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arXiv:cond-mat/0504283 · Physical Review B

Coupled cluster treatment of the Shastry-Sutherland antiferromagnet

R. Darradi, Johannes Richter, DAMIAN J. J. FARNELL

Published Sep 15, 2005• 79 citations
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Abstract

We consider the zero-temperature properties of the spin-half two-dimensional Shastry-Sutherland antiferromagnet by using a high-order coupled cluster method treatment. We find that this model demonstrates various ground-state phases (N\'eel, magnetically disordered, orthogonal dimer), and we make predictions for the positions of the phase transition points. In particular, we find that the orthogonal-dimer state becomes the ground state at ${J}_{2}^{d}∕{J}_{1}\ensuremath{\sim}1.477$. For the critical point ${J}_{2}^{c}∕{J}_{1}$ where the semiclassical N\'eel order disappears we obtain a significantly lower value than ${J}_{2}^{d}∕{J}_{1}$, namely, ${J}_{2}^{c}∕{J}_{1}$ in the range 1.14--1.39. We therefore conclude that an intermediate phase exists between the N\'eel and the dimer phases. An analysis of the energy of a competing spiral phase yields clear evidence that the spiral phase does not become the ground state for any value of ${J}_{2}$. The intermediate phase is therefore magnetically disordered but may exhibit plaquette or columnar dimer ordering.

DOI
10.1103/physrevb.72.104425

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We consider the zero-temperature properties of the spin-half two-dimensional Shastry-Sutherland antiferromagnet by using a high-order coupled cluster method treatment. We find that this model demonstrates various ground-state phases (N'eel, magnetically disordered, orthogonal dimer), and we make predictions for the positions of the phase transition points. In particular, we find that the orthogonal-dimer state becomes the ground state at J2d∕J1\ensuremath∼1.477{J}_{2}^{d}∕{J}_{1}\ensuremath{\sim}1.477J2d​∕J1​\ensuremath∼1.477. For the critical point J2c∕J1{J}_{2}^{c}∕{J}_{1}J2c​∕J1​ where the semiclassical N'eel order disappears we obtain a significantly lower value than J2d∕J1{J}_{2}^{d}∕{J}_{1}J2d​∕J1​, namely, J2c∕J1{J}_{2}^{c}∕{J}_{1}J2c​∕J1​ in the range 1.14--1.39. We therefore conclude that an intermediate phase exists between the N'eel and the dimer phases. An analysis of the energy of a competing spiral phase yields clear evidence that the spiral phase does not become the ground state for any value of J2{J}_{2}J2​. The intermediate phase is therefore magnetically disordered but may exhibit plaquette or columnar dimer ordering.
Using the coupled cluster method for high orders of approximation and complementary exact diagonalization studies we investigate the ground state properties of the spin-1/2 J1−−J2{J}_{1}--{J}_{2}J1​−−J2​ frustrated Heisenberg antiferromagnet on the square lattice. We have calculated the ground state energy, the magnetic order parameter, the spin stiffness, and several generalized susceptibilities to probe magnetically disordered quantum valence-bond phases. We have found that the quantum critical points for both the N\'eel and collinear orders are ${J}_{2}^{c1}\ensuremath{\approx}(0.44\ifmmode\pm\else\textpm\fi{}0.01){J}_{1}$ and ${J}_{2}^{c2}\ensuremath{\approx}(0.59\ifmmode\pm\else\textpm\fi{}0.01){J}_{1}$, respectively, which are in good agreement with the results obtained by other approximations. In contrast to the recent study by [Sirker et al. Phys. Rev. B 73, 184420 (2006)], our data do not provide evidence for the transition from the N\'eel to the valence-bond solid state to be first order. Moreover, our results are in favor of the deconfinement scenario for that phase transition. We also discuss the nature of the magnetically disordered quantum phase.
We use the coupled-cluster method in high orders of approximation to make a comprehensive study of the ground-state (GS) phase diagram of the spin-1/2 J1{J}_{1}J1​-J2{J}_{2}J2​-J3{J}_{3}J3​ model on a two-dimensional honeycomb lattice with antiferromagnetic (AFM) interactions up to third-nearest neighbors. Results are presented for the GS energy and the average local onsite magnetization. With the nearest-neighbor coupling strength ${J}_{1}\ensuremath{\equiv}1$, we find four magnetically ordered phases in the parameter window ${J}_{2},{J}_{3}\ensuremath{\in}[0,1]$, namely, the N\'eel, striped, and N\'eel-II collinear AFM phases, plus a spiral phase. The N\'eel-II phase appears as a stable GS phase in the classical version of the model only for values J3<0{J}_{3}<0J3​<0. Each of these four ordered phases shares a boundary with a disordered quantum paramagnetic (QP) phase, and at several widely separated points on the phase boundaries the QP phase has an infinite susceptibility to plaquette valence-bond crystalline order. We identify all of the phase boundaries with good precision in the parameter window studied, and we find three tricritical quantum critical points therein at (a) $({J}_{2}^{{c}_{1}},{J}_{3}^{{c}_{1}})=(0.51\ifmmode\pm\else\textpm\fi{}0.01,0.69\ifmmode\pm\else\textpm\fi{}0.01)$ between the N\'eel, striped, and QP phases; (b) $({J}_{2}^{{c}_{2}},{J}_{3}^{{c}_{2}})=(0.65\ifmmode\pm\else\textpm\fi{}0.02,0.55\ifmmode\pm\else\textpm\fi{}0.01)$ between the striped, spiral, and QP phases; and (c) $({J}_{2}^{{c}_{3}},{J}_{3}^{{c}_{3}})=(0.69\ifmmode\pm\else\textpm\fi{}0.01,0.12\ifmmode\pm\else\textpm\fi{}0.01)$ between the spiral, N\'eel-II, and QP phases.
We report on recent results for strongly frustrated quantum J1 - J2 antiferromagnets in dimensionality d = 1, 2, 3 obtained by the coupled cluster method (CCM). We demonstrate that the CCM in high orders of approximation allows us to investigate quantum phase transitions driven by frustration and to discuss novel quantum ground states. In detail we consider the ground-state properties of (i) the Heisenberg spin-1/2 antiferromagnet on the cubic lattice in d = 1, 2, 3, and use the results for the energy, the sublattice magnetization and the spin stiffness as a benchmark test for the precision of the method; (ii) coupled frustrated spin chains (the quasi-one-dimensional J1 - J2 model) and discuss the influence of the quantum fluctuations and the interchain coupling on the incommensurate spiral state present in the classical model; (iii) the Shastry-Sutherland antiferromagnet on the square lattice; and (iv) a stacked frustrated square-lattice Heisenberg antiferromagnet (the quasi-two-dimensional J1 - J2 model), and discuss the influence of the interlayer coupling on the quantum paramagnetic ground-state phase that is present for the strictly two-dimensional model.
We use the coupled cluster method (CCM) to study the zero-temperature ground-state (GS) properties of a spin-12\frac{1}{2}21​ ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg antiferromagnet on a triangular lattice with competing nearest-neighbor and next-nearest-neighbor exchange couplings J1>0{J}_{1}>0J1​>0 and ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$, respectively, in the window $0\ensuremath{\le}\ensuremath{\kappa}<1$. The classical version of the model has a single GS phase transition at ${\ensuremath{\kappa}}^{\mathrm{cl}}=\frac{1}{8}$ in this window from a phase with 3-sublattice antiferromagnetic (AFM) ${120}^{\ensuremath{\circ}}$ N\'eel order for $\ensuremath{\kappa}<{\ensuremath{\kappa}}^{\mathrm{cl}}$ to an infinitely degenerate family of 4-sublattice AFM N\'eel phases for $\ensuremath{\kappa}>{\ensuremath{\kappa}}^{\mathrm{cl}}$. This classical accidental degeneracy is lifted by quantum fluctuations, which favor a 2-sublattice AFM striped phase. For the quantum model we work directly in the thermodynamic limit of an infinite number of spins, with no consequent need for any finite-size scaling analysis of our results. We perform high-order CCM calculations within a well-controlled hierarchy of approximations, which we show how to extrapolate to the exact limit. In this way we find results for the case $\ensuremath{\kappa}=0$ of the spin-12\frac{1}{2}21​ model for the GS energy per spin, $E/N=\ensuremath{-}0.5521(2){J}_{1}$, and the GS magnetic order parameter, M=0.198(5)M=0.198(5)M=0.198(5) (in units where the classical value is Mcl=12{M}^{\mathrm{cl}}=\frac{1}{2}Mcl=21​), which are among the best available. For the spin-12\frac{1}{2}21​ ${J}_{1}\ensuremath{-}{J}_{2}$ model we find that the classical transition at $\ensuremath{\kappa}={\ensuremath{\kappa}}^{\mathrm{cl}}$ is split into two quantum phase transitions at ${\ensuremath{\kappa}}_{1}^{c}=0.060(10)$ and ${\ensuremath{\kappa}}_{2}^{c}=0.165(5)$. The two quasiclassical AFM states (viz., the ${120}^{\ensuremath{\circ}}$ N\'eel state and the striped state) are found to be the stable GS phases in the regime $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{1}^{c}$ and $\ensuremath{\kappa}>{\ensuremath{\kappa}}_{2}^{c}$, respectively, while in the intermediate regimes ${\ensuremath{\kappa}}_{1}^{c}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{2}^{c}$ the stable GS phase has no evident long-range magnetic order.
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