Ferromagnetic ground states of the Hubbard model on a complete graph

We use group theory to derive the exact analytical expression of the ferromagnetic ground states of the Hubbard model on a complete graph for arbitrary lattice sites f and for arbitrary fillings N. We find that for t > 0 and for N = f + 1 the ground state is maximally ferromagnetic with total spin S = (f ? 1)/2.For N > f + 1 the ground state is still ferromagnetic but becomes degenerate with respect to S.     

Ferromagnetic Domain Wall and Spiral Ground States in One-Dimensional Deformed Flat-Band Hubbard Model

We construct a set of exact ground states with a localized ferromagnetic domain wall and an extended spiral structure in a quasi-one-dimensional deformed flat-band Hubbard model. In the case of quarter filling, we show the uniqueness of the ground state with a fixed magnetization. The ground states with these structures are degenerate with the all-spin-up and all-spin-down states. This property of the degeneracy is the same as the domain wall solutions in the XXZ Heisenberg–Ising model. We derive a useful recursion relation for the normalization of the domain wall ground state. Using this recursion relation, we discuss the convergence of the ground state expectation values of arbitrary local operators in the infinite-volume limit. In the ground state of the infinite-volume system, the translational symmetry is spontaneously broken by this structure. We prove that the cluster property holds for the domain wall ground state and excited states. We also estimate bounds of the ground state expectation values of several observables, such as one- and two-point functions of spin and electron number density.     

Exchangeable qubit states

We present a characterisation of the two-site marginals of exchangeable and Bose-exchangeable states and provide an elementary proof for the qubit case. A link between the ground state problem for ferromagnetic mean-field models and the additivity of the maximal two-norm for quantum channels is established. We then analyse the corrections on N-particle symmetric states with respect to the exchangeable ones. The finite-size effects on the average ground state energy of the BCS model are explicitly computed.     

Studies of the Ferromagnetic State in Quasi-One-Dimensional Organic Polymer Ferromagnets

The possible ferromagnetic ground state of π-conjugated alternant hydrocarbon chains with unequal number of atoms on two sublattices is studied by the peierls-Hubbard model. Allowing for full lattice relaxation, a set of self-consistent iterative equations are established to study this system. The stabilities of the possible ferromagnetic ground states with respect to two kinds of unsymmetric site energies are also studied. We find that the ground state of the system is a stable ferromagnetic state as a result of the topological structure of the network and the electron-electron interaction. And the unsymmetric site energies, induced by substitutions, will severely weaken the stability of the ferromagnetic ground state.     

Quantum coherent operators: A generalization of coherent states

We introduce a technique to compare different, but related, quantum systems, thereby generalizing the way that coherent states are used to compare quantum systems to classical systems in semiclassical analysis. We then use this technique to estimate the dependence of the free energy of the quantum Heisenberg model on the spin value, and to estimate the relation between the ferromagnetic and antiferromagnetic free energies.Work supported in part by the U.S. National Science Foundation grant PHY-9019433.Work supported in part by the U.S. National Science Foundation grant DMS-9002416.     

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     

Simulation of coexisting ferromagnetic order and disorder of geometrically frustrated Co2Cl(OH)3

The ground state and phase transition of Co₂Cl(OH)₃ were investigated by Monte Carlo simulation. This compound is a magnet, with a pyrochlore structure distorted along one axis. The magnetic structure at low temperatures consists of coexisting ferromagnetism and random spin, according to experiments. However, the formation mechanism of the coexistence and the interaction between the spins were unclear. We assumed an anisotropic Ising model and examined the ground state by multicanonical Monte Carlo simulation. In a nearest neighbor model, the ground states were highly degenerated. Almost all of the states were spin glass states, but a few of the states were ferromagnetic. The latter magnetic states were ferromagnetic at triangular layers and two in-one out random state at Kagome layers. The latter states should be stabilized if weak ferromagnetic interactions exist between second nearest neighbor spins and correspond to the states reported by the experiments. This expectation was confirmed by simulation.     

Droplet States in the XXZ Heisenberg Chain

We consider the ground states of the ferromagnetic XXZ chain with spin up boundary conditions. The ground state of this model, restricted to a sector with a fixed number of down spins, describes a droplet of down spins in an environment of up spins. We find the exact energy and the states that describe these droplets in the limit of an infinite number of down spins. We prove that there is a gap in the spectrum above the droplet states. As the XXZ Hamiltonian has a gap above the fully magnetized ground states as well, this means that the droplet states (for sufficiently large droplets) form an isolated band. The width of this band tends to zero in the limit of infinitely large droplets. We also prove the analogous results for finite chains with periodic boundary conditions and for the infinite chain. Received: 5 September 2000 / Accepted: 8 December 2000     

Ground state phase diagram of the infinite dimensional Hubbard model: A variational study

We use the Gutzwiller variational method to study the ground state phase diagram of the infinite dimensional Hubbard model, paying special attention to features associated with the Gaussian form of the tight binding band density of states. We only consider trial states for which the validity of the Gutzwiller approximation has been proven, i.e., the paramagnetic, ferromagnetic, and two-sublattice antiferromagnetic states. We map out the phase diagram numerically, and give approximate analytic arguments to explain the behaviour in the small-U, and large-U limits. We give two versions of the phase diagram: one restricted to homogeneous phases, and another when phase separation is allowed. In the latter case, a homogeneous antiferromagnetic state is found only at exact half-filling, where the state is also insulating. Off half-filling, four different regions are found: pure paramagnetic, and ferromagnetic states, as well as antiferromagnetic-paramagnetic, and antiferromagnetic-ferromagnetic mixed phases.Dedicated to Professor W. Brenig on the occasion of his 60th birthdayResearch performed within the program of the Sonderforschungsbereich 341 supported by the Deutsche Forschungsgemeinschaft     

Exact ground state of a spin ladder with a quantum phase transition

We introduce a spin ladder with Ising interactions along the legs and intrinsically frustrated Heisenberg-like ferromagnetic interactions on the rungs. The model is solved exactly in the subspaces relevant for the ground state by mapping to the quantum Ising model, and we show that a first order quantum phase transition separates the classical from quantum regime, with the spin correlations on the rungs being either ferromagnetic or antiferromagnetic, and different spin excitations in both regimes. The present case resembles the quantum phase transition found in the compass model in one and two dimensions.     

Thermal entanglement versus mixture in a spin chain: Generation of maximally entangled mixed states

We study the two-body entanglement and mixture in a three-qubit XXZ spin chain in thermal equilibrium state at temperature T with an external magnetic field B. The effects of the magnetic field, the anisotropy and the temperature on the entanglement and mixture are considered. We show that the ground states in this system are fully characterized and distinguished by both entanglement and mixture. Thermal entanglement versus the mixture of all two-spin states is investigated. All pairwise states provide an upper bound on the entanglement for a fixed mixture, and some part of the boundary reaches the boundary allowed by physics. As a result, maximally entangled mixed states can be generated by controlling magnetic field and temperature. Especially, in the ground state of the whole system, the explicit forms of maximally entangled mixed states are given. The results provide a new way to generate maximally entangled mixed states and control entanglement.     

Double-exchange model: phase separation versus canted spins

We study the competition between different possible ground states of the double-exchange model with strong ferromagnetic exchange interaction between itinerant electrons and local spins. Both for classical and quantum treatment of the local spins the homogeneous canted state is shown to be unstable against a phase separation. The conditions for the phase separation into the mixture of the antiferromagnetic and ferromagnetic/canted states are given. We also discuss another possible realization of the phase-separated state: ferromagnetic polarons embedded into an antiferromagnetic surrounding. The general picture of a percolated state, which emerges from these considerations, is discussed and compared with results of recent experiments on doped manganaties. Received 17 March 1999     

Stability of ferromagnetism in the Hubbard model on the kagome lattice

The Hubbard model on the kagome lattice has highly degenerate ground states (the flat lowest band) in the corresponding single-electron problem and exhibits the so-called flat-band ferromagnetism in the many-electron ground states as was found by Mielke [J. Phys. A 24, L73 (1991)]]. Here we study the model obtained by adding extra hopping terms to the above model. The lowest single-electron band becomes dispersive, and there is no band gap between the lowest band and the other band. We prove that, at half filling of the lowest band, the ground states of this perturbed model remain saturated ferromagnetic if the lowest band is nearly flat.     

Agreement percolation and phase coexistence in some Gibbs systems

We extend some relations between percolation and the dependence of Gibbs states on boundary conditions known for Ising ferromagnets to other systems and investigate their general validity: percolation is defined in terms of the agreement of a configuration with one of the ground states of the system. This extension is studied via examples and counterexamples, including the antiferromagnetic Ising and hard-core models on bipartite lattices, Potts models, and many-layered Ising and continuum Widom-Rowlinson models. In particular our results on the hard square lattice model make rigorous observations made by Hu and Mak on the basis of computer simulations. Moreover, we observe that the (naturally defined) clusters of the Widom-Rowlinson model play (for the WR model itself) the same role that the clusters of the Fortuin-Kasteleyn measure play for the ferromagnetic Potts models. The phase transition and percolation in this system can be mapped into the corresponding liquid-vapor transition of a one-component fluid.     

Phase transitions in the 2D J 1-J 2 Heisenberg model with arbitrary signs of exchange interactions

The ground state of the J ₁-J ₂ Heisenberg model with arbitrary signs of exchange is studied for spin S = 1/2 in the case of the two-dimensional (2D) square lattice. The states with different types of spin long-range order (antiferromagnetic checkerboard, stripe, collinear ferromagnetic) as well as the disordered spin liquid states are described in the framework of one analytical approach. In particular, it is shown that the phase transition between the ferromagnetic spin liquid and the ferromagnet with long-range order is of the second order. In the vicinity of such transition, we have found the ferromagnetic state with a rapidly varying condensate function.     

On ground states of the one-dimensional ferromagnetic XXZ model

We obtain the complete list of pure infinite volume ground states for the one-dimensional ferromagnetic XXZ model.     

Nagaoka Ferromagnetism in Two-Band Hubbard Model

In the present paper, we investigate the existence of ferromagnetism in a two-band Hubbard model, by applying a recently-introduced method by us to study ferromagnetism in metallic clusters. We prove rigorously that the ground state of this model is ferromagnetic if the intra-orbital Coulomb repulsion between electrons is infinitely strong and only one hole exists in the system. Our theorem improves a previous result. Furthermore, our method can also be applied to deal with the case of multiple holes.     

Classification and completeness of Bethe states and excitation spectrum for the spin 4 Fateev-Zamolodchikov model

The classification and completeness of Bethe states is undertaken for the spin 4 Fateev-Zamolodchikov model. This special case is of particular interest as the energy can be derived in a simple closed form even for lattices of arbitrary finite size. The excitation spectrum over the ferromagnetic ground state is also derived.     

Exactly solvable spin ladder model with degenerate ferromagnetic and singlet states

We study the spin ladder model with interactions between spins on neighboring rungs. The model Hamiltonian with the exact singlet ground state degenerated with ferromagnetic state is obtained. The singlet ground state wave function has a special recurrent form and depends on two parameters. Spin correlations in the singlet ground state show double-spiral structure with period of spirals equals to the system size. For special values of parameters they have exponential decay. The spectrum of the model is gapless and there are asymptotically degenerated excited states for special values of parameters in the thermodynamic limit. Received 7 May 1999     

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.