Connected-moments expansion for the antiferromagnetic spin chain

Nicholas S. Witte

We present the exact solution to the moment problem for the spin-1/2 isotropic antiferromagnetic XY chain with explicit forms for the moments with respect to the Néel state, the cumulant generating function, and the Resolvent Operator. We verify the correctness of the Horn–Weinstein Theorems, but the analytic structure of the generating function <e-tH> in the complex t-plane is quite different from that assumed by the t-Expansion and the Connected Moments Expansion due to the vanishing gap. This function has a finite radius of convergence about t=0, and for large t has a leading descending algebraic series E(t)-E0~ At-2. The Resolvent has a branch cut and essential singularity near the ground state energy of the form G(s)/s~ B|s+1|-3/4 exp (C|s+1|1/2). Consequently extrapolation strategies based on these assumptions are flawed and in practise we find that the CMX methods are pathological, and cannot be applied, while numerical evidence for two of the t-expansion methods indicates a clear asymptotic convergence behaviour with truncation order.

Jos 'e A. Hoyos, E. Miranda

A. A. Kokin, V. A. Kokin

This article presents the results of studies of the linear antiferromagnetic spin chain with uniaxial anisotropy (XXZ– model) placed in a transverse magnetic field directed along the anisotropy axis of the chain with a constant gradient along the chain. A spin Hamiltonian for the states close to the ground was written in the spin-wave approximation. It was diagonalized by an asymptotic expansion in the small parameter describing the magnitude of the field gradient. Local energy of the ground state and the reduced density matrix of the quantum states for a selected pair of spins in the chain have been considered in the gapped and gapless cases. Local spin polarization and the local toroidal magnetic moment have also been found. Local pair entanglement of quantum states as a characteristic of quantum correlations in the spin chain was studied.

Gang Sun, Fu‐Cho Pu

Stefan Weßel, Stephan Haas

We study the evolution of the dynamical spin structure factor in a spin-1 antiferromagnetic Heisenberg chain which is randomly doped with spin-1/2 moments. Using stochastic series expansion quantum Monte Carlo simulations combined with the maximum entropy method, we monitor the crossover from the spin-1 chain, dominated by a single resonance at the Haldane energy, to the spin-1/2 chain with a continuum of spinon states which diverges at zero frequency. Upon increasing the doping level, spectral weight is rapidly transferred from the Haldane peak to lower energies. If the exchange couplings between the spin-1/2 substituents and the spin-1 sites of the host are sufficiently small, finite-frequency bound states are observed below the spin gap for small doping concentrations.

Roger Arthur Cowley, D. M. Tennant, T. G. Perring +2 more