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arXiv:1502.06806

Coupled cluster treatment of one quasi-one-dimensional coupled spin triangles

Jianjun Jiang, Yongjun Liu, Tang, Fei, Cuihong Yang

Published Feb 24, 2015• 0 citations
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Abstract

By using the coupled cluster method (CCM) and the numerical exact diagonalization (ED) method, we investigated the properties of the one quasi-one-dimensional coupled spin triangles. The results of ED disclose that the system is in the exact tetramer-dimer (TD) state if aac1, we find that CCM results for some physical quantities, such as the ground state energy, the magnetization and the antiferromagnetic gap are in excellent agreement with the results obtained by ED. Thus, CCM can be used to accurately analyze the properties of the quasi-one-dimensional coupled spin triangles in the whole parameter region. We believe that it can also be applied to investigating the properties of other quasi-one spin systems reliably.

DOI
10.48550/arxiv.1502.06806

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By using the coupled cluster method (CCM) and the numerical exact diagonalization (ED) method, we investigated the properties of the one quasi-one-dimensional coupled spin triangles. The results of ED disclose that the system is in the exact tetramer-dimer (TD) state if aac1, we find that CCM results for some physical quantities, such as the ground state energy, the magnetization and the antiferromagnetic gap are in excellent agreement with the results obtained by ED. Thus, CCM can be used to accurately analyze the properties of the quasi-one-dimensional coupled spin triangles in the whole parameter region. We believe that it can also be applied to investigating the properties of other quasi-one spin systems reliably.
By the analytical coupled cluster method (CCM), we study both the ground state and lowest-lying excited-state properties of the alternating bond diamond chain. The numerical exact diagonalization (ED) method is also applied to the chain to verify the accuracy of CCM results. The ED results show that the ground-state phase diagram contains two exact spin cluster solid ground states, namely, the tetramer-dimer (TD) state and dimer state, and the ferrimagnetic long-range-ordered state. We prove that the two exact spin cluster solid ground states can both be formed by CCM. Moreover, the exact spin gap in the TD state can be obtained by CCM. In the ferrimagnetic region, we find that the CCM results for some physical quantities, such as the ground-state energy, the sublattice magnetizations, and the antiferromagnetic gap, are comparable to the results obtained by numerical methods. The critical line dividing the TD state from the ferrimagnetic state is also given by CCM and is in perfect agreement with that determined by the ED method.
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.
The coupled cluster method (CCM) of microscopic quantum many-body theory has become an ab initio method of first choice in quantum chemistry and many fields of nuclear, subnuclear and condensed matter physics, when results of high accuracy are required. In recent years it has begun to be applied with equal success to strongly correlated systems of electrons or quantum spins defined on a regular spatial lattice. One regularly finds that the CCM is able to describe accurately the various zero-temperature phases and the quantum phase transitions between them, even when frustration is present and other methods such as quantum Monte Carlo often fail. We illustrate the use and powerfulness of the method here by applying it to a square-lattice spin-half Heisenberg model where frustration is introduced by competing nearest neighbour bonds. The model exhibits the physically interesting phenomenon of competition between magnetic order and dimerization. Results obtained for the model with the CCM are compared with those found from spin-wave theory and from extrapolating the results of exact diagonalizations of small lattices. We show that the CCM is essentially unique among available methods in being able both to describe accurately all phases of this complex model and to provide accurate predictions of the various phase boundaries and the order of the corresponding transitions.
A high-order coupled cluster method (CCM) for the zero-temperature ground states of quantum lattice spin systems of general spin quantum number (s> 1/2)(s>~1/2)(s> 1/2) is described and illustrated via the spin-1 anisotropic Heisenberg antiferromagnet on the square lattice. Results for the ground-state energy and sublattice magnetization are seen to be in excellent agreement with the best of other approximate methods. Furthermore, we are able to follow the solution to the CCM equations at a given level of approximation with respect to the anisotropy parameter $\ensuremath{\Delta}$ from the trivial Ising limit $(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Delta}}\ensuremath{\infty})$ down to a critical value ${\ensuremath{\Delta}}_{c},$ at which point the physical solution terminates. The results for the ground-state energy, sublattice magnetization, and phase transition point thus support our choice of this model as a good nontrivial test case of our CCM formalism.
The coupled-cluster method (CCM) is applied to anisotropic-quantum-antiferromagnetic models in one and two dimensions (1D and 2D). Several hierarchical approximation schemes of the CCM are defined, which are specialized for the spin-lattice models. Good results are obtained for both ground-state and excited-state energies. The spin-spin correlation functions and the staggered magnetizations are also calculated. We have found that the CCM gives a qualitatively correct description of the entire Heisenberg-Ising phase, including the critical point where a phase transition occurs in 1D. Some interesting differences between 1D and 2D models near the critical point are discussed.
The coupled cluster method (CCM) has previously been applied to study the ground- and excited-state properties of many different types of frustrated and unfrustrated quantum spin systems. A common feature in the application of the CCM is to rotate the local spin axes of the (often classical) model state so that (notationally only) the spins all appear to point in the downwards zzz-direction. Hitherto, we remark that only coplanar model states have been used because they do not lead to imaginary terms in the new Hamiltonian. By contrast, non-coplanar "three-dimensional" (3D) model states can lead to imaginary terms in the new Hamiltonian after rotation. In principle, however, macroscopic quantities predicted by the CCM (such as the ground-state energy and order parameter) should still be real (even though the Hamiltonian may be complex) because the transformations of local spin axes are unitary. Here we explain how we may use such 3D model states for the CCM and how we may solve for the (now possibly complex) CCM correlation coefficients. We present results for the spin-half triangular-lattice antiferromagnet in an external magnetic field. We use both coplanar model states and a single 3D non-coplanar model state. We calculate the ground-state energy and the lattice magnetisation as a function of the magnetic field strength. We find that the energies of the coplanar states lie lower than that of the non-coplanar state for all values of the external field, as seen in other approximate studies for this model. We find that the non-coplanar state does not detect the well-known spin plateau occurring in this model, although (as seen before) it is clearly observed for the coplanar model states using the CCM. These results are an excellent initial validation of the new approach for the application of the CCM using 3D model states.