Spin-1 Antiferromagnetic Heisenberg Chain Research Articles

Ground State Entanglement in Spin Systems

We study the entanglement between arbitrary two spins in the XY and the antiferromagnetic Heisenberg spin chains in a uniform magnetic field. The entanglement of pairwise qubits in these models is obtained as a function of magnetic field by exact and numerical calculations. We find that the behavior of entanglement in the isotropic XY model is qualitatively the same as that in the Heisenberg model. Properties of entanglement length are also discussed.

Conductance of a quantum wire at low electron density

We study the transport of electrons through a long quantum wire connecting two bulk leads. As the electron density in the wire is lowered, the Coulomb interactions lead to short-range crystalline ordering of electrons. In this Wigner crystal state the spins of electrons form an antiferromagnetic Heisenberg spin chain with exponentially small exchange coupling $J$. Inhomogeneity of the electron density due to the coupling of the wire to the leads results in violation of spin-charge separation in the device. As a result the spins affect the conductance of the wire. At zero temperature the low-energy spin excitations propagate freely through the wire, and its conductance remains $2{e}^{2}∕h$. Since the energy of the elementary excitations in the spin chain (spinons) cannot exceed $\ensuremath{\pi}J∕2$, the conductance of the wire acquires an exponentially small negative correction $\ensuremath{\delta}\phantom{\rule{0.2em}{0ex}}G\ensuremath{\propto}\ensuremath{-}\mathrm{exp}(\ensuremath{-}\ensuremath{\pi}J∕2T)$ at low temperatures $T⪡J$. At higher temperatures, $T⪢J$, most of the spin excitations in the leads are reflected by the wire, and the conductance levels off at a new universal value ${e}^{2}∕h$.

Spinons in the strongly correlated copper oxide chains in SrCuO2.

We have investigated the spin dynamics in the strongly correlated chain copper oxide SrCuO2 for energies up to greater, similar 0.6 eV using inelastic neutron scattering. We observe a gapless continuum of magnetic excitations, which is well described by the "Müller ansatz" for the two-spinon continuum in the S=1/2 antiferromagnetic Heisenberg spin chain. The lower boundary of the continuum extends up to approximately 360 meV, which corresponds to an exchange constant J=226(12) meV.

Low-dimensional quantum spin systems in pulsed magnetic fields

Low-dimensional spin systems in high magnetic fields reveal new and unexpected physical phenomena. Typical examples are the distinct plateaus in the magnetization found in quasi-1d and 2d compounds. Even for the well known case of the quasi-1d homogeneous Heisenberg spin chain or its dimerized variant, unexpected elastic anomalies can be detected in high magnetic fields. Since the exchange constants of these low-dimensional spin systems are of the order of the dominant energy scale, pulse-field experiments are particularly well suited for investigations of the magnetic properties. In this contribution we present and discuss our results for selected low-dimensional compounds such as the homogeneous antiferromagnetic Heisenberg spin chain Cu(II)-bispyrazoldihydroxybenzene, which is a new quasi-1d Cu(II)-coordination polymer, the dimerized spin chain (VO) 2P 2O 7, and the plateau systems SrCu 2(BO 3) 2 and NH 4CuCl 3.

Luttinger liquid behavior in spin chains with a magnetic field

Antiferromagnetic Heisenberg spin chains in a sufficiently strong magnetic field are Luttinger liquids, whose parameters depend on the actual magnetization of the chain. Here we present precise numerical estimates of the Luttinger liquid dressed charge Z, which determines the critical exponents, by calculating the magnetization and quadrupole operator profiles for $S=1/2$ and $S=1$ chains using the density matrix renormalization group method. Critical amplitudes and the scattering length at the chain ends are also determined. Although both systems are Luttinger liquids the characteristic parameters differ considerably.

Impurity Spin Effect on the Spin-1 Antiferromagnetic Heisenberg Chain

Low-lying excited states of the spin-1 antiferromagnetic Heisenberg chain with an impurity bond are investigated in terms of domain-wall excitations by means of analytical methods as well as a method of numerical diagonalization. It is shown that 1) the impurity bond brings about a massive triplet mode in the Haldane gap, 2) the triplet state comprises three of the four ground states of an open chain, 3) the excited states with the domain wall trapped at the impurity bond, including the massive triplet mode, exhibit a Neel-type configuration of the magnetic moment around the impurity bond. On the basis of the present results, we propose a new energy versus magnetic-field diagram.

Dynamics of twists on antiferromagnetic spin chains: Theory

The equation of motion of twists on classical antiferromagnetic Heisenberg spin chains are derived. It is shown that twists interact via position- and velocity-dependent long-range two-body forces. A quiescent regime is identified wherein the system conserves momentum. With increasing kinetic energy the system exits this regime and momentum conservation is violated due to walls annihilation. A bitwist system is shown to be integrable and its exact solution is analysed. Many-twist systems are discussed and novel periodic twist lattice solutions are found on closed chains. The stability of these solutions is discussed.

HEISENBERG INTEGER SPIN CHAINS IN A UNIFORM MAGNETIC FIELD

We investigate both numerically and analytically the behavior of a spin-1 antiferromagnetic isotropic Heisenberg chain in an external uniform magnetic field. Extensive DMRG studies of chains up to N = 80 sites extend previous analyses and obtain the zero-temperature correlation functions. We argue that, despite the presence of a magnetic field, the model is still well described by an O(3) nonlinear σ-model. A saddle-point analysis, that also includes Gaussian fluctuations, is developed for the latter both at zero and finite temperatures. Its predictions are compared with those of the numerical analysis and with the existing experimental literature.

Redistribution of spectral weight in Haldane chains doped with spin-12moments

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.

Effects of the single-ion anisotropy and dimerization on 1D spin-1 antiferromagnetic Heisenberg chain

One-dimensional quantum spin-1 antiferromagnetic Heisenberg chain (AFHC) with exchange anisotropy J z , dimerization δ and single-ion anisotropy D∑ n ( S n z ) 2 was investigated on the basis of the continuum representation of the model Hamiltonian. Analytical results for the excitation spectrum, phase order and the phase fluctuation φ were derived in a self-consistent-harmonic-field approach. We studied the effects of the single-ion anisotropy and dimerization on two gaps by taking the different momentum cutoff α i in two scalar field spaces H i ( i=1,2). The occurrences of richer phase transitions were understood in the viewpoints of the phase fluctuation and the z polar spin fluctuation. And the Gaussian critical line was given as J z − D− πα 1 δ=0.

Spin-1 antiferromagnetic Heisenberg chains in an external staggered field

We present in this paper a nonlinear \ensuremath{\sigma}-model analysis of a spin-1 antiferromagnetic Heisenberg chain in an external commensurate staggered magnetic field. After rediscussing briefly and extending previous results for the staggered magnetization curve, the core of the paper is a calculation at the tree level, of the Green functions of the model. We obtain precise results for the elementary excitation spectrum and in particular for the spin gaps in the transverse and longitudinal channels. It is shown that, while the spectral weight in the transverse channel is exhausted by a single magnon pole, in the longitudinal one, besides a magnon pole a two-magnon continuum appears as well whose weight is a steadily increasing function of the applied field, while the weight of the magnon decreases correspondingly. The balance between the two is governed by a sum rule that is derived and discussed. A detailed comparison with the present experimental and numerical state of the art as well as with previous analytical approaches is also made.

Finite-size spectrum, magnon interactions, and magnetization ofS=1Heisenberg spin chains

We report our density matrix renormalization-group and analytical work on S=1 antiferromagnetic Heisenberg spin chains. We study the finite size behavior within the framework of the non-linear sigma model. We study the effect of magnon-magnon interactions on the finite size spectrum and on the magnetization curve close to the critical magnetic field, determine the magnon scattering length and compare it to the prediction from the non-linear $\sigma$ model.

Low-energy excitations of spin-Peierls chains with modified bond impurities

The introduction of modified bond-defects in spin-Peierls systems is investigated in a model of antiferromagnetic Heisenberg spin chains coupled to adiabatic phonons. Generically, new low-energy magnetic or non-magnetic excitations appear below the bulk spin gap energy. When two adjacent bonds are modified, these excitations can be interpreted in terms of boundstates of a soliton with the localized spin-1/2 located on the impurity site. It is shown that the confining potential occurs even in the case of {\it isolated} chains.

Magnetic properties of low-dimensional quantum spin systems made of stable organic biradicals PNNNO,F2PNNNO,and PIMNO

Stable organic biradical crystals PNNNO, ${\mathrm{F}}_{2}\mathrm{PNNNO},$ and PIMNO of the PNNNO family were synthesized. ${\mathrm{PNNNO}=2\ensuremath{-}[{4}^{\ensuremath{'}}\ensuremath{-}$ $(N\ensuremath{-}\mathit{tert}\ensuremath{-}\mathrm{butyl}\ensuremath{-}N\ensuremath{-}\mathrm{oxyamino})\mathrm{phenyl}]\ensuremath{-}4,4,5,5\ensuremath{-}\mathrm{tetramethyl}\ensuremath{-}4,5\ensuremath{-}\mathrm{dihydro}\ensuremath{-}1H\ensuremath{-}\mathrm{imidazol}\ensuremath{-}1\ensuremath{-}\mathrm{oxyl}$ $3\ensuremath{-}\mathrm{oxide},$ ${\mathrm{F}}_{2}\mathrm{PNNNO}=2\ensuremath{-}[{2}^{\ensuremath{'}}{,6}^{\ensuremath{'}},\ensuremath{-}\mathrm{difluoro}\ensuremath{-}{4}^{\ensuremath{'}}\ensuremath{-}(N\ensuremath{-}\mathit{tert}\ensuremath{-}\mathrm{butyl}\ensuremath{-}N\ensuremath{-}\mathrm{oxyamino})\mathrm{phenyl}]\ensuremath{-}\mathrm{}4,4,5,5\ensuremath{-}\mathrm{tetramethyl}\ensuremath{-}4,$ $5\ensuremath{-}\mathrm{dihydro}\ensuremath{-}1H\ensuremath{-}\mathrm{imidazol}\ensuremath{-}1\ensuremath{-}\mathrm{oxyl}$ $3\ensuremath{-}\mathrm{oxide},$ $\mathrm{PIMNO}=2\ensuremath{-}[{4}^{\ensuremath{'}}\ensuremath{-}(N\ensuremath{-}\mathit{tert}\ensuremath{-}\mathrm{butyl}\ensuremath{-}N\ensuremath{-}\mathrm{oxyamino})\ensuremath{-}\mathrm{phenyl}]\ensuremath{-}4,4,5,5\ensuremath{-}\mathrm{tetramethyl}\ensuremath{-}4,5\ensuremath{-}\mathrm{dihydro}\ensuremath{-}1H\ensuremath{-}\mathrm{imidazol}\ensuremath{-}1\ensuremath{-}\mathrm{oxyl}.}$ PNNNO and PIMNO crystallize to form quasi-one-dimensional lattices, but ${\mathrm{F}}_{2}\mathrm{PNNNO}$ to form a quasi-two-dimensional lattice. The temperature dependences of the susceptibility and the high-field magnetization process up to 34 T were measured down to 0.5 K. The results are analyzed by comparing with the theoretical calculations based on the crystal structures. PNNNO and PIMNO are considered to be antiferromagnetic Heisenberg spin chains consisting of $S=1/2$ spin pairs (dimers) in which the two spins are coupled ferromagnetically. At low temperatures, an antiferromagnetic ordering occurs in these crystals, which is confirmed by the thermodynamic discussion through specific heat measurements. On the other hand, ${\mathrm{F}}_{2}\mathrm{PNNNO}$ is thought to be a two-dimensional Heisenberg system, in which the spin pairs are connected by two types of antiferromagnetic interactions. The ground state is singlet. The high-field magnetization process shows a two-step saturation with a plateau of the half value of the saturation magnetization.

Phase Diagram of a Heisenberg Spin-Peierls Model with Quantum Phonons

Using a new version of the density-matrix renormalization group we determine the phase diagram of a model of an antiferromagnetic Heisenberg spin chain where the spins interact with quantum phonons. A quantum phase transition from a gapless spin-fluid state to a gapped dimerized phase occurs at a nonzero value of the spin-phonon coupling. The transition is in the same universality class as that of a frustrated spin chain, to which the model maps in the diabatic limit. We argue that realistic modeling of known spin-Peierls materials should include the effects of quantum phonons.

NonlinearσModel for Inhomogeneous Spin Chains

We derive a nonlinear $\ensuremath{\sigma}$ model (NLSM) that represents antiferromagnetic Heisenberg spin chains with inhomogeneous spin magnitudes and inhomogeneous nearest-neighbor exchange constants arrayed in finite periods. The only restriction is that the average spin magnitude on a sublattice is the same as that on another sublattice. The NLSM yields the gapless condition in terms of the spin magnitudes and exchange constants. We apply this condition to several cases, including systems with impurities. The result shows that the spin gap persists, despite impurities, in many cases.

Thermodynamics of quantum Heisenberg spin chains

Thermodynamic properties of the quantum Heisenberg spin chains with $S=1/2,$ 1, and $3/2$ are investigated using the transfer-matrix renormalization-group method. The temperature dependence of the magnetization, susceptibility, specific heat, spin-spin correlation length, and several other physical quantities in a zero or finite applied field are calculated and compared. Our data agree well with the Bethe ansatz, exact diagonalization, and quantum Monte Carlo results and provide further insight into the quantum effects in the antiferromagnetic Heisenberg spin chains.

Chiral universality class in a frustrated three-leg spin ladder

We study a model of three $S=1/2$ antiferromagnetic Heisenberg spin chains weakly coupled by on-rung and plaquette-diagonal interchain interactions. It is shown that the model exhibits a critical phase with central charge $C=2$ and belongs to the class of ``chirally stabilized'' liquids recently introduced by Andrei, Douglas, and Jerez. By allowing anisotropic interactions in spin space, we find an exact solution at a Toulouse point which captures all universal properties of the model, including the SU(2) symmetric case. At this critical point the massless degrees of freedom are described in terms of an effective $S=1/2$ Heisenberg spin chain and two critical Ising models. We discuss the spectral properties of the model, compute spin-spin correlation functions, and estimate the NMR relaxation rate.

Instability of a one-dimensional quantum antiferromagnet under magnetic anisotropy

It is shown by using the exact quantum-mechanical solution that a one-dimensional antiferromagnetic Heisenberg spin chain is unstable to the emergence of an easy-plane magnetic anisotropy in a real three-dimensional crystal. It is shown that the magnetic anisotropy is due to a Jahn–Teller type effect, i.e., a strong spin–lattice coupling. A change in the equilibrium position of ligands induces magnetic anisotropy in the spin chain.

Monte-Carlo study of correlations in quantum spin chains at non-zero temperature

Antiferromagnetic Heisenberg spin chains with various spin values ($S=1/2,1,3/2,2,5/2$) are studied numerically with the quantum Monte Carlo method. Effective spin $S$ chains are realized by ferromagnetically coupling $n=2S$ antiferromagnetic spin chains with $S=1/2$. The temperature dependence of the uniform susceptibility, the staggered susceptibility, and the static structure factor peak intensity are computed down to very low temperatures, $T/J \approx 0.01$. The correlation length at each temperature is deduced from numerical measurements of the instantaneous spin-spin correlation function. At high temperatures, very good agreement with exact results for the classical spin chain is obtained independent of the value of $S$. For $S$=2 chains which have a gap $\Delta$, the correlation length and the uniform susceptibility in the temperature range $\Delta < T < J$ are well predicted by a semi-classical theory due to Damle and Sachdev.