Quantized spin waves in antiferromagnetic Heisenberg chains

The quantized stationary spin wave modes in one-dimensional antiferromagnetic spin chains with easy axis on-site anisotropy have been studied by means of Landau-Lifshitz-Gilbert spin dynamics. We demonstrate that the confined antiferromagnetic chains show a unique behavior having no equivalent, neither in ferromagnetism nor in acoustics. The discrete energy dispersion is split into two interpenetrating n and n' levels caused by the existence of two sublattices. The oscillations of individual sublattices as well as the standing wave pattern strongly depend on the boundary conditions. Particularly, acoustical and optical antiferromagnetic spin waves in chains with boundaries fixed (pinned) on different sublattices can be found, while an asymmetry of oscillations appears if the two pinned ends belong to the same sublattice.     

Nonlocal topological order in antiferromagnetic Heisenberg chains

We demonstrate the existence of nonlocal topological (string) order in half-integer-spin antiferromagnetic Heisenberg chains on macroscopic scale on the basis of analytical scaling analysis and density matrix renormalization group calculations. Strong numerical evidence leads to a conjecture that chains with S = (2m-1)/2 and m (m = integers) belong to the same topological class defined by the topological angle theta/pi = 1/m that plays a role similar to the fictitious gauge field in the fractional quantum Hall effect.     

Exchange narrowing in random-exchange Heisenberg antiferromagnetic chains

A phenomenological theory of exchange narrowing is developed for random-exchange Heisenberg antiferromagnetic chains at low temperature. The nearly logarithmic epr linewidth of quinolinium (tetracyanoquino-dimethane)₂ is regained as an inhomogeneous superposition of thermally decoupled domains with widely different renormalized exchange fields that also describe the static thermodynamics. The temperature dependence of internal dipolar fields and of interchain interactions are modeled in terms of spin dilution.     

String order in half-integer-spin antiferromagnetic Heisenberg chains

We derive the extended string order parameter O(S) for antiferromagnetic Heisenberg chains with half-integer spin S in the valence-bond-solid picture. We obtain the analytic power-law scaling of O(S) versus the chain length L and show that O(S) scales at an extremely slow pace that decreases rapidly with growing spin magnitude. Furthermore, accurate numerical calculations show that the power-law scaling sets in only when L exceeds a characteristic length scale l(S) which increases very fast with growing S. Consequently, a pseudo-long-range string order exists in half-integer-spin Heisenberg chains. The implications of this result and its relationship to other topological features such as the end-chain states are discussed.     

Field dependent spin dynamics of antiferromagnetic Heisenberg chains

Low temperature data are given for the spectra of longitudinal and transverse correlation functions of an antiferromagnetic classical heisenberg chain. The one dimensional magnet subjected to large external fields is investigated by means of a computer simulation calculation. The results are tied in with the static properties and compared with theoretical predictions.     

Spin structure factors and valence-bond-solid states of the trimerized Heisenberg chains in a magnetic field

By means of the density matrix renormalization group (DMRG) method, the static spin structure factors and the magnetization plateaus of the trimerized Heisenberg ferromagnet-ferromagnet-antiferromagnet and antiferromagnet-antiferromagnet-ferromagnet spin chains in the presence of a magnetic field are elaborately studied. It is found that in the plateau states, the static structure factor with three peaks does not vary with the external magnetic field as well as the exchange couplings; the spin correlation function behaves as a perfect sequence and has a simple relation with the magnetization per site. An approximate wave function for the plateau states is proposed, and a picture based on the valence-bond-solid states is presented in order to understand the origin and the total number of the magnetization plateaus, which are shown to be in agreement with the DMRG results.     

Excitations in a four-leg antiferromagnetic Heisenberg spin tube

Inelastic neutron scattering is used to investigate magnetic excitations in the quasi-one-dimensional quantum spin-liquid system Cu(2)Cl(4).D(8)C(4)SO(2). Contrary to previously conjectured models that relied on bond-alternating nearest-neighbor interactions in the spin chains, the dominant interactions are actually next-nearest-neighbor in-chain antiferromagnetic couplings. The appropriate Heisenberg Hamiltonian is equivalent to that of a S=1/2 4-leg spin-tube with almost perfect one dimensionality and no bond alternation. A partial geometric frustration of rung interactions induces a small incommensurability of short-range spin correlations.     

Excitations in the antiferromagnetic Heisenberg chain

Non-singlet excitations of the antiferromagnetic Heisenberg chain of N atoms with spin $\text{1}\text{2}$ are examined. It is found that the energy of the lowest lying excitations for total spin S and wave number q converges to $\text{(}\text{π}\text{2}\text{)|}\text{sin}\text{q |}\text{as}\text{N → ∞,}\text{if only}\text{S?}\text{ln}\text{N}$.     

Role of the spin anisotropy of the interchain interaction in weakly coupled antiferromagnetic Heisenberg chains

In quasi-one-dimensional(q1D) quantum antiferromagnets, the complicated interplay of intrachain and interchain exchange couplings may give rise to rich phenomena. Motivated by recent progress on field-induced phase transitions in the q1D antiferromagnetic(AFM) compound YbAlO_3, we study the phase diagram of spin-1/2 Heisenberg chains with Ising anisotropic interchain couplings under a longitudinal magnetic field via large-scale quantum Monte Carlo simulations,and investigate the role of the spin anisotropy of the interchain coupling on the ground state of the system. We find that the Ising anisotropy of the interchain coupling can significantly enhance the longitudinal spin correlations and drive the system to an incommensurate AFM phase at intermediate magnetic fields, which is understood as a longitudinal spin density wave(LSDW). With increasing field, the ground state changes to a canted AFM order with transverse spin correlations. We further provide a global phase diagram showing how the competition between the LSDW and the canted AFM states is tuned by the Ising anisotropy of the interchain coupling.     

An estimate for the magnetization reversal time of antiferromagnetic chains within the Heisenberg model

Within the Heisenberg model in the presence of uniaxial magnetic anisotropy, formulas are obtained that allow one to estimate both the spontaneous magnetization reversal time of an antiferromagnetic chain and the magnetization reversal time due to interaction with the conducting tip of a scanning tunneling microscope (STM). Corrections due to a possible difference between the properties of the end and inner atoms of the chain are calculated. Numerical estimates are obtained for typical parameter values of the Heisenberg Hamiltonian.     

Quantum entanglement and criticality of the antiferromagnetic Heisenberg model in an external field

By Lanczos exact diagonalization and the infinite time-evolving block decimation (iTEBD) technique, the two-site entanglement as well as the bipartite entanglement, the ground state energy, the nearest-neighbor correlations, and the magnetization in the antiferromagnetic Heisenberg (AFH) model under an external field are investigated. With increasing external field, the small size system shows some distinct upward magnetization stairsteps, accompanied synchronously with some downward two-site entanglement stairsteps. In the thermodynamic limit, the two-site entanglement, as well as the bipartite entanglement, the ground state energy, the nearest-neighbor correlations, and the magnetization are calculated, and the critical magnetic field h(c) = 2.0 is determined exactly. Our numerical results show that the quantum entanglement is sensitive to the subtle changing of the ground state, and can be used to describe the magnetization and quantum phase transition. Based on the discontinuous behavior of the first-order derivative of the entanglement entropy and fidelity per site, we think that the quantum phase transition in this model should belong to the second-order category. Furthermore, in the magnon existence region (h < 2.0), a logarithmically divergent behavior of block entanglement which can be described by a free bosonic field theory is observed, and the central charge c is determined to be 1.     

The two dimensional antiferromagnetic Heisenberg model in the presence of an external field

We present numerical results on the zero temperature magnetization curve and the static structure factors of the two dimensional antiferromagnetic Heisenberg model in the presence of an external field. The impact of frustration is also studied.