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Physical review. B, Condensed matter

Spin-one-defect description of the antiferromagnetic s=1 Heisenberg chain

Holger Köhler, R. Schilling

Published Feb 1, 1997• 5 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.55.2945

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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 authors investigate a one-dimensional, spin s=1 Heisenberg antiferromagnet with exchange and single-ion anisotropy. A self-consistent approach using defects, which was recently proposed by Gomez-Santos (1989), is applied to determine the phase diagram at T=0 K and is generalised to finite temperatures. The phase diagram for exchange anisotropy constant epsilon >or=1 is in reasonable agreement with earlier numerical results; the three different phases (Neel, Haldane and large-D phases) can be characterised by the defect concentration. It is shown that the ground state and the excitations are BCS-like. The Haldane phase can be interpreted as a BCS phase in particular, and the lowest excitations, as a break-up of 'Cooper pairs'. The specific heat C exhibits a maximum. Its position T max increases with increasing gap energy E g ; below T max , there exists a regime with linear temperature dependence.
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.
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.
The ground-state phase diagram of a frustrated S=1 Heisenberg spin chain with uniaxial single-ion-type anisotropy is studied using the infinite-system density-matrix renormalization-group method. Particular attention is paid to "chiral" phases, in which the long-range order parameter is a vector chirality. It is found that, in addition to the Haldane, large-D (LD), and double-Haldane phases, the phase diagram includes three different chiral phases, i.e., the gapless chiral, chiral-Haldane, and chiral-LD phases. These chiral phases are distinguished from each other by the energy gap and the string long-range order.
The ground state of the ferromagnetic-antiferromagnetic alternating spin-1/2 Heisenberg chain is studied with Ising-type anisotropy on the ferromagnetic bond. This model tends to the spin-1 antiferromagnetic Heisenberg chain with on-site anisotropy in the limit of strong ferromagnetic bond. It is found that the Haldane-gap phase, the large-D phase, and the two types of N\'eel phases appear as the ground state of this model. The duality relations between these four phases are proved for several limiting cases. The string order parameter characterizing the large-D phase is introduced based on these duality relations. The ground-state phase diagram is determined by the numerical diagonalization of the finite-size system.
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.