A numerical study of the formation of magnetisation plateaus in quasi one-dimensional spin-1/2 Heisenberg models

We study the magnetisation process of the one dimensional spin-1/2 antiferromagnetic Heisenberg model with modulated couplings over j=1,2,3 sites. It turns out that the evolution of magnetisation plateaus depends on j and on the wave number q of the modulation according to the rule of Oshikawa, et al. A mapping of two- and three-leg zig-zag ladders on one dimensional systems with modulated couplings yields predictions for the occurence of magnetization plateaus. The latter are tested by numerical computations with the DMRG algorithm.Comment: 7 pages, 10 figures, accepted for publication in Euro. Phys. J.

Quasiparticles governing the zero-temperature dynamics of the 1D spin-1/2 Heisenberg antiferromagnet in a magnetic field

The T=0 dynamical properties of the one-dimensional (1D) $s=1/2$ Heisenberg antiferromagnet in a uniform magnetic field are studied via Bethe ansatz for cyclic chains of $N$ sites. The ground state at magnetization $0<M_z<N/2$, which can be interpreted as a state with $2M_z$ spinons or as a state of $M_z$ magnons, is reconfigured here as the vacuum for a different species of quasiparticles, the {\em psinons} and {\em antipsinons}. We investigate three kinds of quantum fluctuations, namely the spin fluctuations parallel and perpendicular to the direction of the applied magnetic field and the dimer fluctuations. The dynamically dominant excitation spectra are found to be sets of collective excitations composed of two quasiparticles excited from the psinon vacuum in different configurations. The Bethe ansatz provides a framework for (i) the characterization of the new quasiparticles in relation to the more familiar spinons and magnons, (ii) the calculation of spectral boundaries and densities of states for each continuum, (iii) the calculation of transition rates between the ground state and the dynamically dominant collective excitations, (iv) the prediction of lineshapes for dynamic structure factors relevant for experiments performed on a variety of quasi-1D antiferromagnetic compounds, including KCuF$_3$, Cu(C$_4$H$_4$N$_2)(NO_3)_2$, and CuGeO$_3$.Comment: 13 pages, 12 figure

Lineshape predictions via Bethe ansatz for the one-dimensional spin-1/2 Heisenberg antiferromagnet in a magnetic field

The spin fluctuations parallel to the external magnetic field in the ground state of the one-dimensional (1D) s=1/2 Heisenberg antiferromagnet are dominated by a two-parameter set of collective excitations. In a cyclic chain of N sites and magnetization 0<M_z<N/2, the ground state, which contains 2M_z spinons, is reconfigured as the physical vacuum for a different species of quasi-particles, identifiable in the framework of the coordinate Bethe ansatz by characteristic configurations of Bethe quantum numbers. The dynamically dominant excitations are found to be scattering states of two such quasi-particles. For N -> \infty, these collective excitations form a continuum in (q,\omega)-space with an incommensurate soft mode. Their matrix elements in the dynamic spin structure factor S_{zz}(q,\omega) are calculated directly from the Bethe wave functions for finite N. The resulting lineshape predictions for N -> \infty complement the exact results previously derived via algebraic analysis for the exact 2-spinon part of S_{zz}(q,\omega) in the zero-field limit. They are directly relevant for the interpretation of neutron scattering data measured in nonzero field on quasi-1D antiferromagnetic compounds.Comment: 10 page

Line shapes of dynamical correlation functions in Heisenberg chains

We calculate line shapes of correlation functions by use of complete diagonalization data of finite chains and analytical implications from conformal field theory, density of states, and Bethe ansatz. The numerical data have different finite size accuracy in case of the imaginary and real parts in the frequency and time representations of spin-correlation functions, respectively. The low temperature, conformally invariant regime crosses over at $T^*\approx 0.7J$ to a diffusive regime that in turn connects continuously to the high temperature, interacting fermion regime. The first moment sum rule is determined.Comment: 13 pages REVTEX, 18 figure

Numerical renormalization group study of the correlation functions of the antiferromagnetic spin-12\frac{1}{2} Heisenberg chain

We use the density-matrix renormalization group technique developed by White \cite{white} to calculate the spin correlation functions $=(-1)^l \omega(l,N)$ for isotropic Heisenberg rings up to $N=70$ sites. The correlation functions for large $l$ and $N$ are found to obey the scaling relation $\omega(l,N)=\omega(l,\infty)f_{XY}^{\alpha} (l/N)$ proposed by Kaplan et al. \cite{horsch} , which is used to determine $\omega(l,\infty)$. The asymptotic correlation function $\omega(l,\infty)$ and the magnetic structure factor $S(q=\pi)$ show logarithmic corrections consistent with $\omega(l,\infty)\sim a\sqrt{\ln{cl}}/l$, where $c$ is related to the cut-off dependent coupling constant $g_{eff}(l_0)=1/\ln(cl_0)$, as predicted by field theoretical treatments.Comment: Accepted in Phys. Rev. B. 4 pages of text in Latex + 5 figures in uuencoded form containing the 5 postscripts (mailed separately

Spin Chains as Perfect Quantum State Mirrors

Quantum information transfer is an important part of quantum information processing. Several proposals for quantum information transfer along linear arrays of nearest-neighbor coupled qubits or spins were made recently. Perfect transfer was shown to exist in two models with specifically designed strongly inhomogeneous couplings. We show that perfect transfer occurs in an entire class of chains, including systems whose nearest-neighbor couplings vary only weakly along the chain. The key to these observations is the Jordan-Wigner mapping of spins to noninteracting lattice fermions which display perfectly periodic dynamics if the single-particle energy spectrum is appropriate. After a half-period of that dynamics any state is transformed into its mirror image with respect to the center of the chain. The absence of fermion interactions preserves these features at arbitrary temperature and allows for the transfer of nontrivially entangled states of several spins or qubits.Comment: Abstract extended, introduction shortened, some clarifications in the text, one new reference. Accepted by Phys. Rev. A (Rapid Communications

Optimized pulses for the perturbative decoupling of spin and decoherence bath

In the framework of nuclear magnetic resonance, we consider the general problem of the coherent control of a spin coupled to a bath by means of composite or continuous pulses of duration $\tau_\mathrm{p}$. We show explicity that it is possible to design the pulse in order to achieve a decoupling of the spin from the bath up to the third order in $\tau_\mathrm{p}$. The evolution of the system is separated in the evolution of the spin under the action of the pulse and of the bath times correction terms. We derive the correction terms for a general time dependent axis of rotation and for a general coupling between the spin and the environment. The resulting corrections can be made vanish by an appropriate design of the pulse. For $\pi$ and $\pi/2$ pulses, we demonstrate explicitly that pulses exist which annihilate the first and the second order corrections even if the bath is fully quantum mechanical, i.e., it displays internal dynamics. Such pulses will also be useful for quantum information processing.Comment: 9 pages, 7 figures. Published versio

Efficient and perfect state transfer in quantum chains

We present a communication protocol for chains of permanently coupled qubits which achieves perfect quantum state transfer and which is efficient with respect to the number chains employed in the scheme. The system consists of $M$ uncoupled identical quantum chains. Local control (gates, measurements) is only allowed at the sending/receiving end of the chains. Under a quite general hypothesis on the interaction Hamiltonian of the qubits a theorem is proved which shows that the receiver is able to asymptotically recover the messages by repetitive monitoring of his qubits.Comment: 6 pages, 2 figures; new material adde

Transport Control in Low-Dimensional Spin-1/2 Heisenberg Systems

We analyze transport of local magnetization and develop schemes to control transport behavior in finite spin-1/2 Heisenberg chains and spin-1/2 Heisenberg two-leg ladders at zero temperature. By adjusting parameters in the Hamiltonians, these quantum systems may show both integrable and chaotic limits. We provide examples of chaotic systems leading to diffusive and to ballistic transport. In addition, methods of coherent quantum control to induce a transition from diffusive to ballistic transport are proposed.Comment: 8 pages, 5 figure

Intermediate-statistics spin waves

In this paper, we show that spin waves, the elementary excitation of the Heisenberg magnetic system, obey a kind of intermediate statistics with a finite maximum occupation number n. We construct an operator realization for the intermediate statistics obeyed by magnons, the quantized spin waves, and then construct a corresponding intermediate-statistics realization for the angular momentum algebra in terms of the creation and annihilation operators of the magnons. In other words, instead of the Holstein-Primakoff representation, a bosonic representation subject to a constraint on the occupation number, we present an intermediate-statistics representation with no constraints. In this realization, the maximum occupation number is naturally embodied in the commutation relation of creation and annihilation operators, while the Holstein-Primakoff representation is a bosonic operator relation with an additional putting-in-by-hand restriction on the occupation number. We deduce the intermediate-statistics distribution function for magnons. On the basis of these results, we calculate the dispersion relations for ferromagnetic and antiferromagnetic spin waves. The relations between the intermediate statistics that magnons obey and the other two important kinds of intermediate statistics, Haldane-Wu statistics and the fractional statistics of anyons, are discussed. We also compare the spectrum of the intermediate-statistics spin wave with the exact solution of the one-dimensional s = 1/2 Heisenberg model, which is obtained by the Bethe ansatz method. For ferromagnets, we take the contributions from the interaction between magnons (the quartic contribution), the next-to-nearest neighbor interaction, and the dipolar interaction into account for comparison with the experiment.Comment: 22 pages, 2 figure