Quantum Heisenberg Model Research Articles

Topological excitations in a two-dimensional spin system with high spin s ≥1

We construct a class of topological excitations of a mean field in a two-dimensional spin system represented by a quantum Heisenberg model with high powers of exchange interaction. The quantum model is associated with a classical one (the continuous classical analogue) that is based on a Landau-Lifshitz like equation, and describes large-scale fluctuations of the mean field. On the other hand, the classical model is a Hamiltonian system on a coadjoint orbit of the unitary group SU($2s {+} 1$) in the case of spin $s$. We have found a class of mean field configurations that can be interpreted as topological excitations, because they have fixed topological charges. Such excitations change their shapes and grow preserving an energy.

The constraint effective potential of the staggered magnetization in an antiferromagnet

We employ an improved estimator to calculate the constraint effective potential of thestaggered magnetization in the spin quantum Heisenberg model using a loop-cluster algorithm. The first and second momentof the probability distribution of the staggered magnetization are in excellent agreementwith the predictions from the systematic low-energy magnon effective field theory. We alsocompare the Monte Carlo data with the universal shape of the constraint effective potentialof the staggered magnetization and study its approach to the convex effective potentialin the infinite volume limit. In this way the higher-order low-energy parameterk0 is determined from a fit to the numerical data.

Quantum field theory solution for a short-range interacting [formula omitted] quantum spin-glass

We study the quenched disordered magnetic system, which is obtained from the 2D SO(3) quantum Heisenberg model, on a square lattice, with nearest neighbors interaction, by taking a Gaussian random distribution of couplings centered in an antiferromagnetic coupling, J ¯ > 0 and with a width Δ J. Using coherent spin states we can integrate over the random variables and map the system onto a field theory, which is a generalization of the SO(3) nonlinear sigma model with different flavors corresponding to the replicas, coupling parameter proportional to J ¯ and having a quartic spin interaction proportional to the disorder (Δ J). After deriving the CP 1 version of the system, we perform a calculation of the free energy density in the limit of zero replicas, which fully includes the quantum fluctuations of the CP 1 fields z i . We, thereby obtain the phase diagram of the system in terms of ( T , J ¯ , Δ J ). This presents an ordered antiferromagnetic (AF) phase, a paramagnetic (PM) phase and a spin-glass (SG) phase. A critical curve separating the PM and SG phases ends at a quantum critical point located between the AF and SG phases, at T = 0 . The Edwards–Anderson order parameter, as well as the magnetic susceptibilities are explicitly obtained in each of the three phases as a function of the three control parameters. The magnetic susceptibilities show a Curie-type behavior at high temperatures and exhibit a clear cusp, characteristic of the SG transition, at the transition line. The thermodynamic stability of the phases is investigated by a careful analysis of the Hessian matrix of the free energy. We show that all principal minors of the Hessian are positive in the limit of zero replicas, implying in particular that the SG phase is stable.

Dimers on the triangular kagome lattice

We derive exact results for close-packed dimers on the triangular kagome lattice (TKL), formed by inserting triangles into the triangles of the kagome lattice. Because the TKL is a nonbipartite lattice, dimer-dimer correlations are short ranged so that the ground state at the Rokhsar-Kivelson (RK) point of the corresponding quantum dimer model on the same lattice is a short-ranged spin liquid. Using the Pfaffian method, we derive an exact form for the free energy, and we find that the entropy is $\frac{1}{3}\text{ln}\text{ }2$ per site, regardless of the weights of the bonds. The occupation probability of every bond is $\frac{1}{4}$ in the case of equal weights on every bond. Similar to the case of lattices formed by corner-sharing triangles (such as the kagome and squagome lattices), we find that the dimer-dimer correlation function is identically zero beyond a certain (short) distance. We find in addition that monomers are deconfined on the TKL, indicating that there is a short-ranged spin liquid phase at the RK point. We also find exact results for the ground-state energy of the classical Heisenberg model. The ground state can be ferromagnetic, ferrimagnetic, locally coplanar, or locally canted, depending on the couplings. From the dimer model and the classical spin model, we derive upper bounds on the ground-state energy of the quantum Heisenberg model on the TKL.

Evidence for an Unconventional Universality Class from a Two-Dimensional Dimerized Quantum Heisenberg Model

The two-dimensional J-J' dimerized quantum Heisenberg model is studied on the square lattice by means of (stochastic series expansion) quantum Monte Carlo simulations as a function of the coupling ratio alpha=J'/J. The critical point of the order-disorder quantum phase transition in the J-J' model is determined as alpha_c=2.5196(2) by finite-size scaling for up to approximately 10 000 quantum spins. By comparing six dimerized models we show, contrary to the current belief, that the critical exponents of the J-J' model are not in agreement with the three-dimensional classical Heisenberg universality class. This lends support to the notion of nontrivial critical excitations at the quantum critical point.

Renormalized theory of the two-dimensional [formula omitted] dilute spin-wave systems at low temperatures

Due to strong fluctuations, conventional approaches to handling repulsive spin-1/2 spin-waves in three dimensions do not work in low dimensions at temperature T≠0. We have constructed a renormalized theory for the two-dimensional spin-1/2 anisotropic quantum Heisenberg model by means of exact mappings between spin-1/2 systems and their corresponding hard-core Bose–Hubbard systems. With the t-matrix method, hard-core Bose–Hubbard systems can be effectively described by the corresponding soft-core Bose–Hubbard Hamiltonians at low energy. The method of running coupling constant in field theory is used to fix the infrared divergence due to long wavelength fluctuations in low dimensions at T≠0. Our results agree well with previous analytical and numerical works. The method dealing with infinities used by others in 3D is a special case of our renormalization scheme. Our approach works in both two and three dimensions at T=0 and T>0. We think that our renormalization scheme is a more general and systematic approach in condensed matter physics.

Free energy of bcc iron: Integratedab initioderivation of vibrational, electronic, and magnetic contributions

We present ab initio derived thermodynamic properties of ferromagnetic bcc iron up to the bcc-fcc phase-transition temperature (1200 K), including vibrational, electronic, and magnetic contributions. The quasiharmonic approximation and finite-temperature density-functional theory are employed to account for vibrational and electronic excitations. The magnetic contribution is derived from the solution of the quantum Heisenberg model within many-body theory using the mean-field and random-phase approximation. The calculated thermodynamic properties show an excellent agreement with available experimental data and reveal the necessity to consider all three types of excitations.

Theory of electron nematic order in LaFeAsO

We study a spin S quantum Heisenberg model on the Fe lattice of the rare-earth oxypnictide superconductors. Using both large S and large N methods, we show that this model exhibits a sequence of two phase transitions: from a high-temperature symmetric pha

Theory of Néel and Valence-Bond Solid Phases on the Kagome Lattice of Zn Paratacamite

Recently, neutron scattering data on powder samples of Zn paratacamite, ZnxCu4-x(OH)6Cl2, with small Zn concentration has been interpreted as evidence for valence-bond solid and Néel ordering [S.-H. Lee, Nat. Mater. 6, 853 (2007)10.1038/nmat1986]. We study the classical and quantum Heisenberg models on the distorted kagome lattice appropriate for Zn paratacamite at low Zn doping. Our theory naturally leads to the emergence of the valence-bond solid and collinear magnetic order at zero temperature. Implications of our results to the existing experiments are discussed. We also suggest future inelastic neutron and x-ray scattering experiments that can test our predictions.

Anisotropic Heisenberg model on hierarchical lattices with aperiodic interactions: A renormalization-group approach

Using a real-space renormalization-group approximation, we study the anisotropic quantum Heisenberg model on hierarchical lattices, with interactions following aperiodic sequences. Three different sequences are considered, with relevant and irrelevant fluctuations, according to the Luck-Harris criterion. The phase diagram is discussed as a function of the anisotropy parameter Delta (such that Delta=0 and 1 correspond to the isotropic Heisenberg and Ising models, respectively). We find three different types of phase diagrams, with general characteristics: the isotropic Heisenberg plane is always an invariant one (as expected by symmetry arguments) and the critical behavior of the anisotropic Heisenberg model is governed by fixed points on the Ising-model plane. Our results for the isotropic Heisenberg model show that the relevance or irrelevance of aperiodic models, when compared to their uniform counterpart, is as predicted by the Harris-Luck criterion. A low-temperature renormalization-group procedure was applied to the classical isotropic Heisenberg model in two-dimensional hierarchical lattices: the relevance criterion is obtained, again in accordance with the Harris-Luck criterion.

A Short Introduction to Fibonacci Anyon Models

We discuss how to construct models of interacting anyons by generalizing quantum spin Hamiltonians to anyonic degrees of freedom. The simplest interactions energetically favor pairs of anyons to fuse into the trivial (identity) channel, similar to the quantum Heisenberg model favoring pairs of spins to form spin singlets. We present an introduction to the theory of anyons and discuss in detail how basis sets and matrix representations of the interaction terms can be obtained, using non-Abelian Fibonacci anyons as example. Besides discussing the golden a one-dimensional system of anyons with nearest neighbor interactions, we also present the derivation of more complicated interaction terms, such as three-anyon interactions in the spirit of the Majumdar-Ghosh spin chain, longer range interactions and two-leg ladders. We also discuss generalizations to anyons with general non-Abelian su(2)_k statistics. The k to infinity limit of the latter yields ordinary SU(2) spin chains.

Valence Bond Solid Phases in a Cubic Antiferromagnet

We report on a valence bond projector Monte Carlo simulation of the cubic lattice quantum Heisenberg model with additional higher-order exchange interactions in each unit cell. The model supports two different valence bond solid (VBS) ground states. In one of these states, the dimer pattern is a three-dimensional analogue of the columnar pattern familiar from two dimensions. In the other, the dimers are regularly arranged along the four main diagonals in 1/8 of the unit cells. The phases are separated from one another and from a Néel phase by strongly first-order boundaries. Our results strengthen the case for exotic transitions in two dimensions, where no discontinuities have been detected at the Heisenberg Néel-VBS transition driven by four-spin plaquette interactions.

Disorder effects in the quantum Heisenberg model: Extended dynamical mean-field theory analysis

We investigate a quantum Heisenberg model with both antiferromagnetic and disordered nearest-neighbor couplings. We use an extended dynamical mean-field approach, which reduces the lattice problem to a self-consistent local impurity problem that we solve by using a quantum Monte Carlo algorithm. We consider both two- and three-dimensional antiferromagnetic spin fluctuations and systematically analyze the effect of disorder. We find that in three dimensions for any small amount of disorder a spin-glass phase is realized. In two dimensions, while clean systems display the properties of a highly correlated spin liquid (where the local spin susceptibility has a noninteger power-law frequency and temperature dependence), in the present case this behavior is more elusive unless disorder is very small. In fact the spin-glass transition temperature leaves only a limited intermediate temperature regime, where the system displays the spin-liquid behavior.

Interacting Anyons in Topological Quantum Liquids: The Golden Chain

We discuss generalizations of quantum spin Hamiltonians using anyonic degrees of freedom. The simplest model for interacting anyons energetically favors neighboring anyons to fuse into the trivial ("identity") channel, similar to the quantum Heisenberg model favoring neighboring spins to form spin singlets. Numerical simulations of a chain of Fibonacci anyons show that the model is critical with a dynamical critical exponent z=1, and described by a two-dimensional (2D) conformal field theory with central charge c=7/10. An exact mapping of the anyonic chain onto the 2D tricritical Ising model is given using the restricted-solid-on-solid representation of the Temperley-Lieb algebra. The gaplessness of the chain is shown to have topological origin.

Magnetic properties of the geometrically frustrated spin- [formula omitted] Heisenberg model on the triangulated Kagomé lattice

Geometrically frustrated spin- 1 2 quantum Heisenberg model on the triangulated (triangles-in-triangles) Kagomé lattice is examined by the use of variational procedure based on the Bogoliubov inequality. The investigated model system has an obvious relevance in elucidating magnetic properties of a series of polymeric coordination compounds Cu 9 X 2 ( cpa ) 6 ( X = F , Cl, Br and cpa=carboxypentonic acid). A striking magnetization curve with the 1 3 -plateau implies an appearance of compromised non-collinear spin arrangement within the plateau state, whereas a presence of the 5 9 -plateau with a collinear uud spin alignment cannot be definitely ruled out at higher fields. The thermal variation of the susceptibility times temperature data exhibits typical features of the quantum ferrimagnet.

Symmetry adapted finite-cluster solver for quantum Heisenberg model in two dimensions: a real-space renormalization approach

We present a quantum cluster solver for the spin-S Heisenberg model on a two-dimensional lattice. The formalism is based on the real-space renormalization procedure and uses the lattice point group-theoretical analysis and non-Abelian SU(2) spin symmetry technique. The exact diagonalization procedure is used twice at each renormalization group step. The method is applied to the spin-half antiferromagnet on a square lattice, and a calculation of local observables is demonstrated. A symmetry-based truncation procedure is suggested and verified numerically.

Ground state properties of the axially frustrated quantum Heisenberg model

We apply the method of infrared bounds to the axial next-nearest-neighbor Heisenberg model on the d-dimensional hypercubic lattice to examine the existence of d - 1 -dimensional antiferromagnetic long-range order (AFLRO) in the ground state of this model. We construct an upper bound on the Fourier transformed two point correlation function at whole momentum space (infrared bounds), and prove the existence of AFLRO under certain conditions.

Finite quantum Heisenberg spin models and their approach to the classical limit

We determine the temperature range over which classical Heisenberg spin models closely reproduce the zero-field susceptibility of the corresponding quantum Heisenberg models for a finite number $N$ of interacting quantum spins $s$. Using mostly quantum and classical Monte Carlo methods, as well as analytical methods where applicable, we have explored a variety of geometries, including polygons, open chains, and all Platonic and several Archimedean polytopes. These systems range in size from $N=2$ to 120, and we have considered values of $s$ from $1∕2$ to 50 for both antiferromagnetic and ferromagnetic exchange. Particular attention is devoted to quantifying the slow convergence of the large $s$ quantum data to the limiting classical data. This is motivated by the desire to define conditions where classical Monte Carlo methods can provide useful predictions for finite quantum Heisenberg spin systems.

Quantum signatures of the classical topological nonconnectivity threshold

A quantum Heisenberg model with anisotropic coupling and all-to-all interaction has been analyzed using the Bose-Einstein statistics. In Ref.\cite{jsp} the existence of a classical energy disconnection border (EDB) in the same kind of models has been demonstrated. We address here the problem to find quantum signatures of the EDB. An independent definition of a quantum disconnection border, motivated by considerations strictly valid in the quantum regime is given. We also discuss the dynamical relevance of the quantum border with respect to quantum magnetic reversal. Contrary to the classical case the magnetization can flip even below the EDB through Macroscopic Quantum Tunneling. We evaluate the time scale for magnetic reversal from statistical and spectral properties, for a small number of particles and in the semiclassical limit.

Electronic and spin structures of manganese clusters in the photosynthesis II system

Electronic and spin structures of manganese clusters, Mn 4O 4 ( 1), CaMn 3O 4 ( 2), Mn 3O 4 ( 3), MnX ( 4), and CaMn 4O 4 ( 5), in the photosynthesis II system are investigated using the classical and quantum Heisenberg models. The molecular orbital calculations by the use of general spin orbitals (GSO) are performed for cubane-type calcium manganese cluster 2 with noncollinear spin alignment, which has also been concluded in our previous studies of 1 and 3. The calculated results, together with available experiments, enable us to propose possible electronic states (from S 0 to S 4) of tetranuclear manganese cluster 5, which is the active site of oxygen evolution center (OEC). The low-spin (LS) ground states of 2– 5 are consistent with the ESR and other magnetic observations. A new reaction scheme for oxygen evolution from water is resulted from both theoretical and experimental results for manganese clusters 1– 5 in OEC on the basis of the newly determined X-ray structure by Ferreira et al. [Science 303 (2004) 1831]. In this mechanism, both calcium and manganese ions play important roles for formation of peroxide anion bridge, which is the precursor of molecular oxygen. Implications of computational results are discussed in relation to a key role of the high-valent manganese oxo (Mn(V) O) species in OEC for oxygen evolution from water. Our previous and present computations conclude that Mn(V) O plays a crucial role in both native and artificial OEC systems.