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arXiv:1406.4317 · Journal of the Physical Society of Japan

Frustration Induced Noncollinear Magnetic Order Phase in One-Dimensional Heisenberg Chain with Alternating Antiferromagnetic and Ferromagnetic Next Nearest Neighbor Interactions

Jian-Jun Jiang, Fei Tang, Cui-Hong Yang

Published Nov 26, 2015• 8 citations
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Abstract

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 point ac1. The precise critical point ac1 can be determined by using the coupled cluster method and the numerical exact diagonalization method separately. The results of the coupled cluster method and the exact diagonalization method both disclose that the type of phase transition occurring at ac1 changes from a classical second-order transition to a quantum first-order transition due to quantum fluctuation. Although there is another critical point ac2 in a finite system at which the ground state evolves from the canted state to the collinear Neel plus ferromagnetic state, that state is absent because ac2 tends to infinity in the thermodynamic limit.

DOI
10.7566/jpsj.84.124710

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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 point ac1. The precise critical point ac1 can be determined by using the coupled cluster method and the numerical exact diagonalization method separately. The results of the coupled cluster method and the exact diagonalization method both disclose that the type of phase transition occurring at ac1 changes from a classical second-order transition to a quantum first-order transition due to quantum fluctuation. Although there is another critical point ac2 in a finite system at which the ground state evolves from the canted state to the collinear Neel plus ferromagnetic state, that state is absent because ac2 tends to infinity in the thermodynamic limit.
We use the coupled cluster method for infinite chains complemented by exact diagonalization of finite periodic chains to discuss the influence of a third-neighbor exchange J(3) on the ground state of the spin-½ Heisenberg chain with ferromagnetic nearest-neighbor interaction J(1) and frustrating antiferromagnetic next-nearest-neighbor interaction J(2). A third-neighbor exchange J(3) might be relevant to describe the magnetic properties of the quasi-one-dimensional edge-shared cuprates, such as LiVCuO(4) or LiCu(2)O(2). In particular, we calculate the critical point J(2)(c) as a function of J(3), where the ferromagnetic ground state gives way for a ground state with incommensurate spiral correlations. For antiferromagnetic J(3) the ferro-spiral transition is always continuous and the critical values J(2)(c) of the classical and the quantum model coincide. On the other hand, for ferromagnetic J3 is < or approximately equal to -(0.01...0.02)|J1|. the critical value J(2)(c) of the quantum model is smaller than that of the classical model. Moreover, the transition becomes discontinuous, i.e. the model exhibits a quantum tricritical point. We also calculate the height of the jump of the spiral pitch angle at the discontinuous ferro-spiral transition.
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 S1>S2,{S}_{1}>{S}_{2},S1​>S2​, using 1/S1/S1/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 the frustration parameter. In the ferrimagnetic phase we find a disorder point marking the onset of incommensurate real-space short-range spin-spin correlations.
We studied the thermodynamics of the one-dimensional J 1 - J 2 spin-1/2 Heisenberg chain for ferromagnetic nearest-neighbor bonds J 1 < 0 and frustrating antiferromagnetic next- nearest-neighbor bonds J 2 > 0 using full diagonalization of finite rings and a second-order Green-function formalism. Thereby we focus on J 2 < | J 1 |/4 where the ground state is still ferromagnetic, but the frustration influences the thermodynamic properties. We found that their critical indices are not changed by J 2 . The analysis of the low-temperature behavior of the susceptibility χ leads to the conclusion that this behavior changes from χ ∝ T -2 at J 2 < | J 1 |/4 to χ ∝ T -3/2 at the quantum-critical point J 2 = | J 1 |/4. Another effect of the frustration is the appearance of an extra low- T maximum in the specific heat C v ( T ) for J 2 & | J 1 |/8, indicating its strong influence on the low-energy spectrum.
In this work the ordering processes in classical frustrated Ising models and the ground-state behavior of frustrated quantum spin models are investigated. In the first part the phase transition from a high-temperature paramagnetic phase to a antiferromagnetic ground state is analyzed for the square-lattice Ising model with competing antiferromagnetic interactions between nearest- and next-nearest-neighbor spins. In the case of spatially isotropic interactions the phase transition to a collinear state is of special interest. Using Monte-Carlo simulations on finite lattices as well as field-theoretical methods for the continuous model it is shown that depending on the frustration three different sectors can be distinguished that show (i) Ising-universal behavior (ii) Ashkin-Teller-like non-universal behavior (varying critical exponents) and (iii) non-critical first-order behavior. For spatially anisotropic interactions the emergence of an intermediate incommensurate phase is verified by means of Monte-Carlo simulations which has been predicted by earlier mean-field calculations. The nature of this phase is studied analyzing spin-spin correlation functions and its ordering wave-vector reveals a strong temperature and size dependence. In the second part the influence of quantum fluctuations on classical antiferromagnetic ground states are investigated in anisotropic quantum spin-1/2 Heisenberg models with competing interactions. Using quantum Monte-Carlo simulations, exact diagonalization and perturbation theory the ground-state phase diagrams are calculated for a square lattice with nearest- and next-nearest-neighbor interactions and a honeycomb lattice with up to third-nearest-neighbor interactions whereby the fluctuations are chosen to be non-frustrating. For both cases the stability regions of classical magnetic states are identified and an intermediate phase is detected that shows no sign of long-range magnetic order. Further calculations also rule out valence-bond-crystal or topological order for this state, thus a quantum disordered ground state is stabilized in these models.
In this article we study the ground-state properties of two square-lattice Heisenberg quantum spin models with competing bonds using a high-order coupled cluster treatment. The first model is a spin-half model with competing nearest-neighbour bonds with and without frustration. We discuss the influence of quantum fluctuations on the ground-state phase diagram and in particular on the nature of the zero-temperature phase transitions from phases with collinear magnetic order at small frustration to phases with noncollinear spiral order at large frustration. The second model is a highly frustrated ferrimagnet, which contains one sublattice (A) entirely populated with spin-one spins and an other sublattice (B) entirely populated with spin-half spins. Sublattice A sites are nearest-neighbours to sublattice B sites and vice versa and frustration is introduced by next-nearest-neighbour bonds. The model shows two collinear ordered phases and a noncollinear phase in which (classically) the spin-one spins are allowed to cant at an angle. Both examples show that the coupled-cluster method is able to describe the zero-temperature transitions well and provides a consistent description of collinear, noncollinear, and disordered phases, for cases in which other standard techniques (e.g. the quantum Monte Carlo technique for spin systems which are frustrated) are not applicable.
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-neighbor exchange bonds [J>0[J>0[J>0 (antiferromagnetic) and $\ensuremath{-}\ensuremath{\infty}<{J}^{\ensuremath{'}}<\ensuremath{\infty}]$ using the coupled cluster method (CCM) for high orders of approximation (up to LSUB8). We use a N\'eel 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 N\'eel order to a finite-gap quantum disordered phase for sufficiently large antiferromagnetic exchange constants ${J}^{\ensuremath{'}}>0.$ For frustrating ferromagnetic couplings ${J}^{\ensuremath{'}}<0$ we find indications that quantum fluctuations favor a first-order phase transition from the N\'eel order to a quantum helical state, by contrast with the corresponding second-order transition in the corresponding classical model. The results are compared to those of exact diagonalizations of finite systems (up to 32 sites) and those of spin-wave and variational calculations. The CCM results agree well with the exact diagonalization data over the whole range of the parameters. The special case of ${J}^{\ensuremath{'}}=0,$ which is equivalent to the honeycomb lattice, is treated more closely.