Nontrivial Ground State Research Articles

On the nonrelativistic Lee model

In this work we present two rigorous results on the nonrelativistic Lee model following a method proposed by Rajeev in an unpublished article (S. G. Rajeev, hep-th 9902025). Thus this short paper should be considered as a commentary on Rajeev. In the unpublished paper of Rajeev, the renormalization of the Hamiltonian is accomplished at the level of resolvents. We first establish that the renormalized resolvent of the interacting Hamiltonian indeed defines a unique closed densely defined operator acting on the free Fock space of bosons. Next we give a justification in the mean field approximation that the ground state energy is bounded from below and the system has a good thermodynamic limit by elaborating along the original arguments of Rajeev. Our arguments in two dimensions do not yield better bounds, but this could be due to the inadequacy of the method used. In both cases though the ground state energy is not significantly altered to give a nontrivial ground state energy per particle.

Quantum antiferromagnetism in quasicrystals.

The antiferromagnetic Heisenberg model is studied on a two-dimensional bipartite quasiperiodic lattice. Using the stochastic series expansion quantum Monte Carlo method, the distribution of local staggered magnetic moments is determined on finite square approximants with up to 1393 sites, and a nontrivial inhomogeneous ground state is found. A hierarchical structure in the values of the moments is observed which arises from the self-similarity of the quasiperiodic lattice. The computed spin structure factor shows antiferromagnetic modulations that can be measured in neutron scattering and nuclear magnetic resonance experiments. This generic model is a first step towards understanding magnetic quasicrystals such as the recently discovered Zn-Mg-Ho icosahedral structure.

Quantum Quivers and Hall/Hole Halos

Two pictures of BPS bound states in Calabi-Yau compactifications of type II string theory exist, one as a set of particles at equilibrium separations from each other, the other as a fusion of D-branes at a single point of space. We show how quiver quantum mechanics smoothly interpolates between the two, and use this, together with recent mathematical results on the cohomology of quiver varieties, to solve some nontrivial ground state counting problems in multi-particle quantum mechanics, including one arising in the setup of the spherical quantum Hall effect, and to count ground state degeneracies of certain dyons in supersymmetric Yang-Mills theories. A crucial ingredient is a non-renormalization theorem in N=4 quantum mechanics for the first order part of the Lagrangian in an expansion in powers of velocity.

On the ground state structure of monolayers on the (100) face of fcc crystals

While the (classical) ground state structure of an atomic monolayer adsorbed at a smooth substrate with negligible corrugation potential is trivial, namely, a triangular lattice with a spacing given by the minimum of the interatomic (Lennard-Jones) potential, nontrivial ground state structures occur on corrugated substrate surfaces. Assuming as a substrate surface the (100) plane of a face-centered cubic crystal, the possible (classical) ground state structures of the monolayer are studied by Monte Carlo simulation, varying both the density of the adsorbed film and the strength of the potential due to the surface. Different incommensurate structures are found, which can be interpreted as (two-dimensional) patterns of domain walls separating commensurate regions. Typically the heavy walls are oriented along the face diagonals of the square substrate lattice. This nonuniform order also is reflected in the distribution of distances of the adsorbed atoms from the substrate surface plane, which is not a delta function but may even display a bimodal character.

Spin pattern of few [formula omitted] monolayers of the type II antiferromagnet EuTe

A degenerate ground state spin pattern is found for the type II antiferromagnet EuTe in the bulk limit. The model system is EuTe with ferromagnetic nearest neighbor (NN, J 1=0.06 K) and antiferromagnetic next nearest neighbor (NNN, J 2=−0.16 K) exchange interaction. For the non-trivial ground state the spins within a single (1 1 1) plane are no longer all parallel. Instead a quarter of the spins are parallel to the NN spins in the adjacent layer. This state becomes metastable if dipolar interaction is taken into account, or for low-dimensional structures of few (1 1 1)-monolayer systems of EuTe.

Bilayer quantum Hall systems: spin–pseudospin symmetry breaking and quantum phase transitions

We discuss and review recent advances in our understanding of quantum Hall systems where additional quantum numbers associated with spin and/or layer (pseudospin) indices play crucial roles in creating exotic quantum phases. Among the novel quantum phases we discuss are the recently discovered canted antiferromagnetic phase, the spontaneous interlayer coherent phase, and various spin Bose glass phases. We describe the theoretical models used in studying these novel phases and the various experimental techniques being used to search for these phases. Both zero temperature quantum phase transitions and finite temperature phase transitions are discussed. Emphasis in this article is on the recent developments in novel quantum phases and quantum phase transitions in bilayer quantum Hall systems where non-trivial magnetic ground states associated with spontaneous spin symmetry breaking play central role.

Thermo-Mechanical Response of Patched Plates

A review, unie cation, and extension of the analysis and results pertaining to patched beam plates subjected to a uniform temperature e eld (heating and cooling ) and in-plane edge force (compressive or tensile ), is presented. A self-consistent nonlinear formulation has been derived, which lends itself to an exact analytical solution, to within the context of the model. Three nondimensional parameters are seen to characterize the response of the composite system. These are 1 ) a loading parameter, 2 ) a critical temperature, and 3 ) a critical membrane force. Critical behavior includes bifurcation buckling, asymptotic buckling, and sling-shot buckling, nontrivial ground states, and demarcation and transition in dee ection direction. Results for both heating and cooling are consolidated and presented in a unie ed manner, yielding a broader understanding of the problem of interest. UMEROUS aerospace, mechanical, and electronic structural components consist of a primary base structure with a secondary element bonded to it for the purpose of strengthening, stiffening, or providing thermal or electrical contact. Specie c examples are bonded sensors or repair patches on aircraft wings and fuselages or the attachment of electronic components to printed circuit boards. The combination of the primary and secondary structures forms a composite system. Because the structure has been changed with regard to its geometry and structural properties, the structural response canchangesignie cantly with theintroduction ofthepatch, with sometimes unanticipated performance as a result. In particular, the local stiffness has been changed, the neutral axis has been moved, and a thermal mismatch between the base structure and the patch may have been introduced. The last two will independently cause local bending, and together can induce novel behavior of the structure.

Mixed spin ladders with exotic ground states

We study the "mixed spin" isotropic ladder system having S=1 spins on one leg and S=1/2 spins on the other, with general-type exchange interactions between spins on neighboring rungs. A set of model Hamiltonians with exact ground states in the form of a certain matrix product wave function is obtained. We show that sufficiently strong frustration can lead to exotic singlet ground states with infinite (exponential) degeneracy. We also list a couple of rather simple models with nontrivial ground states, including a model with only bilinear exchange.

Landau pole screening in the Gross-Neveu model: [formula omitted] versus operator product expansion

In asymptotically free theories, Landau poles at low energy scales limit the range of validity of perturbative predictions. Taking into account non-perturbative corrections in an operator product expansion (OPE) does not alleviate this problem, however, non-vanishing condensates are believed to prevent the singularities from producing unphysical (tachyonic) poles in Green's functions. We illustrate the mechanism of Landau pole screening by dynamically generated condensates in the Gross-Neveu model, in which a dynamical fermion mass and a scalar boundstate are formed. In the large N limit the pertinent Green's function is an entirely smooth function of the Euclidean momentum transfer. We demonstrate that its asymptotic behaviour nevertheless resembles the renormalisation group improved perturbative result accompanied by OPE corrections for momenta well above the Landau pole. The 1 N expansion is suited to account for non-trivial ground state correlations beyond the range of validity of OPE predictions.

Strongly correlated spin-phonon systems: A scenario for heavy fermions.

A lattice of localized spins, coupled to phonons, is considered. It is shown that in a certain range of coupling constants a nontrivial nonmagnetic ground state of the system can arise, where the spins are screened by the phonons. In this state, groups of an even number of spins form singlet clusters, the spins within each cluster being strongly coupled to each other due to the exchange of phonons. This is a purely quantum phenomenon: average lattice displacements are zero, while amplitudes of zero quantum vibrations within the clusters are enhanced; the effect vanishes in the limit of classical spins. The clusters may, in principle, form either a crystal or quantum liquid. The collective screening of spins by phonons is a nonperturbative effect: it takes place only if the coupling constant exceeds a certain threshold. We have found the ground state exactly for a specific model with a highly symmetric Hamiltonian and discussed corrections to our solution due to variations of the Hamiltonian. The thermodynamics of the system is found. Applications to the physics of heavy-fermion compounds are discussed.

Optimal paths and domain walls in the strong disorder limit.

An optimization problem that may be cast in the context of domain walls in ferromagnets and spin glasses, latice animals, and percolation is described. Numerical calculations in two and three dimensions show that a new universality class is obtained. In the strong disorder limit interfaces are not self-affine but fractal. Further, the nontrivial ground state of frustrated spin glasses is straightforwardly obtained in this limit.

DIRAC FIELD IN THE FIVE-DEMENSIONAL KALUZA-KLEIN THEORY WITH SCALAR FIELD

In this work we investigate the five-dimensional Kaluza-Klein theory with a scalar field contained in the metric, where a Dirac-field is coupled to the metric field. We find that in the four-dimensional theory a nontrivial ground state for the scalar field exists and therefore the mass term in the Dirac equation can be interpreted, for example, as the electron mass.

THE t-J AND FRUSTRATED HEISENBERG MODELS: A STATUS REPORT ON NUMERICAL STUDIES

Recent numerical work on the t-J model and the frustrated spin-[Formula: see text] Heisenberg antiferromagnet is reviewed. Lanczos results are mainly discussed but other methods are also mentioned. Static and dynamical properties of one and more holes in the t-J model are presented. The current active search for nontrivial ground states of the frustrated Heisenberg model is summarized. It is concluded that numerical methods are providing useful information in the study of these models.

NUMERICAL STUDIES OF STRONGLY CORRELATED ELECTRONIC MODELS

Recent numerical work on strongly correlated electronic models using the Lanczos approach is reviewed. In particular static and dynamical properties of the Hubbard, t—J (with one, two and more holes) and the spin-½ Heisenberg antiferromagnet are presented. An attempt to summarize the current active search for nontrivial ground states of the frustrated Heisenberg model is made. Numerical methods like the Lanczos technique are providing useful information in the study of these models.

Nonuniversality in helical and canted-spin systems.

Vector-spin models with competing interactions have in general nontrivial ground states which completely break rotational invariance. We study the prototypical stacked triangular Heisenberg antiferromagnet by means of a O(3)\ifmmode\times\else\texttimes\fi{}O(2)/O(2) nonlinear \ensuremath{\sigma} model in a 2+\ensuremath{\epsilon} expansion. We find a dynamically generated O(4) symmetry. We propose that such systems in three dimensions have a first-order transition or a second-order one with either N=4 or tricritical mean-field exponents. We argue that this view is supported by experimental and numerical data.

Non-trivial ground state of the closed bosonic membrane

The zero-point energy for a spherical membrane in 3+1 dimensions is calculated as a function of its radius. The contribution is negative, normalized to zero at the origin. Summing the classical and quantum contributions to the hamiltonian produces a candidate for the ground state that is tachyonic, stable, and of a well-defined size.

Towards an effective bilocal theory from quantum chromodynamics in a background field

Using the path integral, we show how we can get background gauge-invariant bilocals (to be identified with mesons) from QCD in a nontrivial ground state. We discuss in this paper mainly the formal manipulations, especially how to deal with the zero modes.