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Numerical and approximate analytical results for the frustrated spin- 1/2 quantum spin chain

Bursill, R., Gehring, G. A., DAMIAN J. J. FARNELL, John B. Parkinson, Xiang, T., Chen Zeng

Published Jan 1, 1995• 110 citations
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Abstract

We study the T=0 frustrated phase of the 1D quantum spin- 1/2 system with nearest-neighbour and next-nearest-neighbour isotropic exchange known as the Majumdar-Ghosh Hamiltonian. We first apply the coupled-cluster method of quantum many-body theory based on a spiral model state to obtain the ground-state energy and the pitch angle. These results are compared with accurate numerical results using the density matrix renormalization group method, which also gives the correlation functions. We also investigate the periodicity of the phase using the Marshall sign criterion. We discuss particularly the behaviour close to the phase transitions at each end of the frustrated phase.

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Numerical and approximate analytical results for the frustrated spin- 1/2 quantum spin chain

R Bursill, G A Gehring, DAMIAN J. J. FARNELL +3 more

We study the T=0 frustrated phase of the 1D quantum spin- 1/2 system with nearest-neighbour and next-nearest-neighbour isotropic exchange known as the Majumdar-Ghosh Hamiltonian. We first apply the coupled-cluster method of quantum many-body theory based on a spiral model state to obtain the ground-state energy and the pitch angle. These results are compared with accurate numerical results using the density matrix renormalization group method, which also gives the correlation functions. We also investigate the periodicity of the phase using the Marshall sign criterion. We discuss particularly the behaviour close to the phase transitions at each end of the frustrated phase.

arXiv:cond-mat/9511044•Journal of Physics Condensed Matter•Nov 6, 1995•178 citations

A coupled-cluster treatment of spin- 1/2 systems with nearest- and next-nearest-neighbour interactions

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The coupled-cluster method of quantum many-body theory is applied to 1D and 2D spin- 1/2 systems with nearest-neighbour and next-nearest-neighbour isotropic exchange. Several simple approximation schemes based on a Neel model state are investigated and are found to give satisfactory results in the antiferromagnetic regime. Results are given for the ground-state energy, the order parameter and the sublattice magnetization. We obtain evidence of a phase transition.

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Spiral correlations in frustrated one-dimensional spin-1/2 HeisenbergJ1–J2–J3ferromagnets

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We investigate the influence of an interchain coupling on the spiral ground-state correlations of a spin-1/2 Heisenberg model consisting of a two-dimensional array of coupled chains with nearest- $({J}_{1})$ and frustrating next-nearest-neighbor $({J}_{2})$ in-chain exchange couplings. Using the coupled cluster method we calculate the transition point between the commensurate and the incommensurate (spiral) ground states as well as the quantum pitch angle of the spiral ground state. In addition, we provide a simple empirical formula which describes the relation between the quantum pitch angle and the frustration parameter ${J}_{2}/{J}_{1}$.

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Phase diagram study of a dimerized spin-S zig–zag ladder

J. M. Matera, Carlos Alberto Lamas

The phase diagram of a frustrated spin-S zig-zag ladder is studied through different numerical and analytical methods. We show that for arbitrary S, there is a family of Hamiltonians for which a fully-dimerized state is an exact ground state, being the Majumdar-Ghosh point for a particular member of the family. We show that the system presents a transition between a dimerized phase to a Néel-like phase for S = 1/2, and spiral phases can appear for large S. The phase diagram is characterized by means of a generalization of the usual mean field approximation. The novelty in the present implementation is to consider the strongest coupled sites as the unit cell. The gap and the excitation spectrum is analyzed through the random phase approximation. Also, a perturbative treatment to obtain the critical points is discussed. Comparisons of the results with numerical methods like the Density Matrix Renormalization Group are also presented.

arXiv:1403.3737•Journal of Physics Condensed Matter•Jul 23, 2014•6 citations
We study the T=0 frustrated phase of the 1D quantum spin- 1/2 system with nearest-neighbour and next-nearest-neighbour isotropic exchange known as the Majumdar-Ghosh Hamiltonian. We first apply the coupled-cluster method of quantum many-body theory based on a spiral model state to obtain the ground-state energy and the pitch angle. These results are compared with accurate numerical results using the density matrix renormalization group method, which also gives the correlation functions. We also investigate the periodicity of the phase using the Marshall sign criterion. We discuss particularly the behaviour close to the phase transitions at each end of the frustrated phase.
We study the T=0 frustrated phase of the 1D quantum spin- 1/2 system with nearest-neighbour and next-nearest-neighbour isotropic exchange known as the Majumdar-Ghosh Hamiltonian. We first apply the coupled-cluster method of quantum many-body theory based on a spiral model state to obtain the ground-state energy and the pitch angle. These results are compared with accurate numerical results using the density matrix renormalization group method, which also gives the correlation functions. We also investigate the periodicity of the phase using the Marshall sign criterion. We discuss particularly the behaviour close to the phase transitions at each end of the frustrated phase.
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 investigate the influence of an interchain coupling on the spiral ground-state correlations of a spin-1/2 Heisenberg model consisting of a two-dimensional array of coupled chains with nearest- (J1)({J}_{1})(J1​) and frustrating next-nearest-neighbor (J2)({J}_{2})(J2​) in-chain exchange couplings. Using the coupled cluster method we calculate the transition point between the commensurate and the incommensurate (spiral) ground states as well as the quantum pitch angle of the spiral ground state. In addition, we provide a simple empirical formula which describes the relation between the quantum pitch angle and the frustration parameter J2/J1{J}_{2}/{J}_{1}J2​/J1​.
The ground-state `phase' diagrams and some low-energy properties of isotropic antiferromagnetic spin- and spin-1 chains with a next-nearest-neighbour exchange and an alternation of the nearest-neighbour exchanges have been compared for the first time using the density matrix renormalization group method. In the spin- chain, the system is gapless for and , and is gapped everywhere else in the plane. At , for small , the gap increases as , where is a disorder line. To the left of this line, the structure factor S(q) peaks at (the Néel `phase'), while to the right, decreases from to (the spiral `phase') as increases. We also discover a ` phase' for large values of both and . In the spin-1 case, we find a line running from a gapless point at up to a `gapless' point at such that the open-chain ground state is fourfold degenerate below the line and is unique above it. There is a disorder line in this case also and it has the same equation as in the spin- case, but the line ends at about . Similarly to the spin- case, to the left of this line, the peak in the structure factor is at (the Néel `phase'), while to the right of the line, it is at less than (the spiral `phase'). For , the system corresponds to a spin ladder and the system is gapped for all values of the interchain coupling for both spin- and spin-1 ladders.
The phase diagram of a frustrated spin-S zig-zag ladder is studied through different numerical and analytical methods. We show that for arbitrary S, there is a family of Hamiltonians for which a fully-dimerized state is an exact ground state, being the Majumdar-Ghosh point for a particular member of the family. We show that the system presents a transition between a dimerized phase to a Néel-like phase for S = 1/2, and spiral phases can appear for large S. The phase diagram is characterized by means of a generalization of the usual mean field approximation. The novelty in the present implementation is to consider the strongest coupled sites as the unit cell. The gap and the excitation spectrum is analyzed through the random phase approximation. Also, a perturbative treatment to obtain the critical points is discussed. Comparisons of the results with numerical methods like the Density Matrix Renormalization Group are also presented.