Roberto Pellegrini

The density of states from first principles

We present a novel algorithm to compute the density of states, which is proven to converge to the correct result. The algorithm is very general and can be applied to a wide range of models, in the frameworks of Statistical Mechanics and Lattice Gauge Theory. All the thermal or quantum expectation values can then be obtained by a simple integration of the density of states. As an application, a numerical study of 4d U(1) compact lattice gauge theory is presented.

The density of states approach for the simulation of finite density quantum field theories

Finite density quantum field theories have evaded first principle Monte-Carlo simulations due to the notorious sign-problem. The partition function of such theories appears as the Fourier transform of the generalised density-of-states, which is the probability distribution of the imaginary part of the action. With the advent of Wang-Landau type simulation techniques and recent advances, the density-of-states can be calculated over many hundreds of orders of magnitude. Current research addresses the question whether the achieved precision is high enough to reliably extract the finite density partition function, which is exponentially suppressed with the volume. In my talk, I review the state-of-play for the high precision calculations of the density-of-states as well as the recent progress for obtaining reliable results from highly oscillating integrals. I will review recent progress for the

Renormalisation of the energy-momentum tensor in scalar field theory using the Wilson flow

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Ergodicity of the LLR method for the Density of States

quantum field theory for which results can be obtained from the simulation of the dual theory, which appears to free of a sign problem.

Renormalisation of the scalar energy-momentum tensor with the Wilson flow

A non-perturbative renormalisation prescription for the energy-momentum tensor, based on space-time symmetries along the Wilson flow, has been proposed recently in the context of 4-dimensional gauge theories. We extend this construction to the case of a scalar field theory, and investigate its numerical feasibility by studying Ward identities in 3-dimensional scalar field theory. After introducing the Wilson flow for the scalar field theory we discuss its renormalisation properties and the determination of the renormalisation constants for the energy-momentum tensor.

Computing the density of states with the global Hybrid Monte Carlo

The LLR method is a novel algorithm that enables us to evaluate the density of states in lattice gauge theory. We present our study of the ergodicity properties of the LLR algorithm for the model of Yang Mills SU(3). We show that the use of the replica exchange method alleviates significantly the topological freeze-out that severely affects other algorithms.

Effective string description of the interquark potential in the 3D U(1) Lattice Gauge Theory

Talk presented at the 34th International Symposium on Lattice Field Theory (Lattice 2016) by Susanne Ehret

Recent progress in the effective string theory description of LGTs

The LLR algorithm is a recent proposal for computing the density of states in lattice gauge theory. This algorithm has been tested in several bosonic models at zero and finite chemical potential with impressive results. Its original formulation is based on the simulation of the theory on restricted action intervals using local Monte Carlo updates. We will discuss a new version of the method based on the global Hybrid Monte Carlo algorithm that is suitable for theories with dynamical fermions. We shall present our preliminary result for the study of the SU(2) gauge theory.

The density of states approach at finite chemical potential: a numerical study of the Bose gas

The U(1) lattice gauge theory in three dimensions is a perfect laboratory to study the properties of the confining string. On the one hand, thanks to the mapping to a Coulomb gas of monopoles, the confining properties of the model can be studied semi-classically. On the other hand, high-precision numerical estimates of Polyakov loop correlators can be obtained via a duality map to a spin model. This allowed us to perform high-precision tests of the universal behavior of the effective string and to find macroscopic deviations with respect to the expected Nambu-Goto predictions. These corrections could be fitted with very good precision including a contribution (which is consistent with Lorentz symmetry) proportional to the square of the extrinsic curvature in the effective string action, as originally suggested by Polyakov. Performing our analysis at different values of

An efficient algorithm for numerical computations of continuous densities of states

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