The gauge boson sector ofU(1) lattice theories

We examine theU(1) Hamiltonian lattice gauge theory in (2+1) and (3+1) dimensions. We set up a differential eigenvalue equation for the energy levels of the system, valid for all values of the coupling parameter. We show how the standard strong coupling results are retrieved, and also present a weak coupling solution which exhibits (unconfined) transverse photons as the phonons of the lattice. The lattice approach is thus seen to be appropriate for non-confining as well as for confining systems.     

Calculation of Vacuum Wavefunction and Mass .Gap from Improved (2+l)-Dimensional SU(2) Lattice Gauge Field Hamiltonian

The truncated eigenvalue equation of SU(N) lattice gauge theory is studied by using improved lattice gauge Hamiltonian with a proper truncation scheme that preserves the continuum limit. The calculations of vacuum state wavefunction and glueball mass of (2+1)-dimensional SU(2) theory up to third order are carried out, the results show the improvement of scaling behavior in deep weak coupling region.     

Does the XY model have an integrable continuum limit?

The quantum field theory describing the massive O(2) non-linear sigma-model is investigated through two non-perturbative constructions: the form factor bootstrap based on integrability and the lattice formulation as the XY model. The S-matrix, the spin and current two-point functions, as well as the 4-point coupling are computed and critically compared in both constructions. On the bootstrap side a new parafermionic super selection sector is found; in the lattice theory a recent prediction for the (logarithmic) decay of lattice artifacts is probed.     

Phase diagram of the two-channel kondo lattice model in one dimension

Employing the density matrix renormalization group method and strong-coupling perturbation theory, we study the phase diagram of the SU(2)xSU(2) Kondo lattice model in one dimension. We show that, at quarter filling, the system can exist in two phases depending on the coupling strength. The weak-coupling phase is dominated by RKKY exchange correlations, while the strong-coupling phase is characterized by strong antiferromagnetic correlations of the channel degree of freedom. These two phases are separated by a quantum critical point. For conduction-band fillings of less than one-quarter, we find a paramagnetic metallic phase at weak coupling and a ferromagnetic phase at moderate to strong coupling.     

Two-dimensional disordered lattice networks with substrate

The paper deals with the development of a theory for describing two-dimensional (2D) random lattice networks of resistors with a particular topology. We consider a 2D anisotropic random lattice where each node of the network is connected to a reference node (substrate) through a given random resistor. This topology is of great interest both for theoretical and practical applications. Moreover, the theory is able to take into account the similar, but more interesting problem with a capacitive coupling with the substrate. The analytical results allow us to obtain the average behaviour of such networks, i.e. the electrical characterisation of the corresponding physical systems. This effective medium theory is developed starting from the properties of the lattice Green's function of the network and from an ad hoc mean field procedure. An accurate analytical study of the related lattice Green's functions has been conducted obtaining closed-form results expressed in terms of elliptic integrals. All the theoretical results have been verified by means of numerical Monte-Carlo simulations obtaining a remarkably good agreement between numerical and theoretical values, both in resistive and capacitive systems.     

Itinerant ferromagnetism in the multiorbital Hubbard model: a dynamical mean-field study

In order to resolve the long-standing issue of how itinerant ferromagnetism is affected by lattice structure and Hund's coupling, we compare various three-dimensional lattice structures in the single- and multiorbital Hubbard models with the dynamical mean-field theory with an improved quantum Monte Carlo algorithm that preserves the spin-SU(2) symmetry. The result indicates that both the lattice structure and the d-orbital degeneracy are essential for the ferromagnetism in the parameter region representing a transition metal. Specifically, (a) Hund's coupling, despite the common belief, is important, which is here identified to come from particle-hole scatterings, and (b) the ferromagnetism is a correlation effect (outside the Stoner picture) as indicated from the band-filling dependence.     

Strong coupling expansions for the mass gap in lattice gauge theories

We derive strong coupling expansions for the mass gap in euclidean lattice gauge theories in any space-time dimension. For gauge groups SU(2), SU(3), Z₂ and Z₃ the series are calculated up to order g^?16. They are used to get rough estimates for the lowest glueball mass in continuum SU(2) and SU(3) gauge theories, assuming a sudden crossover from strong to weak coupling behaviour in the lattice theory.     

Finite size Wilson loops

A study of Wilson loop averages for finite size loops is initiated. Within the framework of euclidean four-dimensional lattice SU(2) gauge theory with elementary Wilson action we compute the expectation values of all rectangular loops to 12th order in the strong coupling expansion. The leading term for weak coupling is evaluated for loops up to 4 × 4. A comparison to Monte Carlo data is presented. Other related issues are also discussed.     

Variational determination of the stringtension and the glueball mass in (2+1) dimensionalU (1) lattice gauge theory for all values of the coupling constant

Using variational ansätze of the product type we calculate the massgap and the stringtension of (2+1) dimensionalU(1) lattice gauge theory in the Hamiltonian formalism for all values of the coupling constant. In the strong coupling limit our results agree with high order strong coupling series. In the weak coupling limit both, glueball mass and stringtension vanish exponentially with the coupling constant.     

A technique for analytical calculation of observables in lattice gauge theories

It is shown that the partition function for a finite lattice factorizes into terms that can be associated with each vertex in the finite lattice. This factorization property forms the basis of a well-defined and efficient technique developed to calculate partition functions to high accuracy, on finite lattices for gauge theories. This technique, along with an expansion in finite lattices, provides a powerful means for calculating observables in lattice gauge theories. This is applied to SU(2) lattice gauge theory in four dimensions. The free energy, expectation value of a plaquette and specific heat are calculated. The results are very good both in the strong coupling and the weak coupling region and describe the crossover region quite well, agreeing all the way with the Monte Carlo data.     

MIGDAL SCHEME FOR THE EFFECTIVE COUPLINGS OF POLYAKOV LOOPS

The Migdal renormalization group(MRG) procedure is applied to the finite temperature SU(2) lattice gauge theory.With its effective action form in terms of the Polyakov Zoop we an-alyse the strong and weak coupling approximations of the evolution of renormalized couplings.The distribution of renormalization group trajectory is obtained and the critical coupling is measured.     

2+1维SU(3)格点纯规范场的真空态计算

用连续极限截断的格点本征值方法^[1],研究2+1维SU(3)的格点规范理论的真空态.在强耦合区,上述方法的结果与强耦合展开一致.在过渡区,上述方法的结果显示出较好的标度行为.     

Calculation of the thermal conductivity and the specific heat of the lattice for a spin-boson system at low temperatures

The thermal conductivity of the lattice is calculated for a spin-boson system using the method of inverse linear response theory. The spin-boson Hamiltonian consists of coupled two-level systems (TLS) represented by pseudospin operators, acoustical phonons and an interaction between both systems. The lattice specific heat is determined in the framework of perturbation theory with respect to spin-boson coupling. For the calculation of both quantities results for spin-correlation functions derived within self-consistent random phase approximation are applied. At low temperatures the influence of spin-boson coupling and of interacting TLS on the temperature dependence of the lattice thermal conductivity and of the lattice specific heat is discussed and compared with corresponding experimental investigations.     

Exploration of the phase diagram of 5D anisotropic SU(2) gauge theory

In this paper we attempt a non-perturbative study of the five-dimensional, anisotropic SU(2) gauge theory on the lattice using Monte Carlo techniques. Our goal is the exploration of the phase diagram, defining the various phases and the critical boundary lines. Three phases appear, two of them are continuations of the Strong and the Weak coupling phases of pure 4d SU(2) to non-zero coupling β^′${\beta }^{\prime }$ in the fifth transverse direction and they are separated by a crossover transition, while the third phase is a 5D Coulombic phase. We provide evidence that the phase transition between the 5D Coulomb phase and the Weak coupling phase is a second order phase transition. Assuming that this result is not altered when increasing the lattice volume we give a first estimate of the associated critical exponents. This opens the possibility for a continuum effective five-dimensional field theory.     

Vector meson masses in two-dimensional SU(NC) lattice gauge theory with massive quarks

Using an improved lattice Hamiltonian with massive Wilson quarks a variational method is applied to study the dependence of the vector meson mass Mv on the quark mass m and the Wilson parameter r in in the scaling window 1 ≤ 1/g2 ≤ 2, Mv/g is approximately linear in m, but Mv/g obviously does not depend on r (this differs from the quark condensate). Particularly for m → 0 our numerical results agree very well with Bhattacharya's analytical strong coupling result in the continuum, and the value of ((e)Mv/(e)m) |mm=0 in two-dimensional SU(NC) lattice gauge theory is very close to that in Schwinger model.     

Accurate determinations of alpha(s) from realistic lattice QCD

We obtain a new value for the QCD coupling constant by combining lattice QCD simulations with experimental data for hadron masses. Our lattice analysis is the first to (1) include vacuum polarization effects from all three light-quark flavors (using MILC configurations), (2) include third-order terms in perturbation theory, (3) systematically estimate fourth and higher-order terms, (4) use an unambiguous lattice spacing, and (5) use an [symbol: see text](a2)-accurate QCD action. We use 28 different (but related) short-distance quantities to obtain alpha((5)/(MS))(M(Z)) = 0.1170(12).     

Quantum dimer model for trimerized kagomé antiferromagnet

Low-energy singlet states of a spin-1/2 trimerized kagomé antiferromagnet are mapped to an effective quantum dimer model on a triangular lattice. The mapping is done in the first-order of perturbation theory in a weaker coupling constant of the trimerized model. The derived quantum dimer model is dominated by kinetic energy terms (dimer resonances) on a few shortest loops of the triangular lattice.     

Progress in lattice gauge theory

Two topics of lattice gauge theory are reviewed. They include string tension and β-function calculations by strong coupling Hamiltonian methods for SU(3) gauge fields in 3 + 1 dimensions, and a 1/N-expansion for discrete gauge and spin systems in all dimensions. The SU(3) calculations give solid evidence for the coexistence of quark confinement and asymptotic freedom in the renormalized continuum limit of the lattice theory. The crossover between weak and strong coupling behavior in the theory is seen to be a weak coupling but non-perturbative effect. Quantitative relationships between perturbative and non-perturbative renormalization schemes are obtained for the O(N) nonlinear sigma models in 1 + 1 dimensions as well as the range theory in 3 + 1 dimensions. Analysis of the strong coupling expansion of the β-function for gauge fields suggests that it has cuts in the complex 1/g²-plane. A toy model of such a cut structure which naturally explains the abruptness of the theory's crossover from weak to strong coupling is presented. The relation of these cuts to other approaches to gauge field dynamics is discussed briefly.The dynamics underlying first order phase transitions in a wide class of lattice gauge theories is exposed by considering a class of models-P(N) gauge theories - which are soluble in the N → ∞ limit and have non-trivial phase diagrams. The first order character of the phase transitions in Potts spin systems for N #62; 4 in 1 + 1 dimensions is explained in simple terms which generalizes to P(N) gauge systems in higher dimensions. The phase diagram of Ising lattice gauge theory coupled to matter fields is obtained in a $\text{1}\text{N}$ expansion. A one-plaquette model (1 time-0 space dimensions) with a first-order phase transitions in the N → ∞ limit is discussed.     

Fermions on a lattice at strong coupling

We study the pattern of dynamical symmetry breaking and its dependence on the choice made for the derivative on a lattice, including the possibility that it contains a term which couples a site to itself, in the strong coupling limit of a lattice gauge theory.