Related papers: Equivariant flow-based sampling for lattice gauge …
Formulating gauge theories on a lattice offers a genuinely non-perturbative way of studying quantum field theories, and has led to impressive achievements. In particular, it significantly deepened our understanding of quantum…
Entanglement calculations in quantum field theories are extremely challenging and typically rely on the replica trick, where the problem is rephrased in a study of defects. We demonstrate that the use of deep generative models drastically…
We investigate certain invariance properties of quantum fluids subject to a nonlinear gauge potential. In particular, we derive the covariant transformation laws for the nonlinear potentials under a space-time Galilean boost and consider…
We study the squared width and the profile of flux tubes in compact U(1) lattice gauge theory in three spacetime dimensions. The results obtained from numerical calculations in the dual formulation of this confining theory are compared with…
We present a Hamiltonian Monte Carlo algorithm to sample from multivariate Gaussian distributions in which the target space is constrained by linear and quadratic inequalities or products thereof. The Hamiltonian equations of motion can be…
An overrelaxed variant of simulated annealing is applied to the problem of maximally abelian gauge fixing. The superiority of this algorithm over the commonly used relaxation procedure is demonstrated. Biases on non gauge invariant…
The recent introduction of the gradient flow has provided a new tool to probe the dynamics of quantum field theories. The latest developments have shown how to use the gradient flow for the exploration of symmetries, and the definition of…
Importance sampling is a rare event simulation technique used in Monte Carlo simulations to bias the sampling distribution towards the rare event of interest. By assigning appropriate weights to sampled points, importance sampling allows…
I point out two of the subtleties referred to in the title. The first is that gauge-invariant magnetic systems may realized under general circumstances, as suggested by a simple theorem. The second subtlety is that care is needed to…
Bifurcation phenomena in nonlinear dynamical systems often lead to multiple coexisting stable solutions, particularly in the presence of symmetry breaking. Deterministic machine learning models are unable to capture this multiplicity,…
A detailed analysis is presented to demonstrate the capabilities of the lattice Boltzmann method. Thorough comparisons with other numerical solutions for the two-dimensional, driven cavity flow show that the lattice Boltzmann method gives…
Extracting continuum properties of quantum field theories from discretized spacetime is challenging due to lattice artifacts. Renormalization-group (RG)-improved lattice actions can preserve continuum properties, but are in general…
We apply supervised machine learning techniques to a number of regression problems in fluid dynamics. Four machine learning architectures are examined in terms of their characteristics, accuracy, computational cost, and robustness for…
Stochastic geometric mechanics (SGM) is known for its potential utility in quantifying uncertainty in global climate modelling of the Earth's ocean and atmosphere while also preserving the fundamental advective transport properties of ideal…
The so-called trivializing flows were proposed to speed up Hybrid Monte Carlo simulations, where the Wilson flow was used as an approximation of a trivializing map, a transformation of the gauge fields which trivializes the theory. It was…
Using numerical data coming from Monte Carlo simulations of four-dimensional Causal Dynamical Triangulations, we study how automated machine learning algorithms can be used to recognize transitions between different phases of quantum…
SU(2) lattice gauge theory with four flavors of quarks is simulated at nonzero chemical potential mu and temperature T and the results are compared to the predictions of Effective Lagrangians. Simulations on 16^4 lattices indicate that at…
The gauge theory for random spin systems is extended to quantum spin glasses to derive a number of exact and/or rigorous results. The transverse Ising model and the quantum gauge glass are shown to be gauge invariant. For these models, an…
The multi-level algorithm allows, at least for pure gauge theories, reliable measurement of exponentially small expectation values. The implementation of the algorithm depends strongly on the observable one wants to measure. Here we report…
We show how to construct the measure of the path integral in lattice gauge theory. This measure contains a factor beyond the standard Haar measure. Such factor becomes relevant for the calculation of a single transition amplitude (in…