Strong Coulomb effects in hole-doped Heisenberg chains

Substances such as the “telephone number compound” Sr₁₄Cu₂₄O₄₁ are intrinsically hole-doped. The involved interplay of spin and charge dynamics is a challenge for theory. In this article we propose to describe hole-doped Heisenberg spin rings by means of complete numerical diagonalization of a Heisenberg Hamiltonian that depends parametrically on hole positions and includes the screened Coulomb interaction among the holes. It is demonstrated that key observables like magnetic susceptibility, specific heat, and inelastic neutron scattering cross section depend sensitively on the dielectric constant of the screened Coulomb potential.     

Low-temperature transport in Heisenberg chains

A technique to determine accurately transport properties of integrable and nonintegrable quantum-spin chains at finite temperatures by quantum Monte Carlo is presented. The reduction of the Drude weight by interactions in the integrable gapless regime is evaluated. Evidence for the absence of Drude weight in the gapless regime of a nonintegrable system with longer-ranged interactions is presented. We estimate the effect of the nonintegrability on the transport properties and compare with recent experiments on one-dimensional quantum-spin chains.     

Unified quantum mechanical picture for confined spinons in dimerized and frustrated spin chains

A quantum mechanical picture is presented to describe the behavior of confined spinons in a variety of S =1/2 chains. The confinement is due to dimerization and frustration and it manifests itself as a nonlinear potential , centered at chain ends () or produced by modulation kinks (b > 1). The calculation extends to weak or zero frustration some previous ideas valid for spinons in strongly frustrated spin chains. The local magnetization patterns of the confined spinons are calculated. A (minimum) enhancement of the local moments of about 11/3 over a single S =1/2 is found. Estimates for excitation energies and binding lengths are obtained. Received: 8 May 1998 / Revised and Accepted: 12 August 1998     

Entanglement oscillations in open Heisenberg chains

We study pairwise entanglements in spin-half and spin-one Heisenberg chains with an open boundary condition, respectively. We find out that the ground-state and the first-excited-state entanglements are equal for the three-site spin-one chain. When the number of sites L>3, the concurrences and negativities display oscillatory behaviors, and the oscillations of the ground-state and the first-excited-state entanglements are out of phase or in phase.     

Spin-peierls transition in anisotropic Heisenberg chains

We study spin-Peierls transition for anisotropic Heisenberg chains within mean field theory. We find that dimerization occurs in the absence of a magnetic field and when the field is smaller than a critical field H_c. The transition temperature is obtained as a function of anisotropy and magnetic field.     

On the incommensurate phase in modulated Heisenberg chains

Using the density matrix renormalization group method (DMRG) we calculate the magnetization of frustrated S=1/2 Heisenberg chains for various modulation patterns of the nearest neighbour coupling: commensurate, incommensurate with sinusoidal modulation and incommensurate with solitonic modulation. We focus on the order of the phase transition from the commensurate dimerized phase (D) to the incommensurate phase (I). It is shown that the order of the phase transition depends sensitively on the model. For the solitonic model in particular, a k-dependent elastic energy modifies the order of the transition. Furthermore, we calculate gaps in the incommensurate phase in adiabatic approximation. Received: 9 March 1998 / Accepted: 17 April 1998     

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.     

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.     

On the dynamics of impure classical Heisenberg chains

We present theoretical results on dynamic correlation functions of impure, classical, one-dimensional Heisenberg magnets with both ferromagnetic and antiferromagnetic coupling. The results are obtained in the framework of Mori's theory and in an approximation which includes correctly all moments of the relaxation function to lowest order in impurity concentration and temperature and which preserves the rotational symmetry of the system even at zero temperature. Explicit results are given for lineshifts and linewidths of quasi-spinwaves and the behaviour of correlation functions in the hydrodynamic limit is discussed.     

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.     

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.     

On some additional effects in Heisenberg ferromagnet caused by the presence of dipole-dipole interactions

The Heisenberg ferromagnet with dipole-dipole interactions was studied. It was shown that the presence of dipole-dipole interactions changes the direction of the quantization axis, gives the anharmonical correction to the low temperature magnetization proportional to the square of the temperature, increases the critical point and leads to a fusion process of elementary excitations. All the results obtained are valid only in the presence of an external magnetic field. The absence of the field requires a qualitatively new approach.     

Critical exponents for alternation in Heisenberg antiferromagnetic chains

The ground-state energy per site, λ(δ), and singlet-triplet gap, ΔE(δ), of regular (δ=0) and alternating (δ ≤ 0.01) Heisenberg antiferromagnetic chains are obtained by extrapolating exact numerical solutions of even and odd rings and chains of N ≤ 20 spins. The critical exponents of 1.72 ± 0.02 for λ(δ) and 0.9 ± 0.1 for ΔE(δ) are compared with recent theoretical results for spin-Peierls transitions. Interactions among spinless fermions alter the instability to alternation.     

New universality class in spin-one-half Fibonacci Heisenberg chains

Low energy properties of the S=1/2 antiferromagnetic Heisenberg chains with Fibonacci exchange modulation are studied using the real space renormalization group method for strong exchange modulation. Using the analytical solution of the recursion equation, the true asymptotic behavoir is revealed, which was veiled by the finite size effect in the previous numerical works. It is found that the ground state of this model belongs to a new universality class with a logarithmically divergent dynamical exponent which is neither like Fibonacci XY chains nor like XY chains with relevant aperiodicity.     

Investigation of frustrated and dimerized classical Heisenberg chains

We have considered the 1D dimerized frustrated antiferromagnetic (ferromagnetic) Heisenberg model with arbitrary spin S$S$. The exact classical magnetic phase diagram at zero temperature is determined using the LK cluster method. The cluster method results show that the classical ground-state phase diagram of the model is very rich, including first-order and second-order phase transitions. In the absence of dimerization, a second-order phase transition occurs between antiferromagnetic (ferromagnetic) and spiral phases at the critical frustration _αc=±0.25${\alpha }_c=\pm 0.25$, a well-known result. In the vicinity of the critical points _αc${\alpha }_c$, the exact classical critical exponent of the spiral order parameter is found to be 1/2$1/2$. In the case of a dimerized chain (δ≠0$\delta \ne 0$), the spiral order shows stability and exists in some part of the ground-state phase diagram. We have found two first-order phase boundaries separating antiferromagnetic (uud and duu) phases from the spiral phase.