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Europhysics Letters (EPL)

Phase Diagram and Excitation Spectrum of S = 1 Antiferromagnetic Heisenberg Chains

H.-J. Mikeska

Published May 1, 1992• 25 citations
Publisher

Abstract

We investigate ground-state and low-lying excited states of the S = 1 antiferromagnetic Heisenberg chain with exchange anisotropy, single-ion anisotropy and biquadratic exchange and with free boundary conditions. We present an approximate mapping of the S = 1 model to an effective S = 1/2 chain in an external magnetic field, which can be solved exactly in several limiting cases. We obtain results for the phase diagram, correlation functions and the excitation spectrum. The transition to the Haldane phase is related to the condensation of the lowest soliton modes and the hidden order parameter of the Haldane phase is identified as transverse long-range order in the effective S = 1/2 chain.

DOI
10.1209/0295-5075/19/1/007

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We investigate ground-state and low-lying excited states of the S = 1 antiferromagnetic Heisenberg chain with exchange anisotropy, single-ion anisotropy and biquadratic exchange and with free boundary conditions. We present an approximate mapping of the S = 1 model to an effective S = 1/2 chain in an external magnetic field, which can be solved exactly in several limiting cases. We obtain results for the phase diagram, correlation functions and the excitation spectrum. The transition to the Haldane phase is related to the condensation of the lowest soliton modes and the hidden order parameter of the Haldane phase is identified as transverse long-range order in the effective S = 1/2 chain.
We calculate energies and wave functions of S=1 antiferromagnetic Heisenberg chains with single-ion anisotropy in a symmetry-breaking external magnetic field. From results for the string correlation function for low-lying excited states we identify these states as solitons with respect to the hidden string order. For finite anisotropic chains we investigate the transition to the fully magnetized state at high magnetic fields and conclude that Bose condensation in an external magnetic field occurs also for the anisotropic chain.
We study the ground-state phase diagram and the excitations of a one-dimensional s=1 Heisenberg antiferromagnet including exchange and single ion anisotropy with anisotropy constants \ensuremath{\epsilon} and D, respectively. Starting from the ground state for D=\ensuremath{\infty}, a new class of spin-one defects is introduced. Treating these defects as fermions and performing a mean-field approximation, we find three phases: the N\'eel, the Haldane, and the large-D phase. The corresponding phase diagram is partly in good agreement with existing data. The N\'eel and the string order parameters have the correct behavior in the large-D and the Haldane phase, but not in the N\'eel phase. For a certain variational state, we find a ground-state energy which perfectly agrees with the best quantum Monte Carlo data. Finally we argue that the low-lying one-particle excitations are of fermionic character.
The ground-state phase diagram of S=2S=2S=2 antiferromagnetic Heisenberg chains with coexisting uniform and alternating single-site anisotropies is investigated by the numerical exact diagonalization and density matrix renormalization group methods. We find the Haldane, large-DDD, Néel, period-doubled Néel, gapless spin fluid, quantized and partial ferrimagnetic phases. The Haldane phase is limited to the close neighborhood of the isotropic point. Within numerical accuracy, the transition from the gapless spin-fluid phase to the period-doubled Néel phase is a direct transition. Nevertheless, the presence of a narrow spin-gap phase between these two phases is suggested on the basis of the low-energy effective theory. The ferrimagnetic ground state is present in a wide parameter range. This suggests the realization of magnetized single-chain magnets with a uniform spin magnitude by controlling the environment of each magnetic ion without introducing ferromagnetic interactions.
A spin-1 antiferromagnetic Heisenberg chain with a single-ion anisotropy Dtsumj{\mathit{Dtsum}}_{\mathit{j}}Dtsumj​(Sjz{\mathit{S}}_{\mathit{j}}^{\mathit{z}}Sjz​)2{)}^{2})2 is investigated on the basis of the continuum representation of the model Hamiltonian. Analytical results for the ground state, the excitation spectrum, and the correlation functions are derived in a self-consistent-field approach. We find that the ground state is made of boson pairs and the correlation functions in the ground state decay exponentially. Two Haldane gaps due to the single-ion anisotropy are obtained and a transition at the critical value Dc{\mathit{D}}_{\mathit{c}}Dc​=1 is shown in the lower Haldane gap and the correlation functions.
The ground-state phase diagram of the Kondo chain with an anisotropic exchange is investigated. Four different phases are identified, two types of N\'eel phases, the Haldane phase, and the Kondo singlet phase. The boundaries between these phases in the strong coupling region are determined by mapping to effective models: the spin-1 Heisenberg model with single-ion anisotropy and the Ising model in a transverse magnetic field. It is shown that these transition lines extend to the weak-coupling limit and they are estimated by using the exact numerical diagonalization for a finite system.
Ground-state properties of the spin-1 antiferromagnetic Heisenberg chain with bond alternation and uniaxial single-ion-type anisotropy, which is described by the Hamiltonian \({\cal H}_0 = \sum_{\ell=1}^N\{1-(-1)^\ell\alpha\}{\mib S}_\ell\cdot{\mib S}_{\ell+1} + D\sum_{\ell=1}^N\;(S_\ell^z)^2\) (0.0 ≤α≤1.0, -∞< D < ∞), are studied. An exact diagonalization method by means of the Lanczös technique is used. The ground-state phase diagram on the α versus D plane at the thermodynamic limit is determined by analyzing the Binder parameters associated with Néel order and z -direction string order for finite-size ( N = 6, 8, …, 16) chains. It is found that there exists a multicritical point at which the Haldane, Néel, and singlet-dimer phases meet and that the singlet-dimer phase and the large- D phase belong to the same unique phase. The ground-state magnetization curves at the thermodynamic limit for various values of α and D are obtained for the system described by the Hamiltonian, H 0 plus the Zeeman term - H ∑ ℓ=1 N S ℓ z . The results show that the 1/2-plateau appears in the magnetization curve at least when D ≥0.0 and 0.0≲α≤1.00.0\lesssim\alpha \leq 1.00.0≲α≤1.0.