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Physical review. B, Condensed matter

Excitation spectrum of a spin-(1/2 chain with competing interactions

Jun-ichi Igarashi, Takashi Tonegawa

Published Jul 1, 1989• 21 citations
Publisher

Abstract

The excitation spectrum is studied around the degenerate point at the Ising limit in the one-dimensional anisotropic Heisenberg antiferromagnets with next-nearest-neighbor interactions. Solitons are found as propagation modes in the N\'eel state and in the (2,2) antiphase state, while triplet-dimer excitations are found propagating in the dimer state. These excitations determine the shape of dynamical spin-correlation functions, which are calculated by an exact diagonalization for finite chains. The phase diagram is determined from the condition that the energy gap vanishes in the excitation spectrum.

DOI
10.1103/physrevb.40.756

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The excitation spectrum is studied around the degenerate point at the Ising limit in the one-dimensional anisotropic Heisenberg antiferromagnets with next-nearest-neighbor interactions. Solitons are found as propagation modes in the N'eel state and in the (2,2) antiphase state, while triplet-dimer excitations are found propagating in the dimer state. These excitations determine the shape of dynamical spin-correlation functions, which are calculated by an exact diagonalization for finite chains. The phase diagram is determined from the condition that the energy gap vanishes in the excitation spectrum.
Elementary excitations are studied near the Ising limit close to the degenerate point in the one-dimensional anisotropic Heisenberg antiferromagnets with up to next-nearest-neighbor interactions. Solitons in the Néel and (2,2) antiphase states and triplet-dimer excitations in the dimer state are found as propagating modes. These excitations are found to dominate the shape of the central peak in dynamical spin correlation functions, through the comparison with the numerical results by an exact diagonalization method for finite chains. The temperature dependence of the static correlation function is also discussed, and the shape is found to change gradually with increasing temperature, approaching the zero-temperature correlation function at the degenerate point.
Ground-state properties are studied for the one-dimensional anisotropic spin-1/2 Heisenberg magnet with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions, which are assumed to have the same form as regards the anisotropy. The singlet-triplet energy gap, the magnetization, the energy, and the two-spin correlation function in the ground states of finite-size systems of up to 20 spins are calculated exactly. By extrapolating these results, the values of the above quantities at the infinite-size limit are estimated. Special attention is paid to the limiting ground-state phase diagram on the plane of the ratio of the next-nearest-neighbor interaction constant to the nearest-neighbor one versus the anisotropy parameter. It is found that, when the interactions have the XY-type anisotropy, the limiting ground state is in the spin-fiuid phase or in the dimer phase depending upon whether the ratio between the interaction constants is smaller or larger than a critical value. It is also found that, when the interactions have the Ising-type anisotropy, a novel phase with unsaturated magnetization appears between the ferromagnetic and (2, 2) antiphase phases in the limiting ground-state phase diagram.
Excitation spectrum as well as ground states is studied in detail in the region near the Ising limit with small XY-component in a Heisenberg ferromagnetic chain with competing antiferromagnetic second-neighbor interaction. A spin-fluid-like phase with gapless excitation spectrum, which exhibits ferromagnetic long-range order, is derived in the intermediate region between the saturated ferromagnetic and (2, 2) antiphase states, by mapping onto a system of Bose-like particles with hard core of finite radius. Expressions for the magnetization, the susceptibility and the dispersion relalion of the excitation spectrum are obtained in the intermediate phase. This mapping is expected to be exact in the region near the degenerate point.
We study the ground-state properties of the one-dimensional anisotropic spin-1/2 antiferromagnetic Heisenberg model with competing antiferromagnetic second-neighbor Ising interaction. Using the modified Lanczos method, we obtain the phase diagram in parameter space and different correlation functions, which we use to characterize the different phases. For small next-nearest-neighbor parameters we evaluate the critical exponent \ensuremath{\eta} of the spin-spin correlation function. We find good agreement between the numerical results and those obtained using the Luther and Peschel approach.
Ground-state phase diagram and low-lying excitation spectrum of the one-dimensional S =1 anisotropic Heisenberg antiferromagnetic chain with nearest neighbor and next nearest neighbor interactions are studied by means of an approximate mapping of the original S =1 spin Hamiltonian to the effective fermion Hamiltonian, which describes the dynamics of spin zero defects in antiferromagnetic environments (domain walls in the Néel state). We find that the frustration due to the next nearest neighbor interactions works cooperatively with quantum fluctuation in the Haldane state and stabilizes it. This is naturally explained in terms of the spin zero defect. In addition, we discuss characteristic features of the excitation spectrum in connection with its ground-state properties.
Ground-state properties are studied for the one-dimensional anisotropic spin-1/2 Heisen­ berg magnet with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest­ neighbor interactions, which are assumed to have the same form as regards the anisotropy. The singlet-triplet energy gap, the magnetization, the energy, and the two-spin correlation function in the ground states of finite-size systems of up to 20 spins are calculated exactly. By extrapolating these results, the values of the above quantities at the infinite-size limit are estimated. Special attention is paid to the limiting ground-state phase diagram on the plane of the ratio of the next-nearest-neighbor interaction constant to the nearest-neighbor one versus the anisotropy parameter. It is found that, when the interactions have the XY-type anisotropy, the limiting ground state is in the spin-fluid phase or in the dimer phase depending upon whether the ratio between the interaction constants is smaller or larger than a critical value. It is also found that, when the interactions have the Ising-type anisotropy, a novel phase with unsaturated magnetization appears between the ferromagnetic and (2, 2) antiphase phases in the limiting ground-state phase diagram.