Spin Chain Model Research Articles

Magnetization and specific heat of a ferromagnetic zigzag spin chain compound LaCrOS 2

The magnetization and the specific heat of an oxysulfide LaCrOS 2, in which Cr ions form zigzag spin chains, have been measured. The temperature dependence of the magnetic susceptibility deviates from the Curie–Weiss behavior with the Weiss temperature Θ p =66 K, below 200 K. A peak appears in the low field susceptibility vs. temperature curve at 32 K, which is regarded to signal the ferromagnetic transition. The temperature dependence of the magnetic specific heat shows a broad maximum, which is characteristic of a low dimensional magnetic system. In addition, a small sharp peak is observed at 32 K which is attributed to the three-dimensional ferromagnetic transition. These behaviors are well explained by an effective Ising spin chain model for S=3/2 with a weak interchain interaction.

Basis optimization renormalization group for the quantum hamiltonian

We find an algorithm of numerical renormalization group for spin chain models. The essence of this algorithm is orthogonal transformation of basis states, which is useful for reducing the number of relevant basis states to create effective Hamiltonian. We define two types of rotations and combine them to create appropriate orthogonal transformation.

Chirality tunneling in a ferromagnetic spin chain

The quantum-mechanical oscillations between two domain walls of opposite chirality in a ferromagnetic spin chain with easy and hard axis anisotropies are studied. The equations of motion of the instantons that connect the degenerate ground states in imaginary time are obtained and it is shown that there are two equivalent instantons that contribute to the expression of the splitting of the degenerate energy level. The instanton solutions and the energy splittings are obtained numerically for different values of the anisotropy parameters. It is found that the hard axis anisotropy inhibits chirality tunneling, in contrast to what happens in the single spin problem where the hard axis anisotropy favors tunneling. This behavior is explained as a crossover, driven by the increase of the hard axis anisotropy, from the ferromagnetic spin chain model to the sine-Gordon model.

Exact solution of anisotropic antiferromagnetic alternating Heisenberg–Ising spin chain

We extend the spin (= 1 2 ) chain model with alternating Heisenberg and Ising couplings to the case of anisotropic Heisenberg exchange. The model can be mapped to a bilinear fermion model, which is exactly solved via Jordan–Wigner and Bogoliubov transformations. We find low-energy excitations with a gap when the Ising coupling strength is not equal to 2. And this conclusion will not be changed for any kind of anisotropic Heisenberg exchange.

Quantum control without access to the controlling interaction

In our model a fixed Hamiltonian acts on the joint Hilbert space of a quantum system and its controller. We show conditions under which measurements, state preparations, and unitary implementations on the system can be performed by quantum operations on the controller only. It turns out that a measurement of the observable $A$ and an implementation of the one-parameter group $\mathrm{exp}(\mathrm{iAr})$ can be performed by almost the same sequence of control operations. Furthermore, measurement procedures for $A+B,$ for $(AB+BA),$ and for $i\ensuremath{\lfloor}A,B\ensuremath{\rfloor}$ can be constructed from measurements of $A$ and $B.$ This shows that the algebraic structure of the set of observables can be explained by the Lie group structure of the unitary evolutions on the joint Hilbert space of the measuring device and the measured system. A spin chain model with nearest-neighborhood coupling shows that the border line between controller and system can be shifted consistently.

Observation of the bulk spin-flop in an Fe/Cr superlattice

The layer magnetisation reorientation transition (spin-flop, SF) was studied in an artificial layer antiferromagnet (AF), namely in MgO(0 0 1)/[ 57Fe(2.6 nm)/Cr(1.3 nm)] 20 epitaxial superlattice (SL) by synchrotron Mössbauer reflectometry and Kerr effect (SMOKE). The SF occurs simultaneously in the entire SL stack (bulk SF) in an increasing field of H SF=13 mT along the easy direction parallel to the layer magnetisations. It is recognised by the kink in the SMOKE loop and by the sharp up-rise of the AF Bragg peak in the delayed Mössbauer reflectivity. The moderate value of observed H SF is compared with estimations from a spin-chain model and interpreted as due to intraplane domain-wall motion during SF.

Phase diagram of an asymmetric spin ladder.

We investigate an asymmetric zigzag spin ladder with different exchange integrals on both legs using bosonization and renormalization group approaches. When the leg exchange integrals and frustration both are sufficiently small, renormalization group analysis shows that the Heisenberg critical point flows to an intermediate-coupling fixed point with gapless excitations and a vanishing spin velocity. When they are large, a spin gap opens and a dimer liquid is realized. Here, we find a continuous manifold of Hamiltonians with dimer product ground states, interpolating between the Majumdar-Ghosh and sawtooth spin-chain model.

On Asymptotic Properties of a Number Theoretic Function Arising out of a Spin Chain Model¶in Statistical Mechanics

Let $$$$ Let N be a positive integer and define Φ(N) as the number of matrices, C, which are products of A and B, where both A and B must occur, such that the trace, Tr(C)=N. It has been conjectured that $$$$ see [10]. In this note we consider the summatory function $$$$ and show that $$$$

Strongly reduced gap in the zigzag spin chain with a ferromagnetic interchain coupling

We study a spin 1/2 Heisenberg zigzag spin chain model near decoupled two chains. Taking into account a symmetry breaking perturbation, we discuss the existence of an energy gap in the ferromagnetic interchain coupling as well as the antiferromagnetic one. In the ferromagnetic model, a marginally relevant fixed line reduces the gap strongly, so that the correlation length becomes an astronomical length scale even in order 1 coupling. This result agrees with density matrix renormalization group results.

A novel coproduct of suq(2) and its relation to XXZ spin chain model

While it is normal to restrict the deformation parameter q in the coproduct of the quantum group su q (2) to the positive reals, the naive replacement of q by − q results in a coproduct that does not respect algebra homomorphism. However, it is possible to define a twisted coproduct in this case that respects the algebra homomorphism. Application to XXZ spin chain model is discussed.

Superexchange in the quarter-filled two-leg ladder systemNaV2O5

A theory of superexchange in the mixed valent layer compound NaV2O5 is presented which provides a consistent description of exchange both in the disordered and charge ordered state. Starting from results of band structure calculations for NaV2O5 first an underlying electronic model for a ladder unit in the Trellis lattice is formulated. By using the molecular orbital representation for intra-rung electronic states a second-order perturbation procedure is developed and an effective spin-chain model for a ladder is derived. Variation of the resulting superexchange integral J is examined numerically as the ladder system evolves from a charge disordered to the extreme ('zig-zag') charge ordered state. It is found that the effective intra- ladder superexchange is always antiferromagnetic.

Spin Chain Models with Spectral Curves from M Theory

We construct the integrable model corresponding to the ?= 2 supersymmetric SU(N) gauge theory with matter in the antisymmetric representation, using the spectral curve found by Landsteiner and Lopez through M Theory. The model turns out to be the Hamiltonian reduction of a N+2 periodic spin chain model, which is Hamiltonian with respect to the universal symplectic form we had constructed earlier for general soliton equations in the Lax or Zakharov–Shabat representation.

HIDDEN NONLINEAR SUPERSYMMETRIES IN PURE PARABOSONIC SYSTEMS

The existence of intimate relations between generalized statistics and supersymmetry is established by the observation of hidden supersymmetric structure in pure parabosonic systems. This structure is characterized generally by a nonlinear superalgebra. The nonlinear supersymmetry of parabosonic systems may be realized, in turn, by modifying appropriately the usual supersymmetric quantum mechanics. The relation of nonlinear parabosonic supersymmetry to the Calogero-like models with exchange interaction and to the spin chain models with inverse-square interaction is pointed out.

Magnetic impurities in a one-dimensional spin-orbital model

Using one-dimensional spin-orbital model as a typical example of quantum spin systems with richer symmetries, we study the effect of an isolated impurity on its low energy dynamics in the gapless phase through bosonization and renormalization group methods. In the case of internal impurities, depending on the symmetry, the boundary fixed points can be either an open chain with a residual spin or (and) orbital triplet left behind, or a periodic chain. However, these two fixed points are indistinguishable in the sense that in both cases, the lead-correction-to-scaling boundary operators (LCBO) only show Fermi-liquid like corrections to thermodynamical quantities. (Except the possible Curie-like contributions from the residual moments in the latter cases.) In the case of external (Kondo) impurities, the boundary fixed points, depending on the sign of orbital couplings, can be either an open chain with an isolated orbital doublet due to Kondo screening or it will flow to an intermediate fixed point with the same LCBO as that of the two-channel Kondo problem. Comparison with the Kondo effect in one-dimensional (1D) Heisenberg spin chain and multi-band Hubbard models is also made.

Spin chirality induced by the Dzyaloshinskii-Moriya interaction and polarized neutron scattering

We discuss the influence of the Dzyaloshinskii-Moriya (DM) interaction in the Heizenberg spin chain model for the observables in the polarized neutron scattering experiments. We show that different choices of the parameters of DM interaction may leave the spectrum of the problem unchanged, while the observable spin-spin correlation functions may differ qualitatively. Particularly, for the uniform DM interaction one has the incommensurate fluctuations and polarization-dependent neutron scattering in the paramagnetic phase. We sketch the possible generalization of our treatment to higher dimensions.

Exact dynamics in the Haldane–Shastry spin chain model in magnetic field

Dynamical spin correlation function S zz(Q, ω) with Q smaller than π m ̄ ( m̄ being magnetization) is derived exactly for the spin chain with the 1/ r 2 interaction in magnetic field. It is found that only two spinons and one antispinon contribute to S zz(Q, ω) in the thermodynamic limit. In deriving the result we use the solution of the Sutherland model with internal symmetry in the strong coupling limit. Our theory keeps the full symmetry of the model in contrast to the previous one which is based on mapping onto the single-component Sutherland 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.

Interaction-round-a-face density-matrix renormalization-group method applied to rotational-invariant quantum spin chains

An interaction-round-a-face density-matrix renormalization-group (IRF-DMRG) method is developed for higher integer spin chain models which are rotational invariant. The expressions of the IRF weights associated with the nearest-neighbor spin-$S$ interaction ${\mathbf{S}}_{i}\ensuremath{\cdot}{\mathbf{S}}_{i+1}$ are explicitly derived. Using the IRF-DMRG with these IRF weights, the Haldane gaps $\ensuremath{\Delta}$ and the ground state energy densities ${e}_{0}$ for both $S=1$ and $S=2$ isotropic antiferromagnetic Heisenberg quantum spin chains are calculated by keeping up to only $m=90$ states.

Evolution equations for quark–gluon distributions in multi-color QCD and open spin chains

We study the scale dependence of the twist-3 quark–gluon parton distributions using the observation that in the multi-color limit the corresponding QCD evolution equations possess an additional integral of motion and turn out to be effectively equivalent to the Schrödinger equation for integrable open Heisenberg spin chain model. We identify the integral of motion of the spin chain as a new quantum number that separates different components of the twist-3 parton distributions. Each component evolves independently and its scale dependence is governed by anomalous dimension given by the energy of the spin magnet. To find the spectrum of the QCD induced open Heisenberg spin magnet we develop the Bethe ansatz technique based on the Baxter equation. The solutions to the Baxter equation are constructed using different asymptotic methods and their properties are studied in detail. We demonstrate that the obtained solutions provide a good qualitative description of the spectrum of the anomalous dimensions and reveal a number of interesting properties. We show that the few lowest anomalous dimensions are separated from the rest of the spectrum by a finite mass gap and estimate its value.

A REVIEW OF SYMMETRY ALGEBRAS OF QUANTUM MATRIX MODELS IN THE LARGE N LIMIT

This is a review article in which we will introduce, in a unifying fashion and with more intermediate steps in some difficult calculations, two infinite-dimensional Lie algebras of quantum matrix models, one for the open string sector and the other for the closed string sector. Physical observables of quantum matrix models in the large N limit can be expressed as elements of these Lie algebras. We will see that both algebras arise as quotient algebras of a larger Lie algebra. We will also discuss some properties of these Lie algebras not published elsewhere yet, and briefly review their relationship with well-known algebras like the Cuntz algebra, the Witt algebra and the Virasoro algebra. We will also review how the Yang–Mills theory, various low energy effective models of string theory, quantum gravity, string-bit models, and the quantum spin chain models can be formulated as quantum matrix models. Studying these algebras thus help us understand the common symmetry of these physical systems.