Ferromagnetic Lieb-Mattis theorem

We prove ferromagnetic ordering of energy levels for XXX Heisenberg chains with spins of arbitrary magnitude, thus extending our previous result for the spin-1/2 chain. Ferromagnetic ordering means that the minimum energies in the invariant subspaces of fixed total spin are monotone decreasing as a function of the total spin. This result provides a ferromagnetic analogue of the well-known theorem by Lieb and Mattis about ordering of energy levels in antiferromagnetic and ferrimagnetic systems on bipartite graphs.     

Translational Symmetry Breaking and Soliton Sectors for Massive Quantum Spin Models in 1 + 1 Dimensions

We consider the classification of pure infinite volume ground states and that of soliton sectors for 1+1 dimensional massive quantum spin models. We obtain a proof that non-translationally invariant ground state cannot exist for a class of translationally invariant Hamiltonians including the spin 1 AKLT (Affleck Kennedy Lieb Tasaki) antiferromagnetic spin model. We also obtain a complete classification of soliton sectors (up to unitary equivalence) for certain massive models (e.g. ferromagnetic XXZ models). Received: 13 January 1997 / Accepted: 11 March 1997     

A wavelet basis within Bethe ansatz

We describe here an example of a dynamical system which preserves the distance between constituent particles. Namely, we consider the one-dimensional finite magnetic Heisenberg ring of an even numberN of nodes with the spin 1/2, solved exactly by the well-known Bethe ansatz (XXX model). It is described in terms of a number of spin deviations from the ferromagnetic saturation state (a system of Bethe pseudoparticles) which undergo processes of mutual solitonic scattering when moving on the ring. We point out that, when restricting to (i) the subspace of quantum states with two spin deviations and (ii) to the boundary of the Brillouin zone, Bethe pseudoparticles perfectly avoid any mutual scattering. Therefore, each state with a fixed distance between pseudoparticles (the so called basis of wavelets) is already an eigenstate of the initial Heisenberg Hamiltonian. Presented by T. Lulek at the DI-CRM Workshop held in Prague, 18–21 June 2000. The authors are very much indebted to Professors J. Patera and J. Tolar for their invitation to DI-CRM Workshop on Mathematical Physics, and for their kind hospitality during the Workshop.     

Artificial Haldane gap material on a semiconductor chip

We show how nanostructuring of a metallic gate of a field-effect transistor (FET) converts the electron channel of an FET to an artificial Haldane chain with a gap in the energy spectrum. A specially designed gate structure creates a chain of triple quantum dot molecules. The electrons localized in the molecules realize a spin-half Heisenberg chain with spin–spin interactions alternating between ferromagnetic and antiferromagnetic. The quantum state of an FET is a semiconductor implementation of an integer spin-one antiferromagnetic Heisenberg chain with a unique correlated ground state and a finite energy gap, originally conjectured by Haldane.     

The AKLT Model on a Hexagonal Chain is Gapped

Journal of Statistical Physics - In 1987, Affleck, Kennedy, Lieb, and Tasaki introduced the AKLT spin chain and proved that it has a spectral gap above the ground state. Their concurrent conjecture...     

Effect of Dzyaloshinskii−Moriya interactions on Kagome anti-ferromagnetic clusters

The low energy and low temperature behavior of a few finite size Kagome clusters, including mixed spin systems of S=1/2 and S=1, with the nearest neighbor Heisenberg antiferromagnetic model is studied under the influence of out-of-plane Dzyaloshinskii?Moriya interactions (DMI) within the exact diagonalization formalism. The ground state of all the finite size systems is found to be present in the lowest spin sector with a finite gap to the lowest magnetic excitation irrespective of the strength of out-of-plane DMI. The energy level structures within the non-magnetic ground state and the lowest magnetic state have been studied for all the systems as a function of DMI. The characteristic signature of such low-lying non-magnetic excitations is reflected in the low temperature behavior of the specific heat. It is also found that the ground state chiral structure (characterized by the vector chiral order of the system) in the xy-plane shows sharp changes as a function of out-of-plane DMI at level crossing or avoided crossing regions. The in-plane spin ordering for each system is also studied with the estimation of static structure factor as a response to the varying strength of DMI.     

The spin-1/2 Heisenberg Chains in Constant Magnetic Field and Coherent states1

In the ferromagnetic Heisenberg chains of XXX and XXZ types with the hidden symmetries of Lie bi-algebra su(2) and quantum bi-algebra su_q(2), we show that at thermodynamic limit the algebra contractions give the boson algebra h(4) and the q-deformed boion algebra h_q(2) as the hidden symmetries respectively. The chains in constant magnetic field are studied and the ground states and lowest excited states are given explicitly with energy spectra. The phonon (or angular momentum) excitations are shown to be bosonic for the isotropic case and q-bosonic for the anisotropic case, and the ground states and lowest excited states of the systems of the chains in field are given explicitly. We give the phonon coherent states in the isotropic Heisenberg chain and the q-coherent states of the anisotropic chain at the thermodynamic limit. The q-coherent states are shown to be a squeezed states of phonon excitations.     

Gapless Excitation above a Domain Wall Ground State in a Flat-Band Hubbard Model

We construct a set of exact ground states with a localized ferromagnetic domain wall and with an extended spiral structure in a deformed flat-band Hubbard model in arbitrary dimensions. We show the uniqueness of the ground state for the half-filled lowest band in a fixed magnetization subspace. The ground states with these structures are degenerate with all-spin-up or all-spin-down states under the open boundary condition. We represent a spin one-point function in terms of local electron number density, and find the domain wall structure in our model. We show the existence of gapless excitations above a domain wall ground state in dimensions higher than one. On the other hand, under the periodic boundary condition, the ground state is the all-spin-up or all-spin-down state. We show that the spin-wave excitation above the all-spin-up or -down state has an energy gap because of the anisotropy     

Ground and excited states of spinor fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model

The ground and excited states of a one-dimensional (1D) spin-1/2 Fermi gas (SFG) with both attractive zero-range odd-wave interactions and repulsive zero-range even-wave interactions are mapped exactly to a 1D Lieb-Liniger-Heisenberg (LLH) model with delta-function repulsions depending on isotropic Heisenberg spin-spin interactions, such that the complete SFG and LLH energy spectra are identical. The ground state in the ferromagnetic phase is given exactly by the Lieb-Liniger (LL) Bethe ansatz, and that in the antiferromagnetic phase by a variational method combining Bethe ansatz solutions of the LL and 1D Heisenberg models. There are excitation branches corresponding to LL type I and II phonons and spin waves, the latter behaving quadratically for small wave numbers in the ferromagnetic phase and linearly in the antiferromagnetic phase.     

Néel order in the ground state of spin-1/2 Heisenberg antiferromagnetic multilayer systems

We show existence of Néel order for the ground state of a system withM two-dimensional layers with spin 1/2 and Heisenberg antiferromagnetic coupling, providedM8. The method uses the infrared bounds for the ground state combined with ideas introduced by Kennedy, Lieb, and Shastry.     

Long-range spin-pairing order and spin defects in quantum spin- $${1 \over 2}$$ ladders

For w-legged antiferromagnetic spin-1/2 Heisenberg ladders, a long-range spin pairing order can be identified which enables the separation of the space spanned by finite-range (covalent) valence-bond configurations into w +1 subspaces. Since every subspace has an equivalent counter subspace connected by translational symmetry, twofold degeneracy, breaking translational symmetry is found except for the subspace where the ground state of w = even belongs to. In terms of energy ordering, (non)degeneracy and the discontinuities introduced in the long-range spin pairing order by topological spin defects, the differences between even and odd ladders are explained in a general and systematic way. Received 19 July 1999 and Received in final form 8 October 1999     

Exact valence bond entanglement entropy and probability distribution in the XXX spin chain and the potts model

We determine exactly the probability distribution of the number N_(c) of valence bonds connecting a subsystem of length L>1 to the rest of the system in the ground state of the XXX antiferromagnetic spin chain. This provides, in particular, the asymptotic behavior of the valence-bond entanglement entropy S_(VB)=N_(c)ln2=4ln2/pi(2)lnL disproving a recent conjecture that this should be related with the von Neumann entropy, and thus equal to 1/3lnL. Our results generalize to the Q-state Potts model.     

Carrier-mediated ferromagnetism in N co-doped (Zn, Mn)O-based diluted magnetic semiconductors

Mn-doped ZnO is anti-ferromagnetic spin glass state, however, it becomes half-metallic ferromagnets upon hole doping. In this Letter we report a theoretical study of (Zn, Mn)O system codoped with N, and show that this codoping can change the ground state from anti-ferromagnetic to ferromagnetic. We have carried out the first-principles electronic structure calculations and report total energy to estimate whether the ferromagnetic state was stable or not. Our approach is based on the spin-polarized relativistic Korringa–Kohn–Rostoker (SPR–KKR) density functional theoretical (DFT) method, within the coherent potential approximation (CPA). Self-consistent electronic structure calculations were performed within the local density approximation, using the Vosko–Wilk–Nusair parameterization of the exchange-correlation energy functional. Our results for energy difference between ferromagnetic sate and spin glass state as well as their dependence on concentrations were presented and discussed.     

Itinerant Magnets on a Triangular Cu(111) Lattice

We investigate complex spin structures of frustrated two-dimensional Cr, Mn, and Fe monolayer magnets on a triangular lattice provided by the Cu(111) substrate. First we establish a zero-temperature phase diagram of possible spin structures on the basis of the classical Heisenberg model up to the third-nearest neighbor exchange interaction. Second we carried out first-principles total energy calculations on the basis of the vector-spin density formulation of the density functional theory using the full potential linearized augmented plane wave (FLAPW) method in film geometry for a set of complex non-collinear spin structures. We found, the ground state of Fe is ferromagnetic, Cr exhibits a coplanar, two-dimensional non-collinear 120 Néel state and Mn a three-dimensional non-collinear ground state, the 3Q-state. Incommensurate spin-spiral states are expected for a FeMn alloy on Cu(111). We employ the constrained local moment method to estimate the exchange parameters of the model Hamiltonians. We show that for Mn higher-order spin interactions are the origin of the 3Q-state for Mn. The combination of ab initio calculations and model Hamiltonians provides a powerful tool to investigate the magnetic structures of complex magnetic systems.     

The energy operator for infinite statistics

We construct the energy operator for particles obeying infinite statistics defined by aq-deformation of the Heisenberg algebra.The aim of this paper is to construct the energy operator for particles which obey the so-called infinite statistics defined by theq-deformation of the Heisenberg algebra. This topic was studied in the previous article [1], where a conjecture was formulated concerning the form of the energy operator. Our main result is a proof of this conjecture in a slightly modified form (cf. Remark 1).     

Ground state of ferromagnet with antiferromagnetic impurity

The Heisenberg ferromagnet with an antiferromagnetic impurity and arbitrary spin is considered. The method is suggested for constructing the ground state of such a system, the method using the Jacobi matrix technique. As an example, there has been investigated the ferromagnet with a simple cubic lattice and the matrix spin $\text{S =}\text{1}\text{2}$, and the impurity spin S′ = 1. The energy and wave function of the ground state are found as dependent on the system parameters.     

Ground-state and dynamical properties of a spin-S Heisenberg star

We generalize the Heisenberg star consisting of a spin-1/2 central spin and a homogeneously coupled spin bath modeled by the XXX ring [Richter J and Voigt A 1994 J. Phys. A: Math. Gen. 27 1139-1149] to the case of arbitrary central-spin size S < N/2, where N is the number of bath spins. We describe how to block-diagonalize the model based on the Bethe ansatz solution of the XXX ring, with the dimension of each block Hamiltonian ≤ 2S + 1. We obtain all the eigenenergies and explicit expressions of the sub-ground states in each l-subspace with l being the total angular momentum of the bath. Both the eigenenergies and the sub-ground states have distinct structures depending whether S ≤ l or l < S. The absolute ground-state energy and the corresponding l as functions of the intrabath coupling are numerically calculated for N = 16 and S = 1, 2, ⋯ ,7 and their behaviors are quantitatively explained in the weak and strong intrabath coupling limits. We then study the dynamics of the antiferromagnetic order within an XXX bath prepared in the Néel state. Effects of the initial state of the central spin, the value of S, and the system-bath coupling strength on the staggered magnetization dynamics are investigated. By including a Zeeman term for the central spin and the anisotropy in the intrabath coupling, we also study the polarization dynamics of the central spin for a bath prepared in the spin coherent state. Under the resonant condition and at the isotropic point of the bath, the polarization dynamics for S > 1/2 exhibit collapse-revival behaviors with fine structures. However, the collapse-revival phenomena are found to be fragile with respect to the anisotropy of the intrabath coupling.     

Spin-Wave Excitations and Energy Gap in Quasi-One-Dimensional Organic Polymer Ferromagnets

Based on a theory model proposed for organic ferrornagnets, the spin configuration and spinwave excitations in quasi-one-dimensional organic polymer ferromagnets are studied. The results show that: 1) Owing to the unpaired electrons at side free-radicals, the degeneracy of the spin-wave will be removed, the lower branch of the spin-wave excitations will split off into two branches, and it shows ferromagnetic characters; 2) The anisotropic interactions between the unpaired electrons at side free-radicals will make an energy gap appear between the ground state and the lowest excited state.     

DMRG Studies on Properties of Undoped and Doped Molecule-Based Ferromagnetic Chain

By using density matrix renormalization group （DMRG） method a model for organic molecule-based ferromagnetic chain is proposed. It is found that the ground states of Undoped and doped systems both exhibit ferrimagnetic ordering. The e-e repulsion plays an important role in the stability of the ferromagnetic state either in doped system or undoped system. For the undoped system, each unit cell coatains half of the total spins, which is consistent with Lieb＇s theorem. It is convinced that when the system is doped with one electron, a charge density wave is excited, which decreases the amplitude of spin density wave,therefore acting against the stability of ferromagnetic state.     

Field-induced transitions and spatial chaos in the classical XY spin chain

We study the lowest-lying excitation of a classical ferromagnetic XY spin chain, in the presence of a symmetry breaking magnetic field. Extremizing the energy of this system leads to a two-dimensional nonlinear map, whose allowed phase space shrinks with increasing field in a nontrivial manner. The orbits of the map represent the set of extremum energy spin configurations. For each field, we compute the energy of the members of this set and find the lowest energy among them, excluding the obvious ground state configuration with all spins parallel along the field direction. This state turns out to be the unstable fixed point of the map. We show that up to a certain (primary) critical field, a separatrixlike 2pi soliton configuration is the lowest-energy excitation, with an energy very close to the ground state energy. For any field beyond this critical field, the soliton disappears and lowest excitation is a librational configuration corresponding to the outermost orbit in the phase plot at that field. Further, its energy is found to be much higher than the ground state energy, leading to a sharp jump in the difference in energy between the former and the latter at this field. With further increase in the field, sharp jumps in the excitation energy arise at certain secondary critical fields as well. We show that these appear when the corresponding spin configurations become commensurate. This complex behavior of the energy is interpreted and its effect on the magnetization and static susceptibility of the system is also studied.