arXiv subjects

Wolfgang Bietenholz

Publications and source records attributed to Wolfgang Bietenholz.

At least 55 records · Page 3Linked to original sources

arXiv2016

The Slab Method to Measure the Topological Susceptibility

In simulations of a model with topological sectors, algorithms which proceed in small update steps tend to get stuck in one sector, especially on fine lattices. This distorts the numerical results; in particular it is not straightforward to measure the topological susceptibility chi_t. We test a method to measure chi_t even if configurations from only one sector are available. It is based on the topological charges in sub-volumes, which we denote as "slab". This enables the evaluation of chi_t, as we demonstrate with numerical results for non-linear sigma-models and for 2-flavour QCD. In the latter case, the gradient flow is applied for the smoothing of the gauge configurations, and the slab method results for chi_t are stable over a broad range of flow times.

hep-lat↗

arXiv2016

Interpreting Numerical Measurements in Fixed Topological Sectors

For quantum field theories with topological sectors, Monte Carlo simulations on fine lattices tend to be obstructed by an extremely long auto-correlation time with respect to the topological charge. Then reliable numerical measurements are feasible only within individual sectors. The challenge is to assemble such restricted measurements in a way that leads to a substantiated approximation to the fully fledged result, which would correspond to the correct sampling over the entire set of configurations. We test an approach for such a topological summation, which was suggested by Brower, Chandrasekharan, Negele and Wiese. Under suitable conditions, energy levels and susceptibilities can be obtained to a good accuracy, as we demonstrate for O(N) models, SU(2) Yang-Mills theory, and for the Schwinger model.

hep-lat↗

arXiv2016

Computing the topological susceptibility from fixed topology QCD simulations

The topological susceptibility is an important quantity in QCD, which can be computed using lattice methods. However, at a fine lattice spacing, or when using high quality chirally symmetric quarks, algorithms which proceed in small update steps --- in particular the HMC algorithm --- tend to get stuck in a single topological sector. In such cases, the computation of the topological susceptibility is not straightforward. Here, we explore two methods to extract the topological susceptibility from lattice QCD simulations restricted to a single topological sector. The first method is based on the correlation function of the topological charge density, while the second method relies on measuring the topological charge within spacetime subvolumes. Numerical results for two-flavor QCD obtained by using both methods are presented.

hep-lat↗

arXiv2016

To the Memory of Alexander Grothendieck: a Great and Mysterious Genius of Mathematics

In November 2014 Alexander Grothendieck passed away at the age of 86. There is no doubt that he was one of the greatest and most innovative mathematicians of the 20th century. After a bitter childhood, his meteoric ascent started in the Cartan Seminar in Paris, it led to a breakthrough while he worked in Sao Paulo, and to the Fields Medal. He introduced numerous new concepts and techniques, which were involved in the groundbreaking solutions to long-standing problems. However, dramatic changes were still ahead of him. In recent years hardly anybody knew where he was living, and even if he was still alive; he had withdrawn to a modest life in isolation. Also beyond his achievements in mathematics, Grothendieck was an extraordinary person. This is a tribute of his fascinating life.

math.HO↗

arXiv2016

Hadron Physics from Lattice QCD

We sketch the basic ideas of the lattice regularization in Quantum Field Theory, the corresponding Monte Carlo simulations, and applications to Quantum Chromodynamics (QCD). This approach enables the numerical measurement of observables at the non-perturbative level. We comment on selected results, with a focus on hadron masses and the link to Chiral Perturbation Theory. At last we address two outstanding issues: topological freezing and the sign problem.

hep-ph↗

arXiv2016

NEUTRINOS: Mysterious Particles with Fascinating Features, which led to the Physics Nobel Prize 2015

The most abundant particles in the Universe are photons and neutrinos. Both types of particles are whirling around everywhere, since the early Universe. Hence the neutrinos are all around us, and permanently pass through our planet and our bodies, but we do not notice: they are extremely elusive. They were suggested as a theoretical hypothesis in 1930, and discovered experimentally in 1956. Ever since their properties keep on surprising us; for instance, they are key players in the violation of parity symmetry. In the Standard Model of particle physics they appear in three types, known as "flavors", and since 1998/9 we know that they keep on transmuting among these flavors. This "neutrino oscillation" implies that they are massive, contrary to the previous picture, with far-reaching consequences. This discovery was awarded the Physics Nobel Prize 2015.

physics.pop-ph↗

arXiv2015

Measuring the Topological Susceptibility in a Fixed Sector

For field theories with a topological charge Q, it is often of interest to measure the topological susceptibility chi_t = ( < Q^2 > - < Q >^2 ) / V. If we manage to perform a Monte Carlo simulation where Q changes frequently, chi_t can be evaluated directly. However, for local update algorithms and fine lattices, the auto-correlation time with respect to Q tends to be extremely long, which invalidates the direct approach. Nevertheless, the measurement of chi_t is still feasible, even when the entire Markov chain is topologically frozen. We test a method for this purpose, based on the correlation of the topological charge density, as suggested by Aoki, Fukaya, Hashimoto and Onogi. Our studies in non-linear sigma-models and in 2d Abelian gauge theory yield accurate results for chi_t, which confirm that the method is applicable. We also obtain promising results in 4d SU(2) Yang-Mills theory, which suggest the applicability of this method in QCD.

hep-lat↗

arXiv2015

Combining ordinary and topological finite volume effects for fixed topology simulations

In lattice quantum field theories with topological sectors, simulations at fine lattice spacings --- with typical algorithms --- tend to freeze topologically. In such cases, specific topological finite size effects have to be taken into account to obtain physical results, which correspond to infinite volume or unfixed topology. Moreover, when a theory like QCD is simulated in a moderate volume, one also has to overcome ordinary finite volume effects (not related to topology freezing). To extract physical results from simulations affected by both types of finite volume effects, we extend a known relation between hadron masses at fixed and unfixed topology by additionally incorporating ordinary finite volume effects. We present numerical results for SU(2) Yang-Mills theory.

hep-lat↗

arXiv2015

Proposal for the Quantum Simulation of the CP(2) Model on Optical Lattices

The 2d CP(N-1) models share a number of features with QCD, like asymptotic freedom, a dynamically generated mass gap and topological sectors. They have been formulated and analysed successfully in the framework of the so-called D-theory, which provides a smooth access to the continuum limit. In that framework, we propose an experimental set-up for the quantum simulation of the CP(2) model. It is based on ultra-cold Alkaline-Earth Atoms (AEAs) located on the sites of an optical lattice, where the nuclear spins represent the relevant degrees of freedom. We present numerical results for the correlation length and for the real time decay of a false vacuum, to be compared with such a future experiment. The latter could also enable the exploration of theta-vacua and of the phase diagram at finite chemical potentials, since it does not suffer from any sign problem.

hep-lat↗

arXiv2015

Topological Susceptibility from Slabs

In quantum field theories with topological sectors, a non-perturbative quantity of interest is the topological susceptibility chi_t. In principle it seems straightforward to measure chi_t by means of Monte Carlo simulations. However, for local update algorithms and fine lattice spacings, this tends to be difficult, since the Monte Carlo history rarely changes the topological sector. Here we test a method to measure chi_t even if data from only one sector are available. It is based on the topological charges in sub-volumes, which we denote as slabs. Assuming a Gaussian distribution of these charges, this method enables the evaluation of chi_t, as we demonstrate with numerical results for non-linear sigma-models.

hep-lat↗

arXiv2015

Simulations at fixed topology: fixed topology versus ordinary finite volume corrections

Lattice QCD simulations tend to get stuck in a single topological sector at fine lattice spacing, or when using chirally symmetric quarks. In such cases computed observables differ from their full QCD counterparts by finite volume corrections, which need to be understood on a quantitative level. We extend a known relation from the literature between hadron masses at fixed and at unfixed topology by incorporating in addition to topological finite volume effects, also ordinary finite volume effects. We present numerical results for SU(2) Yang-Mills theory.

hep-lat↗

arXiv2014

The Continuum Phase Diagram of the 2d Non-Commutative lambda phi**4 Model

We present a non-perturbative study of the lambda phi**4 model on a non-commutative plane. The lattice regularised form can be mapped onto a Hermitian matrix model, which enables Monte Carlo simulations. Numerical data reveal the phase diagram; at large lambda it contains a "striped phase", which is absent in the commutative case. We explore the question whether or not this phenomenon persists in a Double Scaling Limit (DSL), which extrapolates simultaneously to the continuum and to infinite volume, at a fixed non-commutativity parameter. To this end, we introduce a dimensional lattice spacing based on the decay of the correlation function. Our results provide evidence for the existence of a striped phase even in the DSL, which implies the spontaneous breaking of translation symmetry. Due to the non-locality of this model, this does not contradict the Mermin-Wagner Theorem.

hep-lat↗

arXiv2014

Extracting Physics from Topologically Frozen Markov Chains

In Monte Carlo simulations with a local update algorithm, the auto-correlation with respect to the topological charge tends to become very long. In the extreme case one can only perform reliable measurements within fixed sectors. We investigate approaches to extract physical information from such topologically frozen simulations. Recent results in a set of sigma-models and gauge theories are encouraging. In a suitable regime, the correct value of some observable can be evaluated to a good accuracy. In addition there are ways to estimate the value of the topological susceptibility.

hep-lat↗

arXiv2014

Features of a 2d Gauge Theory with Vanishing Chiral Condensate

The Schwinger model with $N_f \geq 2$ flavors is a simple example for a fermionic model with zero chiral condensate Sigma (in the chiral limit). We consider numerical data for two light flavors, based on simulations with dynamical chiral lattice fermions. We test properties and predictions that were put forward in the recent literature for models with Sigma = 0, which include IR conformal theories. In particular we probe the decorrelation of low lying Dirac eigenvalues, and we discuss the mass anomalous dimension and its IR extrapolation. Here we encounter subtleties, which may urge caution with analogous efforts in other models, such as multi-flavor QCD.

hep-lat↗

arXiv2014

Scalar fields in a non-commutative space

We discuss the lambda phi**4 model in 2- and 3-dimensional non-commutative spaces. The mapping onto a Hermitian matrix model enables its non-perturbative investigation by Monte Carlo simulations. The numerical results reveal a phase where stripe patterns dominate. In d=3 we show that in this phase the dispersion relation is deformed in the IR regime, in agreement with the property of UV/IR mixing. This "striped phase" also occurs in d=2. For both dimensions we provide evidence that it persists in the simultaneous limit to the continuum and to infinite volume ("Double Scaling Limit"). This implies the spontaneous breaking of translation symmetry.

hep-th↗

arXiv2014

The Higgs Particle: what is it, and why did it lead to a Nobel Prize in Physics?

Back in 1964, the theoretical physicists Francois Englert and Robert Brout, as well as Peter Higgs, suggested an explanation for the fact that most elementary particles - such as the electron - have a mass. This scenario predicted a new particle, which has been observed experimentally only just now at CERN (the European Organization for Nuclear Research). This discovery led to the Physics Nobel Prize 2013. Here we sketch in simple terms the concept of the Higgs mechanism, and its importance in particle physics.

physics.pop-ph↗

arXiv2014

New insight into the Berezinskii-Kosterlitz-Thouless phase transition

We investigate the 2d XY model by using the constraint angle action, which belongs to the class of topological lattice actions. These actions violate important features usually demanded for a lattice action, such as the correct classical continuum limit and the applicability of perturbation theory. Nevertheless, they still lead to the same universal quantum continuum limit and show excellent scaling behavior. By using the constraint angle action we gain new insight into the Berezinskii-Kosterlitz-Thouless phase transition of the 2d XY model. This phase transition is of special interest since it is one of the few examples of a phase transition beyond second order. It is of infinite order and therefore an essential phase transition. In particular, we observe an excellent scaling behavior of the helicity modulus, which characterizes this phase transition. We also observe that the mechanism of (un)binding vortex--anti-vortex pairs follows the usual pattern, although free vortices do not require any energy in the formulation of the 2d XY model using the constraint angle action.

hep-lat↗

arXiv2014

Interpretation of topologically restricted measurements in lattice sigma-models

We consider models with topological sectors, and difficulties with their Monte Carlo simulation. In particular we are concerned with the situation where a simulation has an extremely long auto-correlation time with respect to the topological charge. Then reliable numerical measurements are possible only within single topological sectors. The challenge is to assemble such restricted measurements to obtain an approximation for the full-fledged result, which corresponds to the correct sampling over the entire set of configurations. Under certain conditions this is possible, and it provides in addition an estimate for the topological susceptibility chi_t. Moreover, the evaluation of chi_t might be feasible even from data in just one topological sector, based on the correlation of the topological charge density. Here we present numerical test results for these techniques in the framework of non-linear sigma-models.

hep-lat↗