Searcharxiv⌕ Search

arXiv subjects

Andrei Alexandru

Publications and source records attributed to Andrei Alexandru.

126 records · Page 7Linked to original sources
arXiv2008

The background field method on the lattice

The background field method has been used successfully to determine hadron electromagnetic polarizabilities. Recently questions have been raised regarding the proper way to deal with the electric field on the lattice. In this paper, we show how the presence of a background electric field affects the quark hopping matrix. We use this formulation to carry out simulations on quenched configurations, and we present the results for neutron electric polarizability for pion masses as low as $500\MeV$. We find that the polarizability is roughly constant for the quark masses considered, $α\sim 1.5 \times 10^{-4} \fm^3$. While the polarizability is positive, it is significantly smaller than the experimental value due to the fact that the quark masses used are too large.

hep-lat↗
arXiv2008

Finite Density Simulations with Canonical Ensemble

QCD at non-zero baryon density is expected to have a critical point where the zero-density cross-over turns into a first order phase transition. To identify this point we scan the density-temperature space using a canonical ensemble method. For a given temperature, we plot the chemical potential as a function of density looking for an "S-shape" as a signal for a first order transition. We carried out simulations using Wilson fermions with $m_π\approx 1{GeV}$ on $6^3\times 4$ lattices. As a benchmark, we ran four flavors simulations where we observe a clear signal. In the two flavors case we do not see any signal for temperatures as low as $0.83 T_c$. Preliminary results for the three flavor case are also presented.

hep-lat↗
arXiv2008

Dominance of Sign Geometry and the Homogeneity of the Fundamental Topological Structure

We propose and support the possibility that the shape of topological density 2-point function in pure-glue QCD is crucially, and possibly entirely, determined by the space-time folding (geometry) of the double-sheet sign-coherent structure of Ref.[1], while the distribution of topological density within individual sheets only determines the overall magnitude of the correlator at finite physical distances. A specific manifestation of this, discussed here, is that the shape of the correlation function (encoding e.g. the masses of pseudoscalar glueballs) is reproduced upon the replacement q(x) -> sgn(q(x)), i.e. by considering the double sheet of the same space-time geometry but with constant magnitude of topological density. Combined with previous results on the fundamental topological structure, this suggests that a collective degree of freedom describing topological fluctuations of QCD vacuum can be viewed as a global space-filling homogeneous double membrane. Selected possibilities for practical uses of this are discussed.

hep-lat↗
arXiv2008

Classical Limits of Scalar and Tensor Gauge Operators Based on the Overlap Dirac Matrix

It was recently proposed by the second author to consider lattice formulations of QCD in which complete actions, including the gauge part, are built explicitly from a given Dirac operator D. In a simple example of such theory, the gauge action is proportional to the trace of Ginsparg-Wilson operator D chosen to define the quark dynamics. This construction relies on the proposition that the classical limit of lattice gauge operator tr D(x,x) is proportional to tr F.F(x) (up to an additive constant). Here we show this for the case of the overlap Dirac operator using both analytical and numerical methods. We carry out the same analysis also for the tensor component of D, which is similarly related to the field-strength tensor F, and obtain results identical to our previous derivation that used different approach. The corresponding proportionality constants are computed to high precision for wide range of the negative mass parameter values, and it is verified that they are the same in finite and infinite volumes.

hep-lat↗
arXiv2007

Finite density simulations using a determinant estimator

Previous investigations have shown that the canonical approach to simulating QCD at finite density is promising. The algorithm we used in our earlier work employs an exact calculation of the fermionic determinant which limits the size of the lattices we can simulate. Interesting questions can only be answered if we simulate at larger volume. In this paper we explore an algorithm, Hybrid Noisy Monte Carlo, that employs a determinant estimator rather than an exact calculation. We first present the technical aspects of the estimator, check that the algorithm is correct by comparing it with our previous study, and then discuss its merits. We will also discuss the challenges faced when simulating larger lattice volumes.

hep-lat↗
arXiv2007

New results using the canonical approach to finite density QCD

We present some new results regarding simulations of finite density QCD based on a canonical approach. A previous study has shown that such simulations are feasible, at least on small lattices. In the current study, we investigate some of the issues left open: we study the errors introduced by our approximation of the action and we show how to tune it to reduce the cost of the simulations while keeping the errors under control. To further reduce the cost of the simulations, we check the reliability of reweighting method with respect to the baryon number. Finally, using these optimizations, we carry out the simulations at larger densities than in our previous study to look for signals of a phase transition.

hep-lat↗
arXiv2006

Reweighting method in finite density lattice QCD

Finite density simulations require dynamical fermions which are computationally demanding. We employ Ferrenberg and Swendsen reweighting method to reduce the number of ensembles needed. We use their method to do a combined reweighting in both $β$ and quark number $k$ on an ensemble generated by the Kentucky group.

hep-lat↗
arXiv2006

On the Locality and Scaling of Overlap Fermions at Coarse Lattice Spacings

The overlap fermion offers the considerable advantage of exact chiral symmetry on the lattice, but is numerically intensive. This can be made affordable while still providing large lattice volumes, by using coarse lattice spacing, given that good scaling and localization properties are established. Here, using overlap fermions on quenched Iwasaki gauge configurations, we demonstrate directly that, with appropriate choice of negative Wilson's mass, the overlap Dirac operator's range is comfortably small in lattice units for each of the lattice spacings 0.20 fm, 0.17 fm, and 0.13 fm (and scales to zero in physical units in the continuum limit). In particular, our direct results contradict recent speculation that an inverse lattice spacing of 1 GeV is too low to have satisfactory localization. Furthermore, hadronic masses (available on the two coarser lattices) scale very well.

hep-lat↗
arXiv2005

Locality and Scaling of Quenched Overlap Fermions

The overlap fermion offers the tremendous advantage of exact chiral symmetry on the lattice, but is numerically intensive. This can be made affordable while still providing large lattice volumes, by using coarse lattice spacing, given that good scaling and localization properties are established. Here, using overlap fermions on quenched Iwasaki gauge configurations, we demonstrate directly that the overlap Dirac operator's range is comfortably small in lattice units for each of the lattice spacings 0.20 fm, 0.17 fm, and 0.13 fm (and scales to zero in physical units in the continuum limit). In particular, our direct results contradict recent speculation that an inverse lattice spacing of $1 {\rm GeV}$ is too low to have satisfactory localization. Furthermore, hadronic masses (available on the two coarser lattices) scale very well.

hep-lat↗
arXiv2005

Lattice QCD at finite density via a new canonical approach

We carry out a finite density calculation based on a canonical approach which is designed to address the overlap problem. Two degenerate flavor simulations are performed using Wilson gauge action and Wilson fermions on $4^4$ lattices, at temperatures close to the critical temperature $T_c\approx 170\MeV$ and large densities (5 to 20 times nuclear matter density). In this region, we find that the algorithm works well. We compare our results with those from other approaches.

hep-lat↗
arXiv2004

Progress on a canonical finite density algorithm

We test the finite density algorithm in the canonical ensemble which combines the HMC update with the accept/reject step according to the ratio of the fermion number projected determinant to the unprojected one as a way of avoiding the determinant fluctuation problem. We report our preliminary results on the Polyakov loop in different baryon number sectors which exhibit deconfinement transitions on small lattices. The largest density we obtain around $T_c$ is an order of magnitude larger than that of nuclear matter. From the conserved vector current, we calculate the quark number and verify that the mixing of different baryon sectors is small.

hep-lat↗
arXiv2004

Improved Measure of Local Chirality

It is popular to probe the structure of the QCD vacuum indirectly by studying individual fermion eigenmodes, because this provides a natural way to filter out UV fluctuations. The double-peaking in the distribution of the local chiral orientation parameter (X) has been offered as evidence, by some, in support of a particular model of the vacuum. Here we caution that the X-distribution peaking varies significantly with various versions of the definition of X. Furthermore, each distribution varies little from that resulting from a random reshuffling of the left-handed (and independently the right-handed) fields, which destroys any QCD-induced left-right correlation; that is, the double-peaking is mostly a phase-space effect. We propose a new universal definition of the X parameter whose distribution is uniform for randomly reshuffled fields. Any deviations from uniformity for actual data can then be directly attributable to QCD-induced dynamics. We find that the familiar double peak disappears.

hep-lat↗
arXiv2002

Using Approximating Polynomials in Partial-Global Dynamical Simulations

Smeared link fermionic actions can be straightforwardly simulated with partial-global updating. The efficiency of this simulation is greatly increased if the fermionic matrix is written as a product of several near-identical terms. Such a break-up can be achieved using polynomial approximations for the fermionic matrix. In this paper we will focus on methods of determining the optimum polynomials.

hep-lat↗
arXiv2002

Partial-Global Stochastic Metropolis Update for Dynamical Smeared Link Fermions

We performed dynamical simulations with HYP smeared staggered fermions using the recently proposed partial-global stochastic Metropolis algorithm with fermion matrix reduction and determinant breakup improvements. In this paper we discuss our choice of the action parameters and study the autocorrelation time both with four and two fermionic flavors at different quark mass values on approximately 10 fm^4 lattices. We find that the update is especially efficient with two flavors making simulations on larger volumes feasible.

hep-lat↗
arXiv2002

Connections between Thin,Thick and Projection Vortices in SU(2) Lattice Gauge Theory

We elucidate the connection between $SO(3) \times Z(2)$ and the usual SU(2) configuration variables. By exploiting the freedom of choosing a particular SO(3) representative we find a direct connection between the two configuration spaces. We are then able to compare the Kovacs-Tomboulis formulation of center vortices with the projection vortex formulation on the same configuration. Choosing a different representative, and going to the maximal center gauge, we show that projection vortices occur without approximation. The projection vortex dominance approximation results from dropping a factor in an exact expression for the Wilson loop.

hep-lat↗
arXiv2002

Evaluating the Fermionic Determinant of Dynamical Configurations

We propose and study an improved method to calculate the fermionic determinant of dynamical configurations. The evaluation or at least stochastic estimation of ratios of fermionic determinants is essential for a recently proposed updating method of smeared link dynamical fermions. This update creates a sequence of configurations by changing a subset of the gauge links by a pure gauge heat bath or over relaxation step. The acceptance of the proposed configuration depends on the ratio of the fermionic determinants on the new and original configurations. We study this ratio as the function of the number of links that are changed in the heat bath update. We find that even when every link of a given direction and parity of a 10fm^4 configuration is updated, the average of the determinant ratio is still close to one and with the improved stochastic estimator the proposed change is accepted with about 20% probability. This improvement suggests that the new updating technique can be efficient even on large lattices.

hep-lat↗
arXiv2001

Center vortices on SU(2) lattices

We show that gauge invariant definition of thin, thick and hybrid center vortices, defined by Kovacs and Tomboulis on SO(3) x Z(2) configurations, can also be defined in SU(2). We make this connection using the freedom of choosing a particular SU(2) representative of SO(3). We further show that in another representative the Tomboulis σ- ηthin vortices are P (projection) vortices. The projection approximation corresponds to dropping the perimeter factor of a Wilson loop after appropriate gauge fixing. We present results for static quark potentials based on these vortex counters and compare pojection vortex counters with gauge invariant ones on the same configuration.

hep-lat↗