Employing exact diagonalization, we systematically study the anisotropic Heisenberg model which is related to rare-earth triangular-lattice materials. We probe its full 3D phase diagram afresh and identify a large region of quantum spin liquid (QSL) phase which can extend to the QSL region of the $J_1$--$J_2$ triangular Heisenberg model. Furthermore, we explore the magnetization curves of different phases and reproduce the 1/3-magnetization plateau in the quantum spin liquid phase region. More importantly, to study the possible chemical disorders in real materials, we consider the randomness of exchange interactions and find no spin glass order. And there is a large region of random-singlet phase which contains strongly random spin networks, dominated by two-spin singlets, four-spin singlets and other singlet domains. Our comprehensive ED study can give detailed insightful understanding of the microscopic Hamiltonian related to the YbMgGaO$_4$ and some other related rare-earth triangular-lattice materials.
Motivated by the recent experiment on a rare-earth material YbMgGaO$_4$ [Y. Li \textit{et al.}, Phys. Rev. Lett. \textbf{115}, 167203 (2015)], which found that the ground state of YbMgGaO$_4$ is a quantum spin liquid, we study the ground-state phase diagram of an anisotropic spin-$1/2$ model that was proposed to describe YbMgGaO$_4$. Using the density-matrix renormalization group method in combination with the exact diagonalization, we calculate a variety of physical quantities, including the ground-state energy, the fidelity, the entanglement entropy and spin-spin correlation functions. Our s…
Using an exact diagonalization treatment of Ising and Heisenberg model Hamiltonians, we study field-induced phase transition for two-dimensional antiferromagnets. For the system of Ising antiferromagnet the predicted field-induced phase transition is of first order, while for the system of Heisenberg antiferromagnet it is the second-order transition. We find from the exact diagonalization calculations that the second-order phase transition (metamagnetism) occurs through a spin-flop process as an intermediate step.
We present an exact diagonalization study of the ground state of the spin-half $J_1{-}J_2$ model. Dimer correlation functions and the susceptibility associated to the breaking of the translational invariance are calculated for the $4\times 4$ and the $6\times 6$ clusters. These results -- especially when compared to the one dimensional case, where the occurrence of a dimerized phase for large enough frustration is well established -- suggest either a homogeneous spin liquid or, possibly, a dimerized state with a rather small order parameter.
We study the phase diagram of the anisotropic spin-1 Heisenberg chain with single ion anisotropy (D) using a ground-state fidelity approach. The ground-state fidelity and its corresponding susceptibility are calculated within the quantum renormalization group scheme where we obtained the renormalization of fidelity preventing to calculate the ground state. Using this approach, the phase boundaries between the antiferromagnetic Néel, Haldane and large-D phases are obtained for the whole phase diagram, which justifies the application of quantum renormalization group to trace the symmetery protec…
Based on exact diagonalization and density matrix renormalization group (DMRG) method, we show that an anisotropic triangle lattice Heisenberg spin model has three distinct quantum phases. In particular, a spin-liquid phase is present in the weak interchain coupling regime, which is characterized by an exponentially-decaying spin correlator along the weaker coupling direction and a quasi-one-dimensional spin structure factor along the chain direction, in agreement with experiments on the Cs2CuCl4 compounds. In the obtained phase diagram, the spin liquid phase is found to persist up to a relati…
We present an exact diagonalization study of the quantum Heisenberg antiferromagnet on the fractal Sierpinski gasket for spin quantum numbers s=1/2,s=1 and s=3/2. Since the fractal dimension of the Sierpinski gasket is between one and two we compare the results with corresponding data of one- and two-dimensional systems. By analyzing the ground-state energy, the low-lying spectrum, the spin-spin correlation and the low-temperature thermodynamics we find arguments, that the Heisenberg antiferromagnet on the Sierpinski gasket is probably disordered not only in the extreme quantum case s=1/2 but …
Motivated by recent experiments on low-dimensional frustrated quantum magnets with competing nearest-neighbor exchange coupling J1 and next nearest-neighbor exchange coupling J2 we investigate the magnetic susceptibility of two-dimensional J1-J2 Heisenberg models with arbitrary spin quantum number s. We use exact diagonalization and high-temperature expansion up to order 10 to analyze the influence of the frustration strength J2/J1 and the spin quantum number s on the position and the height of the maximum of the susceptibility. The derived theoretical data can be used to get information on th…
The spin-1 Heisenberg model on a triangular lattice with the ferromagnetic nearest- and antiferromagnetic third-nearest-neighbor exchange interactions, $J_1=-(1-p)J$ and $J_2=pJ$, $J>0$ $ (0 \leq p \leq 1)$, is studied with the use of the SPINPACK code. This model is applicable for the description of the magnetic properties of NiGa$_2$S$_4$. The ground, low-lying excited state energies and spin-spin correlation functions have been found for lattices with N=16 and N=20 sites with the periodic boundary conditions. These results are in qualitative agreement with earlier authors' results obtained …
Motivated by magnetization studies of the "telephon number compound" Sr_14Cu_24O_41 we investigate doped Heisenberg spin rings by means of complete numerical diagonalization of a Heisenberg Hamiltonian that depends parametrically on hole positions. A comparison with experimental magnetization data reveals rather accurate information about the screened electrostatic interaction between the charged holes on the ring which appears to be astonishingly strong.
We present a comprehensive list of ground state energies and spin gaps of finite kagome clusters with up to 42 spins obtained using large-scale exact diagonalization techniques. This represents the current limit of this exact approach. For a fixed number of spins N we study several cluster shapes under periodic boundary conditions in both directions resulting in a toroidal geometry. The clusters are characterized by their side length and diagonal as well as the shortest "Manhattan" diameter of the torii. A finite-size scaling analysis of the ground state energy as well as the spin gap is then …
Motivated by recent experimental progress in the context of ultra-cold multi-color fermionic atoms in optical lattices, we have developed a method to exactly diagonalize the Heisenberg $SU(N)$ Hamiltonian with several particles per site living in a fully symmetric or antisymmetric representation of $SU(N)$. The method, based on the use of standard Young tableaux, takes advantage of the full $SU(N)$ symmetry, allowing one to work directly in each irreducible representations of the global $SU(N)$ group. Since the $SU(N)$ singlet sector is often much smaller than the full Hilbert space, this enab…
Spectral Mapping Theorem between SU(N) and SU(Ns/N) Heisenberg Models and Exact Diagonalization of SU(4) and SU(7) Long-Range Ordered Phases on the Triangular Lattice
Laboratoire de Physique et Modélisation des Milieux Condensés, Université Grenoble Alpes and CNRS（凝聚态介质物理与建模实验室，格勒诺布尔阿尔卑斯大学及法国国家科学研究中心）
The anisotropic triangular model, which is believed to describe the materials Cs$_2$CuCl$_4$ and Cs$_2$CuBr$_4$, among others, is dominated by incommensurate spiral physics and is thus extremely resistant to numerical analysis on small system sizes. In this paper we use twisted boundary conditions and exact diagonalization techniques to study the phase diagram of this model. With these boundary conditions we are able to extract the inter- and intrachain ordering $q$-vectors for the $\frac{J'}{J} < 1$ region finding very close agreement with recent DMRG results on much larger systems. Our resul…
The magnetization process of the $S=1$ antiferromagnetic chain with the single-ion anisotropy $D$ and the biquadratic interaction is investigated using the numerical diagonalization. Both interactions stabilize the 2-magnon Tomonaga-Luttinger liquid (TLL) phase in the magnetization process. Based on several excitation gaps calculated by the numerical diagonalization, some phase diagrams of the magnetization process are presented. These phase diagrams reveal that the spin nematic dominant TLL phase appears at higher magnetizations for sufficiently large negative $D$.
We present a method for the exact diagonalization of the $\mathrm{SU}(N)$ Heisenberg interaction Hamiltonian, using Young tableaux to work directly in each irreducible representation of the global $\mathrm{SU}(N)$ group. This generalized scheme is applicable to chains consisting of several particles per site, with any $\mathrm{SU}(N)$ symmetry at each site. Extending some of the key results of substitutional analysis, we demonstrate how basis states can be efficiently constructed for the relevant $\mathrm{SU}(N)$ subsector, which, especially with increasing values of $N$ or numbers of sites, h…
We study the system size dependence of the singlet-triplet excitation gap in the $S=1/2$ kagome-lattice Heisenberg antiferromagnet by numerical diagonalization. We successfully obtain a new result of a cluster of 42 sites. The two sequences of gaps of systems with even-number sites and that with odd-number sites are separately analyzed. Careful examination clarifies that there is no contradiction when we consider the system to be gapless.
We have studied the zero and low-temperature behavior of anisotropic alternating antiferromagnetic-ferromagnetic Heisenberg spin-1/2 chains in a transverse magnetic field. Using the analytical spinless fermion approach, the thermodynamic behavior of the model has been studied. We have introduced a new order parameter to distinguish the gapless Luttinger liquid phase from the other gapped phases. The exact diagonalization Lanczos results are also used to compare with the spinless fermion ones. We have found a double peak structure in the specific heat curves for the region between the two quant…
Numerical Diagonalization Study of the Phase Boundaries of the S=2 Heisenberg Antiferromagnet on the Orthogonal Dimer Lattice
University of Hyogo（兵库大学）；National Institutes for Quantum and Radiological Science and Technology（量子辐射科学和技术国立研究所）；Osaka Metropolitan University（大阪公立大学）
We present numerical exact results for the ground state and the low-lying excitations for the spin-1/2 J1-J2 Heisenberg antiferromagnet on finite square lattices of up to N=40 sites. Using finite-size extrapolation we determine the ground-state energy, the magnetic order parameters, the spin gap, the uniform susceptibility, as well as the spin-wave velocity and the spin stiffness as functions of the frustration parameter J2/J1. In agreement with the generally excepted scenario we find semiclassical magnetically ordered phases for J2 < J2^{c1} and J2 > J2^{c2} separated by a gapful quantum para…
By using the coupled cluster method, the numerical exact diagonalization method, and the numerical density matrix renormalization group method, we investigated the properties of the one-dimensional Heisenberg chain with alternating antiferromagnetic and ferromagnetic next nearest neighbor interactions. In the classical limit, the ground state is in the collinear Neel state if a<1/2, while for a>1/2, there is an noncollinear canted state. For the quantum case, we found that, although the classical Neel state is absent, the canted state exists if the frustration parameter a exceeds a critical po…
Using both exact diagonalizations and diagonalizations in a subset of short-range valence bond singlets, we address the nature of the groundstate of the Heisenberg spin-1/2 antiferromagnet on the square lattice with competing next-nearest and next-next-nearest neighbor antiferromagnetic couplings (J1-J2-J3 model). A detailed comparison of the two approaches reveals a region along the line (J2+J3)/J1=1/2, where the description in terms of nearest-neighbor singlet coverings is excellent, therefore providing evidence for a magnetically disordered region. Furthermore a careful analysis of dimer-di…
Chiral bosonic quantum spin liquid in the integer-spin Heisenberg-Kitaev model
Institut Néel, Université Grenoble Alpes and CNRS（内勒研究所，格勒诺布尔阿尔卑斯大学及法国国家科学研究中心）；Departamento de Física Teórica de la Materia Condensada, Condensed Matter Physics Center (IFIMAC) and Instituto Nicolás Cabrera, Universidad Autónoma de Madrid（凝聚态物理理论系，凝聚态物理中心（IFIMAC）及尼古拉斯·卡布雷拉研究所，马德里自治大学）
In this paper, we study the spin and energy dynamic correlations of the one dimensional spin 1/2 Heisenberg model, using mostly exact diagonalization numerical techniques. In particular, observing that the uniform spin and energy currents decay to finite values at long times, we argue for the absence of spin and energy diffusion in the easy plane anisotropic Heisenberg model.
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|…
Calculations of nuclear spin-lattice relaxation rates are carried out by means of exact diagonalization on small (2 x 6) antiferromagnetic Heisenberg ladders, using the simplest forms permitted by symmetry for the hyperfine couplings for the three nuclear sites in Cu2O3 ladders. Several values of the rung/chain exchange ratio have been considered. Comparisons with experimental results, field theoretic calculations, and the Gaussian approximation highlight some open problems.
A proposed ground state for the Kagome Lattice Heisenberg Model (KLHM) consists of a Valence Bond Crystal (VBC) with a 36-site unit cell. We calculate the low-lying triplet and singlet excitations in the VBC phase for the infinite-lattice model and for the 36-site cluster. For the infinite lattice, the lowest triplet excitation is found to have a spin gap of approximately $0.08 \pm 0.02 J$ and a bandwidth of only about $0.01 J$. For the 36-site cluster, consisting of a single unit cell with periodic boundary conditions, there are substantial finite-size effects: the spin gap there is estimated…
We investigate the zero- and finite-temperature properties of the bond-random $s=1/2$ Heisenberg antiferromagnet on the pyrochlore lattice by the exact diagonalization and the Hams--de Raedt methods. We find that the randomness induces the gapless quantum spin liquid (QSL) state, the random-singlet state. Implications to recent experiments on the mixed-anion pyrochlore-lattice antiferromagnet Lu$_2$Mo$_2$O$_5$N$_2$ exhibiting gapless QSL behaviors are discussed.
Spin-1/2 Heisenberg diamond-like decorated honeycomb lattice in a magnetic field from the perspective of localized magnons and exact diagonalization
Faculty of Science, P. J. Šafárik University（帕·约·沙法里克大学理学院）；Laboratoire de Physique Théorique et Modélisation, CNRS UMR 8089, CY Cergy Paris Université（CY塞尔吉巴黎大学，CNRS UMR 8089理论物理与建模实验室）
We investigate the non magnetic phase of the spin-half frustrated Heisenberg antiferromagnet on the square lattice using exact diagonalization (up to 36 sites) and quantum Monte Carlo techniques (up to 144 sites). The spin gap and the susceptibilities for the most important crystal symmetry breaking operators are computed. A genuine and somehow unexpected `plaquette RVB', with spontaneously broken translation symmetry and no broken rotation symmetry, comes out from our numerical simulations as the most plausible ground state for $J_2/J_1 \simeq 0.5 $.
We study the phase diagram of the spin-1 quantum bilinear-biquadratic antiferromagnet on the kagome lattice using exact diagonalization and the density matrix renormalization group algorithm. The SU(3)-symmetric point of this model Hamiltonian is a spontaneously trimerized state whose qualitative nature persists even at the Heisenberg point, a finding that contrasts previous proposals. We report the ground state energy per site of the Heisenberg model to be -1.410(2) and establish the presence of a spin gap.
We clarify the existence of several magnetization plateaux for the kagome $S=1/2$ antiferromagnetic Heisenberg model in a magnetic field. Using approximate or exact localized magnon eigenstates, we are able to describe in a similar manner the plateau states that occur for magnetization per site $m=1/3$, $5/9$, and $7/9$ of the saturation value. These results are confirmed using large-scale Exact Diagonalization on lattices up to 63 sites.
An alternative triplet-wave expansion formalism for dimerized spin systems is presented, a modification of the 'bond operator' formalism of Sachdev and Bhatt. Projection operators are used to confine the system to the physical subspace, rather than constraint equations. The method is illustrated for the case of the alternating Heisenberg chain, and comparisons are made with the results of dimer series expansions and exact diagonalization. Some discussion is included of the phenomenon of 'quasiparticle breakdown', as it applies to the two-triplon bound states in this model.
We consider the fully anisotropic Heisenberg spin-1/2 antiferromagnet in a uniform magnetic field, whose ground-state is characterized by broken spin rotation symmetry and gapped spinon excitations. We expand on a recent mean-field approach to the problem by incorporating fluctuations in a loop expansion. Quantitative results for the magnetization, excitation gap and specific heat are obtained. We compare our predictions with new DMRG and exact diagonalization data and, for zero field, with the exact solution of the ${XYZ}$ spin chain from the Bethe Ansatz.
Magnetization processes of spin-1/2 Heisenberg ladders are studied using strong-coupling expansions, numerical diagonalization of finite systems and a bosonization approach. We find that the magnetization exhibits plateaux as a function of the applied field at certain rational fractions of the saturation value. Our main focus are ladders with 3 legs where plateaux with magnetization one third of the saturation value are shown to exist.
The spin-wave excitation spectrum, the magnetization, and the Néel temperature for the quasi-two-dimensional spin-1/2 antiferromagnetic Heisenberg model with compass-model interaction in the plane proposed for iridates are calculated in the random phase approximation. The spin-wave spectrum agrees well with data of Lanczos diagonalization. We find that the Neel temperature is enhanced by the compass-model interaction and is close to the experimental value for Ba2IrO4.
The spin Green's function of the antiferromagnetic Heisenberg model on a triangular lattice is calculated using Mori's projection operator technique. At T=0 the spin excitation spectrum is shown to have gaps at the wave vectors of the classical Neel ordering. This points to the absence of the antiferromagnetic long-range order in the ground state. The calculated spin correlation on the neighboring sites of the same sublattice is in good agreement with the value derived from exact diagonalization. The temperature dependencies of the spin correlations and the gaps are calculated.
Using numerical diagonalization techniques, we explore the effect of local and bond disorder on the finite temperature spin and thermal conductivities of the one dimensional anisotropic spin-1/2 Heisenberg model. High-temperature results for local disorder show that the dc conductivties are finite, apart from the uncorrelated - XY case - where dc transport vanishes. Moreover, at strong disorder, we find finite dc conductivities at all temperatures $T$, except T=0. The low frequency conductivities are characterized by a nonanalytic cusp shape. Similar behavior is found for bond disorder.
Employing numerical linked-cluster expansions (NLCEs) along with exact diagonalizations of finite clusters with periodic boundary condition, we study the energy, specific heat, entropy, and various susceptibilities of the antiferromagnetic Heisenberg model on the checkerboard lattice. NLCEs, combined with extrapolation techniques, allow us to access temperatures much lower than those accessible to exact diagonalization and other series expansions. We find that the high-temperature peak in specific heat decreases as the frustration increases, consistent with the large amount of unquenched entro…
We identify fingerprints of a proximate quantum spin-liquid (QSL), observable by finite-temperature dynamical thermal transport within a minimal version of the idealized Kitaev model on a two-leg ladder, if subjected to inevitably present Heisenberg couplings. Using exact diagonalization and quantum typicality, we uncover (i) an insulator-conductor crossover induced by fracton recombination at infinitesimal Heisenberg coupling, (ii) low- and high-energy signatures of fractons, which survive far off the pure QSL point, and (iii) a non-monotonous current life-time versus Heisenberg couplings. Gu…
The thermodynamic properties of S>=1 ferromagnetic chains with an easy-axis single-ion anisotropy are investigated at arbitrary temperatures by both a Green-function approach, based on a decoupling of three-spin operator products, and by exact diagonalizations of chains with up to N=12 sites using periodic boundary conditions. A good agreement between the results of both approaches is found. For the S=1 chain, the temperature dependence of the specific heat reveals two maxima, if the ratio of the anisotropy energy D and the exchange energy J exceeds a characteristic value, D/J >7.4, and only o…
We present numerical evidence that the spin-1/2 Heisenberg model on the two-dimensional checkerboard lattice exhibits several magnetization plateaux for m=0, 1/4, 1/2 and 3/4, where m is the magnetization normalized by its saturation value. These incompressible states correspond to somehow similar valence-bond crystal phases that break lattice symmetries, though they are different from the already established plaquette phase for m=0. Our results are based on Exact Diagonalization as well as Density Matrix Renormalization Group large-scale simulations, and interpreted in terms of simple trial w…
The Haldane gap of the S=2 Heisenberg antiferromagnet in a one-dimensional linear chain is examined by a numerical-diagonalization method. A precise estimate for the magnitude of the gap is successfully obtained by a multistep convergence-acceleration procedure applied to finite-size diagonalization data under the twisted boundary condition.
Dynamical structure factors of the S=1 bond-alternating spin chains in the dimer phase are calculated at finite temperature, using the pair dynamical correlated-effective-field approximation. At T=0, the delta-function-type peak of the one-magnon mode appears. When temperature is increased, such a sharp peak is broadened and the additional weak peak caused by the excitation from the triplet state to the quintet state emerges in the higher energy region. The results are discussed in comparison with those obtained by the exact diagonalization method.
The excitation spectrum of the frustrated spin-$1/2$ Heisenberg chain is reexamined using variational and exact diagonalization calculations. We show that the overlap matrix of the short-range resonating valence bond states basis can be inverted which yields tractable equations for single and two spinons excitations. Older results are recovered and new ones, such as the bond-state dispersion relation and its size with momentum at the Majumdar-Ghosh point are found. In particular, this approach yields a gap opening at $J_2=0.25J_1$ and an onset of incommensurability in the dispersion relation a…
By explicitly computing wavefunction overlap via exact diagonalization in finite systems, we provide evidence indicating that, in the limit of strong coupling, i.e., $Δ/t \to \infty$, the ground state of the Gutzwiller-projected BCS Hamiltonian (accompanied by proper particle-number projection) is identical to the exact ground state of the 2D antiferromagnetic Heisenberg model on the square lattice. This identity is adiabatically connected to a very high overlap between the ground states of the projected BCS Hamiltonian and the t-J model at moderate doping.
We study the spin gap of the S=1/2 Heisenberg model on the distorted diamond chain, which is recently proposed to represent magnetic properties of Cu_3 Cl_6 (H_2 O)_2 2H_8 C_4 SO_2. This model is composed of stacked trimers and has three kinds of exchange interactions J_1, J_2 and J_3. Using the numerical diagonalization, we obtain a contour map of the spin gap in the J_2/J_1-J_3/J_1 plane. We argue possible values of the exchange constants based on the contour map and the observed value of the spin gap.
The magnetization process of the spin-S Heisenberg antiferromagnet on the kagome lattice is studied by the numerical-diagonalization method. Our numerical-diagonalization data for small finite-size clusters with S=1, 3/2, 2, and 5/2 suggest that a magnetization plateau appears at one-third of the height of the saturation in the magnetization process irrespective of S. We discuss the S dependences of the edge fields and the width of the plateau in comparison with recent results obtained by real-space perturbation theory.
The spin-$\frac{1}{2}$ delta-chain (sawtooth chain) with antiferromagnetic Heisenberg basal chain and Ising apical-basal interactions is studied. The basal-apical interactions involve the bond alternation. The limiting cases of the model include the symmetrical delta-chain and the antiferromagnetic chain in the staggered magnetic field. We study ground state properties of the model by the exact diagonalization and density matrix renormalization group methods. The ground state phase diagram as a function of the bond alternation consists of magnetic and various non-magnetic phases. All phases ex…
Finite-temperature Drude weight (spin stiffness) D(T) is evaluated within the anisotropic spin-1/2 Heisenberg model on a chain using the exact diagonalization for small systems. It is shown that odd-side chains allow for more reliable scaling and results, in particular, if one takes into account corrections due to low-frequency finite-size anomalies. At high T and zero magnetization D is shown to scale to zero approaching the isotropic point Δ=1. On the other hand, for Δ>2 at all magnetizations D is nearly exhausted with the overlap with the conserved energy current. Results for the T variatio…
We explore the effect of a (non) magnetic impurity on the thermal transport of the spin-1/2 Heisenberg chain model. This unique system allows to probe Kondo-type phenomena in a prototype strongly correlated system. Using numerical diagonalization techniques we study the scaling of the frequency dependent thermal conductivity with system size and host-impurity coupling strength as well as the dependence on temperature. We focus in particular on the analysis of cutting-healing of weak links or a magnetic impurity by the host chain via Kondo-like screening as the temperature is lowered.
We calculate the low-temperature thermodynamic quantities (magnetization, correlation functions, transverse and longitudinal correlation lengths, spin susceptibility, and specific heat) of the frustrated one-dimensional spin-half J1-J2 Heisenberg ferromagnet, i.e. for J2< 0.25|J1|, in an external magnetic field using a second-order Green-function formalism and full diagonalization of finite systems. We determine power-law relations for the field dependence of the position and the height of the maximum of the uniform susceptibility. Considering the specific heat at low magnetic fields, two maxi…
The finite temperature transport properties of a spin-1/2 anisotropic Heisenberg chain with an embedded spin-S impurity are studied. Using primarily numerical diagonalization techniques, we study the dependence of the dynamical spin and thermal conductivities on the lattice size, the magnitude of the impurity spin, the host-impurity coupling, the easy axis anisotropy, as well as the dependence on temperature. Particularly for the temperature dependence, we discuss the screening of the impurity by the chain eventually leading to the cutting or healing of the host chain. Numerical results are su…
We study ferrimagnetism in the ground state of the antiferromagnetic Heisenberg model on the spatially anisotropic kagome lattice, in which ferrimagnetism of the conventional Lieb-Mattis type appears in the region of weak frustration whereas the ground state is nonmagnetic in the isotropic case. Numerical diagonalizations of small finite-size clusters are carried out to examine the spontaneous magnetization. We find that the spontaneous magnetization changes continuously in the intermediate region between conventional ferrimagnetism and the nonmagnetic phase. Local magnetization of the interme…
Using mean-field theory, exact diagonalizations and SU(3) flavour theory, we have precisely mapped out the phase diagram of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice in a magnetic field, with emphasis on the quadrupolar phases and their excitations. In particular, we show that ferroquadrupolar order can coexist with short-range helical magnetic order, and that the antiferroquadrupolar phase is characterized by a remarkable 2/3 magnetization plateau, in which one site per triangle retains quadrupolar order while the other two are polarized along the field. Implicat…
We derive and study a spin one-half Hamiltonian on a honeycomb lattice describing the exchange interactions between Ir$^{4+}$ ions in a family of layered iridates $A_2$IrO$_3$ ($A$=Li,Na). Depending on the microscopic parameters, the Hamiltonian interpolates between the Heisenberg and exactly solvable Kitaev models. Exact diagonalization and a complementary spin-wave analysis reveal the presence of an extended spin-liquid phase near the Kitaev limit and a conventional Néel state close to the Heisenberg limit. The two phases are separated by an unusual stripy antiferromagnetic state, which is t…
We consider the two-dimensional (2D) quantum Heisenberg antiferromagnet at zero temperature with two types of locally frustrating perturbations - an isolated ferromagnetic bond (FMB) and a quantum impurity spin, coupled symmetrically to the two sublattices. An analytic technique is developed to study strong defect-environment interaction. In the case of a FMB we find that, contrary to the previous linear spin-wave result, the local magnetization stays finite even for strong frustration. For an antiferromagnetic coupling of a quantum impurity spin with its environment, we find a local ground st…
We study the ground-state properties of weakly frustrated Heisenberg ferrimagnetic chains with nearest and next-nearest neighbor antiferromagnetic exchange interactions and two types of alternating sublattice spins S_1 > S_2, using 1/S spin-wave expansions, density-matrix renormalization group, and exact- diagonalization techniques. It is argued that the zero-point spin fluctuations completely destroy the classical commensurate- incommensurate continuous transition. Instead, the long-range ferrimagnetic state disappears through a discontinuous transition to a singlet state at a larger value of…
We study the zero-temperature phase diagram and the low-lying excitations of a square-lattice spin-half Heisenberg antiferromagnet with two types of regularly distributed nearest-neighbour exchange bonds (J>0 (antiferromagnetic) and J'>0, J'<0) using the coupled cluster method (CCM) for high orders of approximation (up to LSUB8). We use a Neel model state as well as a helical model state as a starting point for the CCM calculations. We find a second-order transition from a phase with Neel order to a finite-gap quantum disordered phase for sufficiently large antiferromagnetic exchange constants…
