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Journal of the Physical Society of Japan

Ground State and Excitation Spectrum of a Spin-1/2 Ising-Like Ferromagnetic Chain with Competing Interactions

Jun-ichi Igarashi

Published Dec 15, 1989• 16 citations
Publisher

Abstract

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.

DOI
10.1143/jpsj.58.4600

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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.
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.
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.
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.
The ground state of an Ising-type spin-1/2 chain with ferromagnetic bond-alternating nearest-neighbor and anti-ferromagnetic uniform next-nearest-neighbor interactions is studied by using the exact-diagonalization method and the density-matrix renormalization-group method. The Hamiltonian describing the system is expressed as H = – Σi h2i–1,2i – J1 Σi h2i,2i+1 + J2 Σi hi,i+2 with hi,i' = γ(Six Si'x + Siy Si'y) + Siz Si'z, where J1 0, J2 0, and 1 > γ 0. Special attention is paid to the ground-state phase diagram on the J1 versus J2 plane for a given value of γ. The phase diagram is composed of the ferromagnetic, intermediate, and up-up-down-down phases, the intermediate phase being characterized by its magnetization, which takes finite but unsaturated values. The phase diagram obtained for γ = 0.5 shows that the region of the intermediate phase for a given value of J1 is widest when J1 = 1.0 and becomes narrower rather rapidly as J1 decreases or increases from 1.0. The J2-dependence of the ground-state magnetization for γ = 0.5 and J1 = 0.85 is also discussed. PACS Nos.: 75.10Jm, 75.40Mg
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.
The ground state of the spin-1/2 Ising–Heisenberg distorted diamond chain in the presence of an external magnetic field is investigated in the case of the ferromagnetic Ising and antiferromagnetic XXZ Heisenberg interactions, that exhibits a geometric frustration of spins. The influence of the quantum fluctuations, the magnetic field, and the distortion on the ground state are studied in detail. It is established that the zero-temperature magnetization curve may show intermediate plateaus at zero and one-third of the saturation magnetization.