arXiv subjects

R. Darradi

Publications and source records attributed to R. Darradi.

14 recordsLinked to original sources

arXiv2011

The spin-half Heisenberg antiferromagnet on two Archimedian lattices: From the bounce lattice to the maple-leaf lattice and beyond

We investigate the ground state of the two-dimensional Heisenberg antiferromagnet on two Archimedean lattices, namely, the maple-leaf and bounce lattices as well as a generalized $J$-$J'$ model interpolating between both systems by varying $J'/J$ from $J'/J=0$ (bounce limit) to $J'/J=1$ (maple-leaf limit) and beyond. We use the coupled cluster method to high orders of approximation and also exact diagonalization of finite-sized lattices to discuss the ground-state magnetic long-range order based on data for the ground-state energy, the magnetic order parameter, the spin-spin correlation functions as well as the pitch angle between neighboring spins. Our results indicate that the "pure" bounce ($J'/J=0$) and maple-leaf ($J'/J=1$) Heisenberg antiferromagnets are magnetically ordered, however, with a sublattice magnetization drastically reduced by frustration and quantum fluctuations. We found that magnetic long-range order is present in a wide parameter range $0 \le J'/J \lesssim J'_c/J $ and that the magnetic order parameter varies only weakly with $J'/J$. At $J'_c \approx 1.45 J$ a direct first-order transition to a quantum orthogonal-dimer singlet ground state without magnetic long-range order takes place. The orthogonal-dimer state is the exact ground state in this large-$J'$ regime, and so our model has similarities to the Shastry-Sutherland model. Finally, we use the exact diagonalization to investigate the magnetization curve. We a find a 1/3 magnetization plateau for $J'/J \gtrsim 1.07$ and another one at 2/3 of saturation emerging only at large $J'/J \gtrsim 3$.

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arXiv2010

Field-dependent spin and heat conductivities of dimerized spin-1/2 chains

We study the spin and heat conductivity of dimerized spin-1/2 chains in homogeneous magnetic fields at finite temperatures. At zero temperature, the model undergoes two field-induced quantum phase transitions from a dimerized, into a Luttinger, and finally into a fully polarized phase. We search for signatures of these transitions in the spin and heat conductivities. Using exact diagonalization, we calculate the Drude weights, the frequency dependence of the conductivities, and the corresponding integrated spectral weights. As a main result, we demonstrate that both the spin and heat conductivity are enhanced in the gapless phase and most notably at low frequencies. In the case of the thermal conductivity, however, the field-induced increase seen in the bare transport coefficients is suppressed by magnetothermal effects, caused by the coupling of the heat and spin current in finite magnetic fields. Our results complement recent magnetic transport experiments on spin ladder materials with sufficiently small exchange couplings allowing access to the field-induced transitions.

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arXiv2010

The frustrated spin-1/2 J1-J2 Heisenberg ferromagnet on the square lattice: Exact diagonalization and Coupled-Cluster study

We investigate the ground-state magnetic order of the spin-1/2 J1-J2 Heisenberg model on the square lattice with ferromagnetic nearest-neighbor exchange J1<0 and frustrating antiferromagnetic next-nearest neighbor exchange J2>0. We use the coupled-cluster method to high orders of approximation and Lanczos exact diagonalization of finite lattices of up to N=40 sites in order to calculate the ground-state energy, the spin-spin correlation functions, and the magnetic order parameter. We find that the transition point at which the ferromagnetic ground state disappears is given by J2^{c1}=0.393|J1| (exact diagonalization) and J2^{c1}=0.394|J1| (coupled-cluster method). We compare our results for ferromagnetic J1 with established results for the spin-1/2 J1-J2 Heisenberg model with antiferromagnetic J1. We find that both models (i.e., ferro- and antiferromagnetic J1) behave similarly for large J2, although significant differences between them are observed for J2/|J1| \lesssim 0.6. Although the semiclassical collinear magnetic long-range order breaks down at J2^{c2} \approx 0.6J1 for antiferromagnetic J1, we do not find a similar breakdown of this kind of long-range order until J2 \sim 0.4|J1| for the model with ferromagnetic J1. Unlike the case for antiferromagnetic J1, if an intermediate disordered phase does occur between the phases exhibiting semiclassical collinear stripe order and ferromagnetic order for ferromagnetic J1 then it is likely to be over a very small range below J2 \sim 0.4|J1|.

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arXiv2008

Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment

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 $J_1$--$J_2$ 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 Néel and collinear orders are $J_2^{c1}\approx (0.44 \pm 0.01)J_1$ and $J_2^{c2}\approx (0.59 \pm 0.01)J_1$ 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 {\bf 73}, 184420 (2006)], our data do not provide evidence for the transition from the Néel 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.

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arXiv2008

The ground-state magnetic ordering of the spin-1/2 frustrated J1-J2 XXZ model on the square lattice

Using the coupled-cluster method for infinite lattices and the exact diagonalization method for finite lattices, we study the influence of an exchange anisotropy Delta on the ground-state phase diagram of the spin-1/2 frustrated J1-J2 XXZ antiferromagnet on the square lattice. We find that increasing Delta>1 (i.e. an Ising type easy-axis anisotropy) as well as decreasing Delta<1 (i.e. an XY type easy-plane anisotropy) both lead to a monotonic shrinking of the parameter region of the magnetically disordered quantum phase. Finally, at Delta~1.9 this quantum phase disappears, whereas in pure XY limit (Delta=0) there is still a narrow region around J2 =0.5J1 where the quantum paramagnetic ground-state phase exists.

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arXiv2008

The quantum $J_{1}$--$J_{1}'$--$J_{2}$ spin-1 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D

We study the phase diagram of the isotropic $J_{1}$--$J_{1}'$--$J_{2}$ Heisenberg model for spin-1 particles on an anisotropic square lattice, using the coupled cluster method. We find no evidence for an intermediate phase between the Néel and stripe states, as compared with all previous results for the corresponding spin-1/2 case. However, we find a quantum tricritical point at $J_{1}'/J_{1} \approx0.66 \pm 0.03$, $J_{2}/J_{1} \approx0.35\pm0.02$, where a line of second-order phase transitions between the quasi-classical Néel and stripe-ordered phases (for $J_{1}'/J_{1} \lesssim 0.66$) meets a line of first-order phase transitions between the same two states (for $J_{1}'/J_{1} \gtrsim 0.66$)

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arXiv2008

Effect of anisotropy on the ground-state magnetic ordering of the spin-half quantum $J_1^{XXZ}$--$J_2^{XXZ}$ model on the square lattice

We study the zero-temperature phase diagram of the 2D quantum $J_{1}^{XXZ}$--$J_{2}^{XXZ}$ spin-1/2 anisotropic Heisenberg model on the square lattice. In particular, the effects of the anisotropy $Δ$ on the $z$-aligned Néel and (collinear) stripe states, as well as on the $xy$-planar-aligned Néel and collinear stripe states, are examined. All four of these quasiclassical states are chosen in turn as model states on top of which we systematically include the quantum correlations using a coupled cluster method analysis carried out to very high orders. We find strong evidence for two {\it quantum triple points} (QTP's) at ($Δ^{c} = -0.10 \pm 0.15, J_{2}^{c}/J_{1} = 0.505 \pm 0.015$) and ($Δ^{c} = 2.05 \pm 0.15, J_{2}^{c}/J_{1} = 0.530 \pm 0.015$), between which an intermediate magnetically-disordered phase emerges to separate the quasiclassical Néel and stripe collinear phases. Above the upper QTP ($Δ\gtrsim 2.0$) we find a direct first-order phase transition between the Néel and stripe phases, exactly as for the classical case. The $z$-aligned and $xy$-planar-aligned phases meet precisely at $Δ= 1$, also as for the classical case. For all values of the anisotropy parameter between those of the two QTP's there exists a narrow range of values of $J_{2}/J_{1}$, $α^{c_1}(Δ)<J_{2}/J_{1} <α^{c_2}(Δ)$, centered near the point of maximum classical frustration, $J_{2}/J_{1} = {1/2}$, for which the intermediate phase exists. This range is widest precisely at the isotropic point, $Δ= 1$, where $α^{c_1}(1) = 0.44 \pm 0.01$ and $α^{c_2}(1) = 0.59 \pm 0.01$. The two QTP's are characterized by values $Δ= Δ^{c}$ at which $α^{c_1}(Δ^{c})=α^{c_2}(Δ^{c})$.

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arXiv2008

The quantum $J_1$-$J_1'$-$J_2$ spin-1/2 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D

We study the phase diagram of the 2D $J_1$-$J_1'$-$J_2$ spin-1/2 Heisenberg model by means of the coupled cluster method. The effect of the coupling $J_1'$ on the Neel and stripe states is investigated. We find that the quantum critical points for the Neel and stripe phases increase as the coupling strength $J_1'$ is increased, and an intermediate phase emerges above the region at $J_1' \approx 0.6$ when $J_1=1$. We find indications for a quantum triple point at $J_1' \approx 0.60 \pm 0.03$, $J_2 \approx 0.33 \pm 0.02$ for $J_1=1$.

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arXiv2006

Frustrated Quantum Antiferromagnets: Application of High-Order Coupled Cluster Method

We report on recent results for strongly frustrated quantum $J_1$-$J_2$ 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 $J_1$--$J_2$ 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 $J_1$--$J_2$ 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.

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arXiv2006

Quantum $J_1$--$J_2$ antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering

Using the coupled-cluster method (CCM) and the rotation-invariant Green's function method (RGM), we study the influence of the interlayer coupling $J_\perp$ on the magnetic ordering in the ground state of the spin-1/2 $J_1$-$J_2$ frustrated Heisenberg antiferromagnet ($J_1$-$J_2$ model) on the stacked square lattice. In agreement with known results for the $J_1$-$J_2$ model on the strictly two-dimensional square lattice ($J_\perp=0$) we find that the phases with magnetic long-range order at small $J_2< J_{c_1}$ and large $J_2> J_{c_2}$ are separated by a magnetically disordered (quantum paramagnetic) ground-state phase. Increasing the interlayer coupling $J_\perp>0$ the parameter region of this phase decreases, and, finally, the quantum paramagnetic phase disappears for quite small $J_\perp \sim 0.2 ... 0.3 J_1$.

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arXiv2006

Direct calculation of the spin stiffness on square, triangular and cubic lattices using the coupled cluster method

We present a method for the direct calculation of the spin stiffness by means of the coupled cluster method. For the spin-half Heisenberg antiferromagnet on the square, the triangular and the cubic lattices we calculate the stiffness in high orders of approximation. For the square and the cubic lattices our results are in very good agreement with the best results available in the literature. For the triangular lattice our result is more precise than any other result obtained so far by other approximate method.

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arXiv2005

Coupled Cluster Treatment of the Shastry-Sutherland Antiferromagnet

We consider the zero-temperature properties of the spin-half two-dimensional Shastry-Sutherland antiferromagnet by using a high-order coupled cluster method (CCM) treatment. We find that this model demonstrates various groundstate phases (Néel, magnetically disordered, orthogonal dimer), and we make predictions for the positions of the phase transition points. In particular, we find that orthogonal-dimer state becomes the groundstate at ${J}^{d}_2/J_1 \sim 1.477$. For the critical point $J_2^{c}/J_1$ where the semi-classical Néel order disappears we obtain a significantly lower value than $J_2^{d}/J_1$, namely, ${J}^{c}_2/J_1$ in the range $[1.14, 1.39]$. We therefore conclude that an intermediate phase exists between the \Neel 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 groundstate for any value of $J_2$. The intermediate phase is therefore magnetically disordered but may exhibit plaquette or columnar dimer ordering.

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arXiv2004

Influence of Ising-anisotropy on the zero-temperature phase transition in the square lattice spin-1/2 J-J' model

We use a variational mean-field like approach, the coupled cluster method (CCM) and exact diagonalization to investigate the ground-state order-disorder transition for the square lattice spin-half XXZ model with two different nearest-neighbor couplings $J$ and $J'$. Increasing $J' > J$ the model shows in the isotropic Heisenberg limit a second-order transition from semi-classical Néel order to a quantum paramagnetic phase with enhanced local dimer correlations on the $J'$ bonds at about $J'_{c} \sim 2.5 ... 3 J$. This transition is driven by the quantum competition between $J'$ and $J$. Increasing the anisotropy parameter $Δ> 1$ we diminish the quantum fluctuations and thus the degree of competition. As a result the transition point $J'_{c}$ is shifted to larger values. We find indications for a linear increase of $J'_{c}$ with $Δ$, i.e. the transition disappears in the Ising limit $Δ\to \infty$.

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arXiv2004

Influence of the spin quantum number $s$ on the zero-temperature phase transition in the square lattice $J$-$J'$ model

We investigate the phase diagram of the Heisenberg antiferromagnet on the square lattice with two different nearest-neighbor bonds $J$ and $J'$ ($J$-$J'$ model) at zero temperature. The model exhibits a quantum phase transition at a critical value $J'_c > J$ between a semi-classically ordered Néel and a magnetically disordered quantum paramagnetic phase of valence-bond type, which is driven by local singlet formation on $J'$ bonds. We study the influence of spin quantum number $s$ on this phase transition by means of a variational mean-field approach, the coupled cluster method, and the Lanczos exact-diagonalization technique. We present evidence that the critical value $J'_c$ increases with growing $s$ according to $J'_c \propto s(s+1)$.

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