We present first results of our study on the Euclidean topological charge density correlation function. In order to get a well defined topological charge density and to improve the signal of the correlation function at large separations we make use of the gradient flow. We investigate the flow-time dependence on fine quenched lattices. The final goal of this study is to perform a continuum extrapolation for the pure SU(3) plasma and to extract the related transport coefficient, the sphaleron rate.
The two-dimensional U(1)-gauged Higgs model is studied on an euclidean lattice of size $L_1\times L_2$, where the temperature $T=L_2^{-1}$ is of the order of the sphaleron mass. The simulation parameters are taken from zero temperature results. By comparison with classical and semiclassical results I discuss, whether the sphaleron transition rate can be extracted from the behavior of the Chern-Simons number and from the formation of vortices in an euclidean simulation at high temperatures.
We show how the topological susceptibility in the Minkowskian theory of QCD is related to the corresponding quantity in the Euclidean theory, which is measured on the lattice. We discuss both the zero-temperature case (T = 0) and the finite-temperature case (T > 0). It is shown that the two quantities are equal when T = 0, while the relation between them is much less trivial when T > 0. The possible existence of ``Kogut-Susskind poles'' in the matrix elements of the topological charge density between states with equal four-momenta turns out to invalidate the equality of these two quantities in…
We study the Euclidean two-point correlation function $G_q(x)$ of the topological charge density in QCD. A general statement based on reflection positivity tells us that $G_q(x)<0$ for $x\neq 0 $. On the other hand the topological susceptibility $χ_q=\int d^d x G_q(x)$ is a positive quantity. This indicates that $G_q(x)$ developes a positive contact term at $x=0$, that contributes to the determination of the physical value of $χ_q$. We show explicitly these features of $G_q(x)$ in a solvable nontrivial continuum model, the two-dimensional $CP^{N-1}$ model in the large-N limit. A similar analys…
Local topological charge structure in the 2D CP(N-1) sigma models is studied using the overlap Dirac operator. Long-range coherence of topological charge along locally 1D regions in 2D space-time is observed. We discuss the connection between these results and the recent discovery of coherent 3D sheets of topological charge in 4D QCD. In both cases, coherent regions of topological charge form along surfaces of approximmate codimension 1.
Comparative study of topological charge is performed. Topological charges are measured by a cloverleaf operator on smoothed gauge configurations. Various types of smoothing techniques are employed. Agreement of topological charges in fermionic and gluonic definitions is examined. High consistency is observed between topological charges obtained by improved smoothing methods and those by the index theorem with the overlap-Dirac operator.
We analyze topological charge contributions from classical SU(2) center vortices with shapes of planes and spheres using different topological charge definitions, namely the center vortex picture of topological charge, a discrete version of FF in the plaquette and hypercube definitions and the lattice index theorem. For the latter the zeromodes of the Dirac operator in the fundamental and adjoint representations using both the overlap and asqtad staggered fermion formulations are investigated. We find several problems for the individual definitions and discuss the discrepancies between the dif…
Topological charge distributions in 2 dimensional CP^2 model with theta-term is calculated. In strong coupling regions, topological charge distribution is approximately given by Gaussian form as a function of topological charge and this behavior leads to the first order phase transition at θ=π. In weak coupling regions it shows non-Gaussian distribution and the first order phase transition disappears. Free energy as a function of θshows "flattening" behavior at theta=theta_f<pi, when we calculate the free energy directly from topological charge distribution. Possible origin of this flattening …
We introduce vortex configurations with fractional topological charges where one unicolor or colorful intersection of two perpendicular vortex pairs contributes to the topological charge of the configurations. Using both, the overlap and asqtad staggered fermion formulations, the lowest modes of the Dirac operator on the noninteger $Q$ configurations are studied in the fundamental and adjoint representations. We analyze the behavior of the fundamental and adjoint fermions in the background of the topological charge contributions of $|Q|=0.5$.
We present a theoretically consistent definition of the topological charge operator based on renormalization group arguments. Results of the measurement of the topological susceptibility at zero and finite temperature for SU(2) gauge theory are presented.
The topological charge is studied on lattices of large physical volume and fine lattice spacing. We illustrate how a parity transformation on the SU(3) link-variables of lattice gauge configurations reverses the sign of the topological charge and leaves the action invariant. Random applications of the parity transformation are proposed to traverse from one topological charge sign to the other. The transformation provides an improved unbiased estimator of the ensemble average and is essential in improving the ergodicity of the Markov chain process.
The improvement of simulations of QCD with dynamical Wilson fermions by combining the Hybrid Monte Carlo algorithm with parallel tempering is studied. As an indicator for decorrelation the topological charge is used.
We study the improvement of simulations of QCD with dynamical Wilson fermions by combining the Hybrid Monte Carlo algorithm with parallel tempering. As an indicator for decorrelation we use the topological charge.
The improvement of simulations of QCD with dynamical Wilson fermions by combining the Hybrid Monte Carlo algorithm with parallel tempering is studied on $10^4$ and $12^4$ lattices. As an indicator for decorrelation the topological charge is used.
We study the topological charge and the topological susceptibility in lattice QCD with two degenerate flavors of naive Wilson fermions at two values of lattice spacings and different volumes, for a range of quark masses. Configurations are generated with DDHMC/HMC algorithms and smoothened with HYP smearing. We present integrated autocorrelation time for both topological charge and topological susceptibility at the two lattice spacing values studied. The spanning of different topological sectors as a function of the hopping parameter kappa is presented. The expected chiral behaviour of the top…
We show how the sphaleron rate (the Minkowski rate for topological charge diffusion) can be determined by analytical continuation of the Euclidean topological-charge-density two-point function, which we investigate on the lattice, using gradient flow to reduce noise and provide improved operators which more accurately measure topology. We measure the correlators on large, fine lattices in the quenched approximation at $1.5\,T_c$ with high precision. Based on these data we first perform a continuum extrapolation at fixed physical flow time and then extrapolate the continuum estimates to zero fl…
In an effort to clarify the significance of the recent observation of long-range topological charge coherence in QCD gauge configurations, we study the local topological charge distributions in two-dimensional $CP^{N-1}$ sigma models, using the overlap Dirac operator to construct the lattice topological charge. We find long-range sign coherence of topological charge along extended one-dimensional structures in two-dimensional spacetime. We discuss the connection between the long range topological structure found in $CP^{N-1}$ and the observed sign coherence along three-dimensional sheets in fo…
We study the effect of cooling on the spatial distribution of the topological charge density in quenched SU(2) lattice gauge theory with overlap fermions. We show that as the gauge field configurations are cooled, the Hausdorff dimension of regions where the topological charge is localized gradually changes from d = 2..3 towards the total space dimension. Therefore, the cooling procedure destroys some of the essential properties of the topological charge distribution.
A new mechanism for suppression of the instanton density in the infrared is considered. This mechanism is based on the phenomenon of topological charge screening, which leads to an effective cutoff in the contribution of large instantons.
Topological or deconfined phases of matter exhibit emergent gauge fields and quasiparticles that carry a corresponding gauge charge. In systems with an intrinsic conserved U(1) charge, such as all electronic systems where the Coulombic charge plays this role, these quasiparticles are also characterized by their intrinsic charge. We show that one can take advantage of the topological order fairly generally to produce periodic Hamiltonians which endow the quasiparticles with continuously variable, generically irrational, intrinsic charges. Examples include various topologically ordered lattice m…
It is proved that the fermionic topological charge of SU(N) lattice gauge fields on the 4-torus, given in terms of a spectral flow of the Hermitian Wilson--Dirac operator, or equivalently, as the index of the Overlap Dirac operator, reduces to the continuum topological charge in the classical continuum limit when the parameter $m_0$ is in the physical region $0<m_0<2$.
