Some predictions for an improved fermion action on the lattice

We propose an improved fermion action on the lattice by adding a next nearest neightbor interaction term to Wilson action. The proposed action is expected to approach the continuum limit more rapidly. Using the improved action, the predictions for the critical value of the hopping parameter at weak and strong coupling are given. The relationship between quark masses on the lattice and in the continuum is also discussed.     

Universality in Ising model gauge-field analogues

The lattice dependence of a class of gauge-invariant Ising models is investigated. Any lattice dependence would indicate that the lattice could not be regarded as irrelevent and that it would be incorrect to define gauge models on a lattice as a basis for investigating the continuum limit. The models investigated lie within the class of multispin Ising models which show a wide variety of lattice-dependent behaviour and so these models should provide a significant test of the importance of the gauge-invariance constraint. Two and three dimensional models are investigated and lattice independence is confirmed. This indicates that imposing gauge symmetries on lattice models can restrict the possible behaviour in such a way that lattice independent continuum limits can be defined.     

Boundary Hamiltonian Theory for Gapped Topological Orders

We report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces,with explicit boundary terms. We do this mainly for the Levin-Wen string-net model. The full Hamiltonian in our approach yields a topologically protected, gapped energy spectrum, with the corresponding wave functions robust under topology-preserving transformations of the lattice of the system. We explicitly present the wavefunctions of the ground states and boundary elementary excitations. The creation and hopping operators of boundary quasi-particles are constructed. It is found that given a bulk topological order, the gapped boundary conditions are classified by Frobenius algebras in its input data. Emergent topological properties of the ground states and boundary excitations are characterized by(bi-) modules over Frobenius algebras.     

Scalar lattice gauge theory

Scalar lattice gauge theories are models for scalar fields with local gauge symmetries. No fundamental gauge fields, or link variables in a lattice regularization, are introduced. The latter rather emerge as collective excitations composed from scalars. For suitable parameters scalar lattice gauge theories lead to confinement, with all continuum observables identical to usual lattice gauge theories. These models or their fermionic counterpart may be helpful for a realization of gauge theories by ultracold atoms. We conclude that the gauge bosons of the standard model of particle physics can arise as collective fields within models formulated for other “fundamental” degrees of freedom.     

THE EFFECT OF DIRECT f-f HOPPING ON THE HYBRIDIZATION GAP INSULATING BEHAVIOR OF THE PERIODIC ANDERSON LATTICE

By using the well known slave-boson technique and within the framework of mean field approximation, we study the effect of the direct f-f hopping on the low-temperature hybridization gap insulating behavior of the periodic Anderson lattice. The results show that the direct f-f hopping will decrease the hybridization gap or lead it to vanish. In the latter case, the lattice will exhibit no hybridization gap insulating behavior even if the lower renormalized band is fully occupied.     

The supersymmetric Ward identities on the lattice

Supersymmetric (SUSY) Ward identities are considered for the N=1 SU(2) SUSY Yang-Mills theory discretized on the lattice with Wilson fermions (gluinos). They are used in order to compute non-perturbatively a subtracted gluino mass and the mixing coefficient of the SUSY current. The computations were performed at gauge coupling and hopping parameter , 0.194, 0.1955 using the two-step multi-bosonic dynamical-fermion algorithm. Our results are consistent with a scenario where the Ward identities are satisfied up to O(a) effects. The vanishing of the gluino mass occurs at a value of the hopping parameter which is not fully consistent with the estimate based on the chiral phase transition. This suggests that, although SUSY restoration appears to occur close to the continuum limit of the lattice theory, the results are still affected by significant systematic effects. Received: 8 November 2001 / Revised version: 14 January 2001 / Published online: 15 March 2002     

Discrete breathers in classical ferromagnetic lattices with easy-plane anisotropy

Discrete breathers (nonlinear localized modes) have been shown to exist in various nonlinear Hamiltonian lattice systems. This paper is devoted to the investigation of a classical d-dimensional ferromagnetic lattice with easy plane anisotropy. Its dynamics is described via the Heisenberg model. Discrete breathers exist in such a model and represent excitations with locally tilted magnetization. They possess energy thresholds and have no analogs in the continuum limit. We are going to review the previous results on such solutions and also to report new results. Among the new results we show the existence of a big variety of these breather solutions, depending on the respective orientation of the tilted spins. Floquet stability analysis has been used to classify the stable solutions depending on their spatial structure, their frequency, and other system parameters, such as exchange interaction and local (single-ion) anisotropy.     

Direct evidence for the localized single-triplet excitations and the dispersive multitriplet excitations in SrCu2(BO3)2

We performed inelastic neutron scattering on the 2D Shastry-Sutherland system SrCu2(11BO3)2 with an exact dimer ground state. Three energy levels at around 3, 5, and 9 meV were observed at 1.7 K. The lowest excitation at 3.0 meV is almost dispersionless with a bandwidth of 0.2 meV at most, showing a significant constraint on a single-triplet hopping owing to the orthogonality of the neighboring dimers. In contrast, the correlated two-triplet excitations at 5 meV exhibit a more dispersive behavior.     

Emergent fermions and anyons in the kitaev model

We study the gapped phase of the Kitaev model on the honeycomb lattice using perturbative continuous unitary transformations. The effective low-energy Hamiltonian is found to be an extended toric code with interacting anyons. High-energy excitations are emerging free fermions which are composed of hard-core bosons with an attached string of spin operators. The excitation spectrum is mapped onto that of a single particle hopping on a square lattice in a magnetic field. We also illustrate how to compute correlation functions in this framework. The present approach yields analytical perturbative results in the thermodynamical limit without using the Majorana or the Jordan-Wigner fermionization initially proposed to solve this problem.     

Study of Some Factors Affecting Thermodynamic Properties of the Insulating Phase of the Periodic Anderson Lattice Model

Within the framework of slave-boson mean-field theory, we study the thermodynamic properties of the periodic Anderson lattice model with half-filled conduction band and one 4f electron at each primitive cell and the degeneracy N_d = 2. It is found that after taking into account the direct nearest-neighbor f-f hopping, such a periodic Anderson lattice model can exhibit both an insulating ground state and a heavy-fermion metal ground state depending on the value of the bare f energy level E_f, the hybridization matrix element V, and the direct f-f hopping strength δ. This is unlike the case neglecting the direct f-f hopping, in which such a periodic Anderson lattice model will predict an insulating ground state only.     

Quantum fluctuations and magnetic solitons: Equivalence of discrete lattice and renormalized continuum approaches

We discuss quantitative calculations for nonlinear excitations in one-dimensional magnets in the semiclassical regime. We show that the field-theoretic approach—calculating zero point fluctuations in the continuum limit and using counterterms to deal consistently with ultraviolet divergencies—is equivalent to calculating quantum fluctuations for a discrete lattice, if the parameters are identified properly. The latter, technically simpler approach is applied to a calculation of the reduction of soliton induced correlation functions by quantum and thermal fluctuations.Dedicated to Professor W. Brenig on the occasion of his 60th birthday     

Excitations of one-dimensional Bose-Einstein condensates in a random potential

We examine bosons hopping on a one-dimensional lattice in the presence of a random potential at zero temperature. Bogoliubov excitations of the Bose-Einstein condensate formed under such conditions are localized, with the localization length diverging at low frequency as l(omega) approximately 1/omega(alpha). We show that the well-known result alpha=2 applies only for sufficiently weak random potential. As the random potential is increased beyond a certain strength, alpha starts decreasing. At a critical strength of the potential, when the system of bosons is at the transition from a superfluid to an insulator, alpha=1. This result is relevant for understanding the behavior of the atomic Bose-Einstein condensates in the presence of random potential, and of the disordered Josephson junction arrays.     

Nonlinear travelling waves in φ6 polarizable model

We present a complete theoretical analysis of the periodic and non-periodic travelling waves in a diatomic chain model, in the continuum limit by incorporating nonlinear sixth order polarization potential (φ⁶) at the anion site. We have formulated a nonlinear lattice dynamical theory in which various energy curves are obtained for different types and magnitudes of the core-shell force constants. For periodic solutions, we have obtained two types of commensurate wave amplitudes which propagate in the opposite direction with respect to each other. For nonperiodic solutions, we have obtained various travelling excitations such as kink, antikink, excitons etc. for different values of the mass ratio and velocity parameter. The dipole moment per unit charge for SrTiO₃ has been calculated and it is found that the nonlinear excitations in this model carry large amount of energy as compared to those obtained from harmonic and anharmonic optical phonons in the φ⁴-polarizable model.     

Spin-wave renormalization by mobile holes in a two-dimensional quantum antiferromagnet

The coupling of antiferromagnetic spin excitations and propagating holes has been studied theoretically on a square lattice in order to investigate the dependence of antiferromagnetic order on hole doping, being of relevance, e.g., for the Cu–3 d⁹ system in antiferromagnetic CuO₂-planes of high-T_c superconductors. An effective Hamiltonian has been used, which results from a 2D Hubbard model (hopping integral t) with holes and with strong on-site Coulomb repulsion U. Bare antiferromagnetic excitations and holes with energies of the same order of magnitude t²/U are interacting via a coupling term being proportional to t and allowing holes to hop by emitting and absorbing spinwaves. In terms of a self-consistent one-loop approximation the renormalization of the spectral function both of holes and antiferromagnetic spin excitations are calculated.     

Gauge theory of two-dimensional spin- Heisenberg antiferromagnet

A gauge theory of the spin- Heisenberg antiferromagnet (HA) on a two-dimensional square lattice is developed, which is based on the diagonal G_D of the group product SO(3)×SU(2). For classical gauge fields G_D is homeomorphic to SO(3). The structure of the theory is such that the quantum spin- field propagates on the background gauge field. For special gauges the excitations of the spin-field are computed and compared to the excitations of the O(3) σ model for the same gauge. The significance of negative excitational modes with respect to a semiclassical actionГ_sc of the spin- HA is discussed. Some properties ofГ_sc represented as a chiral SO(3) model in a continuum representation are worked out.     

Phase transitions in quantum field theory. I. Phases of the Thirring model

In this series of papers we exhibit and analyse phase transitions in quantum field theory. In this paper we consider the Thirring model. We show that when the interaction becomes sufficiently attractive there is a transition to a vacuum that is ‘dead” in the sense there are no finite energy excitations. Nevertheless the corresponding continuum Green's functions exist. We make this demonstration precise by considering the model on a lattice and constructing the continuum limit explicitly on either side of the critical point. For this we extensively use the connection between the $\text{spin}\text{-}\text{1}\text{2}$x-y-z chain and the lattice model. We also show a new continuum theory with four fermion interactions exists in 1 + 1 dimensions. This theory corresponds to taking the continuum limit of the spin chain in absence of any external magnetic field. Its Hamiltonian differs from that of the Thirring model by addition of fermion number operator with an infinite coefficient and is not renormalizable in the conventional sense. It has more interesting critical properties and a different spectrum.     

Extended Bose-Hubbard model with pair hopping on triangular lattice

We study systematically an extended Bose-Hubbard model on the triangular lattice by means of a meanfield method based on the Gutzwiller ansatz. Pair hopping terms are explicitly included and a three-body constraint is applied. The zero-temperature phase diagram and a variety of quantum phase transitions are investigated in great detail. In particular, we show the existence and the stability of the pair supersolid phase.     

Relativistic Continuum Random Phase Approximation and Applications II. Applications

The fully consistent relativistic continuum random phase approximation （RCRPA） has been constructed in the momentum representation in the first part of this paper. In this part we describe the numerical details for solving the Bethe-Salpeter equation. The numerical results are checked by the inverse energy weighted sum rules in the isoscalar giant monopole resonance, which are obtained from the constraint relativistic mean field theory and also calculated with the integration of the RCRPA strengths. Good agreement between them is achieved. We study the effects of the self-consistency violation, particularly the currents and Coulomb interaction to various collective multipole excitations. Using the fully consistent RCRPA method, we investigate the properties of isoscalar and isovector collective multipole excitations for some stable and exotic from light to heavy nuclei. The properties of the resonances, such as the centroid energies and strength distributions are compared with the experimental data as well as with results calculated in other models.