt the classical structures, for S = 1/2. For the regime J β < Jα, it is shown that the incommensurate spiral phases survive until J β /Jα = 0.27, leaving a wide region where the ground state is disordered. The existence of such nonmagnetic states suggests the possibility of spin liquid behavior for intermediate values of the anisotropy.
Magnetic and quantum disordered phases in triangular-lattice Heisenberg antiferromagnets
Physical Review B, 1999
We study, within the Schwinger-boson approach, the ground-state structure of two Heisenberg antiferromagnets on the triangular lattice: the J1−J2 model, which includes a next-nearest-neighbor coupling J2, and the spatially-anisotropic J1 − J ′ 1 model, in which the nearest-neighbor coupling takes a different value J ′ 1 along one of the bond directions. The motivations for the study of these systems range from general theoretical questions concerning frustrated quantum spin models to the concrete description of the insulating phase of some layered molecular crystals. For both models, the inclusion of one-loop corrections to saddle-point results leads to the prediction of nonmagnetic phases for particular values of the parameters J1/J2 and J ′ 1 /J1. In the case of the J1 −J2 model we shed light on the existence of such disordered quantum state, a question which is controversial in the literature. For the J1 −J ′ 1 model our results for the ground-state energy, quantum renormalization of the pitch in the spiral phase, and the location of the nonmagnetic phases, nicely agree with series expansions predictions.
2010
Magnetic phase diagram of a spatially anisotropic, frustrated spin-1 2 Heisenberg antiferromagnet on a stacked square lattice is investigated using second-order spin-wave expansion. The effects of interlayer coupling and the spatial anisotropy on the magnetic ordering of two ordered ground states are explicitly studied. It is shown that with increase in next nearest neighbor frustration the second-order corrections play a significant role in stabilizing the magnetization. We obtain two ordered magnetic phases (Neél and stripe) separated by a paramagnetic disordered phase. Within second-order spin-wave expansion we find that the width of the disordered phase diminishes with increase in the interlayer coupling or with decrease in spatial anisotropy but it does not disappear. Our obtained phase diagram differs significantly from the phase diagram obtained using linear spin-wave theory.
2011
Magnetic phase diagram of a spatially anisotropic, frustrated spin-1/2 Heisenberg antiferromagnet on a stacked square lattice is investigated using second-order spin-wave expansion. The effects of interlayer coupling and the spatial anisotropy on the magnetic ordering of two ordered ground states are explicitly studied. It is shown that with increase in next nearest neighbor frustration the second-order corrections play a significant role in stabilizing the magnetization. We obtain two ordered magnetic phases (Neel and stripe) separated by a paramagnetic disordered phase. Within second-order spin-wave expansion we find that the width of the disordered phase diminishes with increase in the interlayer coupling or with decrease in spatial anisotropy but it does not disappear. Our obtained phase diagram differs significantly from the phase diagram obtained using linear spin-wave theory.
Frustrated spin-1/2 Heisenberg antiferromagnet on a chevron-square lattice
Physical Review B, 2013
The coupled cluster method (CCM) is used to study the zero-temperature properties of a frustrated spin-half (s = 1 2) J1-J2 Heisenberg antiferromagnet (HAF) on a two-dimensional (2D) chevron-square lattice. On an underlying square lattice each site of the model has 4 nearestneighbor exchange bonds of strength J1 > 0 and 2 frustrating next-nearest-neighbor (diagonal) bonds of strength J2 ≡ κJ1 > 0, such that each fundamental square plaquette has only one diagonal bond. The diagonal J2 bonds are arranged in a chevron pattern such that along one of the two basic square axis directions (say, along rows) the J2 bonds are parallel, while along the perpendicular axis direction (say, along columns) alternate J2 bonds are perpendicular to each other, and hence form one-dimensional (1D) chevron chains in this direction. The model thus interpolates smoothly between 2D HAFs on the square (κ = 0) and triangular (κ = 1) lattices, and also extrapolates to disconnected 1D HAF chains (κ → ∞). The classical (s → ∞) version of the model has collinear Néel order for 0 < κ < κ cl and a form of noncollinear spiral order for κ cl < κ < ∞, where κ cl = 1 2. For the s = 1 2 model we use both these classical states, as well as other collinear states not realized as classical ground-state (GS) phases, as CCM reference states, on top of which the multispin-flip configurations resulting from quantum fluctuations are incorporated in a systematic truncation hierarchy, which we carry out to high orders and then extrapolate to the physical limit. At each order we calculate the GS energy, GS magnetic order parameter, and the susceptibilities of the states to various forms of valence-bond crystalline (VBC) order, including plaquette and two different dimer forms. We find strong evidence that the s = 1 2 model has two quantum critical points, at κc 1 ≈ 0.72(1) and κc 2 ≈ 1.5(1), such that the system has Néel order for 0 < κ < κc 1 , a form of spiral order for κc 1 < κ < κc 2 that includes the correct three-sublattice 120 • spin ordering for the triangular-lattice HAF at κ = 1, and parallel-dimer VBC order for κc 2 < κ < ∞.
Journal of Physics: Condensed Matter, 2011
Magnetic phase diagram of a spatially anisotropic, frustrated spin-1 2 Heisenberg antiferromagnet on a stacked square lattice is investigated using second-order spin-wave expansion. The effects of interlayer coupling and the spatial anisotropy on the magnetic ordering of two ordered ground states are explicitly studied. It is shown that with increase in next nearest neighbor frustration the second-order corrections play a significant role in stabilizing the magnetization. We obtain two ordered magnetic phases (Neél and stripe) separated by a paramagnetic disordered phase. Within second-order spin-wave expansion we find that the width of the disordered phase diminishes with increase in the interlayer coupling or with decrease in spatial anisotropy but it does not disappear. Our obtained phase diagram differs significantly from the phase diagram obtained using linear spin-wave theory.
Ground states of spin-12 triangular antiferromagnets in a magnetic field
Physical Review B, 2013
We use a combination of numerical density matrix renormalization group (DMRG) calculations and several analytical approaches to comprehensively study a simplified model for a spatially anisotropic spin-1/2 triangular lattice Heisenberg antiferromagnet: the three-leg triangular spin tube (TST). The model is described by three Heisenberg chains, with exchange constant J, coupled antiferromagnetically with exchange constant J ′ along the diagonals of the ladder system, with periodic boundary conditions in the shorter direction. Here we determine the full phase diagram of this model as a function of both spatial anisotropy (between the isotropic and decoupled chain limits) and magnetic field. We find a rich phase diagram, which is remarkably dominated by quantum states -the phase corresponding to the classical ground state appears only in an exceedingly small region. Among the dominant phases generated by quantum effects are commensurate and incommensurate coplanar quasi-ordered states, which appear in the vicinity of the isotropic region for most fields, and in the high field region for most anisotropies. The coplanar states, while not classical ground states, can at least be understood semiclassically. Even more strikingly, the largest region of phase space is occupied by a spin density wave phase, which has incommensurate collinear correlations along the field. This phase has no semiclassical analog, and may be ascribed to enhanced one-dimensional fluctuations due to frustration. Cutting across the phase diagram is a magnetization plateau, with a gap to all excitations and "up up down" spin order, with a quantized magnetization equal to 1/3 of the saturation value. In the TST, this plateau extends almost but not quite to the decoupled chains limit. Most of the above features are expected to carry over to the two dimensional system, which we also discuss. At low field, a dimerized phase appears, which is particular to the one dimensional nature of the TST, and which can be understood from quantum Berry phase arguments. arXiv:1211.1676v2 [cond-mat.str-el]
Nematic phase in the spin one two dimensional anisotropic antiferromagnet
Journal of Magnetism and Magnetic Materials, 2018
We study quantum phase transitions in the anisotropic Heisenberg model with a pseudodipolar interaction on the square lattice, at zero temperature, using the SU(3) Schwinger boson technique in a mean field approximation. We present the dispersion relation for several values of the parameters. When we take into account the effect of the next near neighbor interaction, the phase diagram, at zero temperature shows the existence of a region in the intermediate frustrated regime, even for zero anisotropy parameter, where the system is magnetically disordered. A prediction of our model is the existence of a finite gap in this region.
The ground state of the spin-½ Heisenberg antiferromagnet on an Archimedean 4-6-12 lattice
Journal of Physics: Condensed Matter, 2001
An investigation of the Néel Long Range Order (NLRO) in the ground state of antiferromagnetic Heisenberg spin system on the two-dimensional, uniform, bipartite lattice consisting of squares, hexagons and dodecagons is presented. Basing on the analysis of the order parameter and the long-distance correlation function the NLRO is shown to occur in this system. Exact diagonalization and variational (Resonating Valence Bond) methods are applied.