Related papers: Topological Susceptibility from Slabs
This is a series of lectures on Monte Carlo results on the non-perturbative, lattice formulation approach to quantum field theory. Emphasis is put on 4D scalar quantum field theory. I discuss real space renormalization group, fixed point…
The behavior of the one-dimensional random-force-driven Burgers equation is investigated in the path integral formalism on a discrete space-time lattice. We show that by means of Monte Carlo methods one may evaluate observables, such as…
We broaden the scope of quantum field theory by introducing a general class of discrete gauge theories that realize either topological order or fracton behavior across dimensions. We start from translation-invariant systems endowed with…
In a novel application of the tools of topological data analysis (TDA) to nonperturbative quantum gravity, we introduce a new class of observables that allows us to assess whether quantum spacetime really resembles a ``quantum foam" near…
We introduce topological methods for quantifying spatially heterogeneous dynamics, and use these tools to analyze particle-tracking data for a quasi-two-dimensional granular system of air-fluidized beads on approach to jamming. In…
The first part of this paper extends the Doplicher-Haag-Roberts theory of superselection sectors to quantum field theory on arbitrary globally hyperbolic spacetimes. The statistics of a superselection sector may be defined as in flat…
We analyze the topological and fermionic vacuum structure of four-dimensional QCD on the lattice by means of correlators of fermionic observables and topological densities. We show the existence of strong local correlations between the…
We study comparison estimates on metric measure spaces admitting a synthetic variable Ricci curvature lower bound. We obtain geometric and functional inequalities assuming that the deficit of the lower bound from a given constant is…
Within the framework of SU(2) chiral perturbation theory, we derive the general solution of the QCD $\theta$-vacuum for an arbitrary vacuum phase, explicitly incorporating isospin-breaking effects from the light quark mass difference, and…
Reliable inference for spatial regression remains challenging because it requires the correct specification of the spatial dependence structure, the mean trend, and the error distribution. Existing parametric testing methods rely on…
We study the topological susceptibility and fourth cumulant of the QCD vacuum in a background magnetic field using three-flavor chiral perturbation theory ($\chi$PT) for arbitrary quark masses and $n$-flavor $\chi$PT with degenerate quark…
A method is presented to tackle the sign problem in the simulations of systems having indefinite or complex-valued measures. In general, this new approach is shown to yield statistical errors smaller than the crude Monte Carlo using…
Subset Simulation is a Markov chain Monte Carlo method used to compute small failure probabilities in structural reliability problems. This is done by iteratively sampling from nested subsets in the input space of a performance function,…
We consider lattice field theories with topological actions, which are invariant against small deformations of the fields. Some of these actions have infinite barriers separating different topological sectors. Topological actions do not…
Emerging magnetic fields related to the presence of topologically protected spin textures such as skyrmions are expected to give rise to additional, topology-related contributions to the Hall effect. In order to doubtlessly identify this…
Monte Carlo simulations of quantum field theories on a lattice become increasingly expensive as the continuum limit is approached since the cost per independent sample grows with a high power of the inverse lattice spacing. Simulations on…
In the framework of uncertainty quantification, we consider a quantity of interest which depends non-smoothly on the high-dimensional parameter representing the uncertainty. We show that, in this situation, the multilevel Monte Carlo…
Graphity models are characterized by configuration spaces in which states correspond to graphs and Hamiltonians that depend on local properties of graphs such as the degrees of vertices and numbers of short cycles. As statistical systems,…
Topological phases of matter have sparked an immense amount of activity in recent decades. Topological materials are classified by topological invariants that act as a non-local order parameter for any symmetry and condition. As a result,…
Using the trace anomaly relation, low-energy theorem and Witten-Veneziano formula, we have developed an analytical formalism which allows one to calculate the gluon condensate, the topological susceptibility and the mass of the $\eta'$…